JPH10191091A - Data converter and its coefficient decision device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To allow the device to learn coefficients stably and simply even in the case that data are converted by using coefficients taking discrete values. SOLUTION: An input buffer 11 stores m-dimension input data received externally. A data converter 12 uses coefficients taking discrete values to convert m-dimension input data into n-dimension output data. An output buffer 13 stores n-dimension output data outputted from the data converter 12. An error calculation section 15 calculates an error between the output data and ideal output data and gives the error to a coefficient update section 19. A random number distribution control section 17 varies distribution of a random number depending on the history of each error and a step control section 18 varies the size of each step depending on the history of each error. Thus, annealing is conducted. The coefficient update section 19 selects a coefficient where a sum of the error and the random number is minimized to be a new coefficient.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a data conversion device defined by an appropriate number of discrete-valued coefficients, wherein a coefficient for obtaining an output having a small error from ideal output data corresponding to predetermined input data is obtained. A method and an apparatus for determining. The present invention is, for example, a coefficient determination of a color conversion device by a hierarchical neural network having discrete value coefficients,
The present invention can be applied to a representative point table and determination of a representative point value of color conversion using interpolation.

[0002]

2. Description of the Related Art In a data converter defined by an appropriate number of discrete-valued coefficients, the number of possible values of each coefficient is finite if the range of possible coefficients is limited. Therefore,
If the error is evaluated for all coefficient combinations, there is at least one optimal coefficient among them. And
As described above, according to the method of searching the entire space of coefficients, it is possible to surely obtain the optimum coefficients. However, in general, the number of combinations is enormous, which is not practical as a method for calculating coefficients. Therefore, it is common to calculate coefficients by a deductive method or various approximate methods based on the characteristics of each data conversion device.

In a data conversion device including discrete-valued coefficients, when an optimum coefficient is determined a priori for a given arbitrary input / output correspondence, it is possible to determine the coefficient by that method. There is no problem with using technology.

On the other hand, even when coefficients are determined a priori, they may not be discrete value coefficients. For example, in a data conversion device using a matrix operation composed of discrete-valued coefficients, each coefficient with the smallest error can be calculated a priori, but the calculation result is not a discrete value, and this is rounded, rounded up, rounded down, etc. Requires an operation of rounding to a discrete value. Since each coefficient has a value different from the optimum value due to the rounding, an error is generally increased.

Similarly, even in a method such as a matrix operation,
In the case where the effective precision is limited in the operation process, for example, in the case of the finite-precision fixed-point product-sum operation, the accuracy is further reduced due to the rounding of the calculation process in the operation process of the data converter. In such a case, it is necessary to consider characteristics such as rounding in the calculation process in order to calculate the optimal coefficient, but since the correspondence between the coefficient and the error has a very complicated relationship, it must be considered in the past. There was no. In order to improve the accuracy by the conventional technique, generally, techniques such as effective accuracy in a calculation process and finer increments of coefficients have been used.

In a data conversion apparatus using a representative point table and interpolation, converted data is recorded in advance in a table at grid points composed of representative points of each input dimension, and interpolation is performed to obtain a conversion result. In such a data conversion apparatus, the coefficient recorded in the table generally uses data after conversion of the representative point. In general,
Although an interpolation error occurs due to the interpolation, there is no method for optimizing the coefficients recorded at the lattice points in consideration of the conversion error of the input other than the lattice points. In order to improve the accuracy by the conventional technique, a technique of increasing the number of representative points of the input dimension has been generally used.

As for a data conversion device in which coefficients are continuous values and an error can be partially differentiated by each coefficient, a method of determining coefficients by successive approximation of a differential equation is known. In particular, in a neural network, a coefficient calculation method represented by a back propagation method is generally used.

However, in the case of including coefficients of discrete values, it is impossible to partially differentiate an error with those coefficients, and the above-described method represented by back propagation cannot be used.

Therefore, conventionally, in the case where a data converter capable of performing partial differentiation can be configured with the same configuration, a technique of calculating coefficients in advance by continuous values and rounding the result to obtain coefficients of discrete values has been proposed. Has been used. In this case, as in the case of the determinant described above, there is a problem that the accuracy is reduced due to rounding.

In learning by hardware, a technique similar to back propagation in which the same differential equation is approximated with finite precision has been used. In this technique, there is a problem that the learning is stopped when the backpropagating error falls below the calculation accuracy.

Further, in a neural network or the like based on finite-precision fixed-point arithmetic, as in the case of a fixed-point determinant, there is an effect of rounding in the calculation process, and the relationship between coefficients and errors is further complicated. It was difficult to obtain the optimal discrete value for In order to improve the accuracy by the conventional technique, generally, techniques such as effective accuracy in a calculation process and finer increments of coefficients have been used. In the case where the effective precision and the step size of the coefficient are reduced, the configuration of the data conversion device becomes complicated.

Also, in this method, since it is necessary to solve the differential equation by successive approximation, there is a problem that the configuration of the device based on this method becomes complicated.

If the neural network is limited, a learning method having a relatively simple structure is disclosed in Japanese Patent Laid-Open No. 4-282.
As disclosed in Japanese Patent No. 476 (U.S. Pat. No. 5,459,817), there has been a method in which an update difference amount of a coefficient is generated by a random number, and the coefficient is updated by alternatives before and after the update. This method requires a mechanism that generates random numbers for each synapse. Furthermore, since the update amount itself is not controlled but only the code is controlled by random numbers, the update amount is not controlled from the beginning of learning to the stage at which successive learning has progressed.
Therefore, there is a problem in that the learning speed has a problem, and if the alternative configuration is not properly performed, the convergence becomes extremely small.

[0014]

Among the methods described above, except for the method of searching the entire space of coefficients, the method of calculating coefficients based on the configuration of each data conversion device is different. When a device based on this is configured, there is a problem that the configuration of the device is complicated. In addition, as described above, an apparatus based on a method of searching the entire space of coefficients has a simple configuration, but searches an enormous space.
It was not realistic.

In order to improve the accuracy of the data conversion device, it is necessary to change the configuration of the device and the method.

In addition, when updating coefficients based on differential coefficients, it is essential to construct a differential equation. For non-differentiable countermeasures such as cancellation of digits, a differential equation cannot be constructed. I could not decide.

Therefore, the present invention takes into account the effects of the coefficients themselves and the rounding of the calculation process, etc., and does not depend on the configuration of each data conversion device, but in a shorter time than the method of searching the entire space of the coefficients. It is an object to calculate a coefficient having a small error.

[0018]

SUMMARY OF THE INVENTION According to the present invention, a coefficient having a small error is calculated by reducing the error by repeating the operation based on the calculation of the error and the selection of a stochastic coefficient depending on the error. It is characterized by.

That is, according to the present invention, in order to achieve the above object, m-dimensional input data is converted to n-dimensional output data in accordance with k coefficients including at least one coefficient having a discrete value. A coefficient determining device that optimizes a coefficient in a data conversion device that converts the current coefficient value into a coefficient value larger than the current coefficient value by a predetermined step s1 for each of the coefficients having the discrete values; Means for calculating an output data group for a predetermined input data group for at least two coefficient values among coefficient values smaller than the current coefficient value by a predetermined step s2; and an output data group calculated for the at least two coefficient values. One of the at least two coefficient values has a probability that the smaller the error from the ideal output data group corresponding to the predetermined input data group becomes, the higher the error becomes. One of so that provided the coefficient value selecting means for selecting as a new coefficient value.

In this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value having a smaller error is set as a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeating the updating of the coefficient value.

In this configuration, the coefficient value selecting means adds a random number according to a predetermined distribution to each error in the at least two coefficient values, and selects a coefficient value giving a minimum value of the sum. Means may be provided.

Further, there is provided means for controlling the degree of the gradual decrease of the probability with respect to the magnitude of the error or differential coefficient, or the predetermined steps s1 and s2, or both, in accordance with the error history. It may be.

Further, the means for controlling the degree of the gradual decrease of the probability with respect to the magnitude of the error according to the history of the error may be realized by means for controlling the predetermined distribution of random numbers.

Also, at least one of the above discrete values is taken.
For the two coefficients, discrete values corresponding to n outputs are recorded in advance for each representative point in the table of m-dimensional representative points corresponding to m-dimensional input data, and values corresponding to outputs are interpolated. Means for updating the coefficient by defining an error and an ideal output value group for an appropriate input value group, the value being a value corresponding to the output of the representative point of the data conversion device that obtains an n-dimensional output. can do.

According to the present invention, in order to achieve the above-mentioned object, the data conversion device outputs m-dimensional input data according to k coefficients including at least one coefficient taking a discrete value. a data conversion means for converting the data into n-dimensional output data; a current coefficient value; a coefficient value larger than the current coefficient value by a predetermined step s1 for each of the coefficients having the discrete values; Means for calculating an output data group for a predetermined input data group for at least two coefficient values among coefficient values smaller than a numerical value by a predetermined step s2; an output data group calculated for the at least two coefficient values; One of the at least two coefficient values is set as a new coefficient value with a probability that the smaller the error from the ideal output data group corresponding to the data group becomes, the higher the error becomes. It is provided with coefficient value selecting means for selecting.

Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error has a higher probability as a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeating the updating of the coefficient value.

According to the present invention, in order to achieve the above-mentioned object, the color conversion apparatus has a first m-dimensional coefficient in accordance with k coefficients including at least one coefficient having a discrete value. Color conversion means for converting the color data into n-dimensional second color data, and a current coefficient value and a coefficient value larger than the current coefficient value by a predetermined step s1 for each of the coefficients having discrete values. Means for calculating a second color data group with respect to a predetermined first color data group for at least two coefficient values among coefficient values smaller than the current coefficient value by a predetermined step s2; The second color data group calculated for the numerical value and the predetermined first
Coefficient value selecting means for selecting any one of the at least two coefficient values as a new coefficient value with a probability that the smaller the error from the ideal second color data group corresponding to the color data group, the higher the error. Is provided.

Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value having a smaller error has a higher probability as a new coefficient value. Therefore, the coefficient value can be optimized by repeating the updating of the coefficient value.

Further, in this configuration, the above error can be regarded as a color difference.

According to the present invention, in order to achieve the above-mentioned object, a color image forming apparatus (for example, a color copying machine or a color printing machine) is provided with means for receiving m-dimensional first color data, The m-dimensional first color data is represented by n according to k coefficients including at least one coefficient having a typical value.
Color conversion means for converting to two-dimensional second color data, output means for performing a predetermined output operation based on the second color data output from the color conversion means, and a coefficient for taking the discrete value For each of at least two of a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and a coefficient value smaller than the current coefficient value by a predetermined step s2. Means for calculating a second color data group for one color data group, and a second color data group calculated for the at least two coefficient values.
Any one of the at least two coefficient values is set to a new probability with a probability that the smaller the error between the color data group and the ideal second color data group corresponding to the predetermined first color data group becomes, the higher the error becomes. A coefficient value selecting means for selecting a coefficient value is provided.

Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value having a smaller error is set as a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeating the updating of the coefficient value.

In this configuration, the output means may receive the second color data via a subsequent color conversion means.

According to the present invention, in order to achieve the above-described object, the electronic device includes means for receiving m-dimensional input data, and k coefficients including at least one coefficient taking a discrete value. Data conversion means for converting the m-dimensional input data into n-dimensional output data in accordance with the following; output means for performing a predetermined output operation based on the n-dimensional output data output from the data conversion means; For each of the coefficients taking discrete values, at least two of a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and a coefficient value smaller than the current coefficient value by a predetermined step s2. Means for calculating an output data group for a predetermined input data group with respect to one coefficient value; and an output data group calculated for the at least two coefficient values and the predetermined input data group. At a probability becomes higher as the error between the ideal output data group corresponding to the data group is small, the at least 2
Coefficient value selecting means for selecting any one of the two coefficient values as a new coefficient value.

Also in this configuration, an error is calculated for the candidate coefficient value, and the smaller the error is, the higher the probability that a new coefficient value is obtained with a higher probability. Therefore, the coefficient value can be optimized by repeating the updating of the coefficient value.

Further, according to the present invention, a coefficient is converted in a data conversion device for converting m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient having a discrete value. A coefficient determining device for optimizing, for each of the coefficients taking the discrete values, means for calculating an output data group for p kinds of coefficient values in an appropriate section including the current coefficient value; Calculating means for calculating an error between the output data group calculated for the coefficient value and the ideal output data group corresponding to the predetermined input data group to obtain p kinds of errors; Assuming a predetermined function from a coefficient value to an error that can be differentiated in a numerical value, a differential coefficient calculating means for calculating a differential coefficient at the current coefficient value, and a coefficient determined stochastically or deterministically based on the differential coefficient. Change And it is provided with a coefficient value updating means for.

Here, instead of obtaining p kinds of coefficients from an appropriate section including the current coefficient values, p kinds of predetermined functions are applied to the current coefficient values to calculate p kinds of coefficient values. be able to. This function can take an arbitrary function. In particular, it is also possible to add an appropriate discrete value to the current coefficient value to obtain a function value, and to set an appropriate value to the current coefficient value. The value obtained by multiplying the result and rounding the resulting product to a discrete value can be used as a function value. Means for controlling the number of p and the predetermined p kinds of functions according to the error history may be further provided. Further, the predetermined function may be a function value in which an appropriate discrete value is added to the current coefficient value. In addition, the predetermined function is obtained by multiplying an appropriate value by a current coefficient value or dividing the current coefficient value by an appropriate value, and rounding a product or quotient of the result to a discrete value. It may be a function value.

In this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on the error, and a differential coefficient of the error function at the current coefficient value is obtained based on the function. I have. Then, a new coefficient value is obtained based on this differential coefficient. Optimization of the coefficient value can be performed by repeating the updating of the coefficient value.

In this configuration, the current coefficient value,
At least one of the coefficient value obtained by adding the predetermined step s1 to the current coefficient value and the coefficient value obtained by subtracting the predetermined step s2 from the current coefficient value can be included in the p types of coefficients. .

Further, means may be provided for controlling the degree of the gradual decrease of the probability with respect to the magnitude of the differential coefficient and one or both of the predetermined steps s1 and s2 according to the error history.

At least one of the discrete values
For the two coefficients, discrete values corresponding to n outputs are recorded in advance for each representative point in the table of m-dimensional representative points corresponding to m-dimensional input data, and values corresponding to outputs are interpolated. Means for updating a coefficient by defining an error and an ideal output value group for an appropriate input value group, the value being a value corresponding to the output of the representative point of the data conversion device which obtains an n-dimensional output. You may.

According to the present invention, in order to achieve the above-described object, the data conversion device transmits m-dimensional input data to the data conversion device in accordance with k coefficients including at least one coefficient having a discrete value. data conversion means for converting the data into n-dimensional output data, and means for calculating an output data group for p kinds of coefficient values in an appropriate section including a current coefficient value for each of the coefficients having discrete values. Calculating means for calculating an error between the output data group calculated for the p kinds of coefficient values and the ideal output data group corresponding to the predetermined input data group, and obtaining p kinds of errors; A differential coefficient calculating means for calculating a differential coefficient in the current coefficient value by assuming a function from an appropriate count value that can be differentiated in the current coefficient value to an error; and a stochastic or fixed method based on the differential coefficient. Typically And it is provided with a coefficient value updating means for updating the number.

Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on the error, and a differential coefficient of the error function at the current coefficient value is obtained based on the function. I have. Then, a new coefficient value is obtained based on this differential coefficient. Optimization of the coefficient value can be performed by repeating the updating of the coefficient value.

According to the present invention, in order to achieve the above-mentioned object, the color conversion apparatus includes a first m-dimensional coefficient corresponding to k coefficients including at least one coefficient having a discrete value. Color conversion means for converting the color data into n-dimensional second color data; and for each of the coefficients taking discrete values, a second conversion is performed for p kinds of coefficient values in an appropriate section including the current coefficient value. Means for calculating the color data group of the first, second color data groups calculated for the p kinds of coefficient values and the predetermined first
A calculating means for calculating an error from an ideal second color data group corresponding to the color data group of the above, and obtaining p kinds of errors; and
Differential coefficient calculating means for calculating a differential coefficient at the current coefficient value, assuming a predetermined function from the coefficient value to the error, and a coefficient value updating means for stochastically or deterministically updating the coefficient based on the differential coefficient Are provided.

Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on the error, and a differential coefficient of the error function at the current coefficient value is obtained based on the function. I have. Then, a new coefficient value is obtained based on this differential coefficient. Optimization of the coefficient value can be performed by repeating the updating of the coefficient value.

Further, in this configuration, the above error can be a color difference.

According to the present invention, in order to achieve the above object, a means for receiving m-dimensional first color data is provided to a color image forming apparatus (for example, a color copying machine or a color printing machine). Color conversion means for converting the m-dimensional first color data into n-dimensional second color data in accordance with k coefficients including at least one coefficient having a typical value, and an output from the color conversion means. Output means for performing a predetermined output operation on the basis of the obtained second color data, and for each of the coefficients having discrete values, for p kinds of coefficient values in an appropriate section including the current coefficient value Means for calculating a second color data group, and a second color data group
Calculating means for calculating an error between the color data group of the first color data group and the ideal second color data group corresponding to the predetermined first color data group to obtain p kinds of errors; A differential coefficient calculating means for calculating a differential coefficient at the current coefficient value, assuming a predetermined function from the coefficient value to an error that is differentiable at the current coefficient value, and a stochastic or deterministic method based on the differential coefficient. And a coefficient value updating means for updating the coefficient.

Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on the error, and the differential coefficient of the error function at the current coefficient value is obtained based on the function. I have. Then, a new coefficient value is obtained based on this differential coefficient. Optimization of the coefficient value can be performed by repeating the updating of the coefficient value.

In this configuration, the output means may receive the second color data via the subsequent color conversion means.

According to the present invention, in order to achieve the above-mentioned object, the electronic device includes means for receiving m-dimensional input data, and k coefficients including at least one coefficient taking discrete values. Data conversion means for converting the m-dimensional input data into n-dimensional output data in accordance with the following; output means for performing a predetermined output operation based on the n-dimensional output data output from the data conversion means; Means for calculating an output data group for p kinds of coefficient values in an appropriate section including a current coefficient value for each of coefficients having discrete values, and an output data group calculated for the p kinds of coefficient values. Calculating means for calculating an error from an ideal output data group corresponding to the predetermined input data group to obtain p kinds of errors;
Differential coefficient calculating means for calculating a differential coefficient in the current coefficient value, assuming a predetermined function from the coefficient value to the error, which is differentiable in the current coefficient value from the p kinds of errors,
A coefficient value updating means for stochastically or deterministically updating the coefficient based on the differential coefficient is provided.

Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on the error, and a differential coefficient of the error function at the current coefficient value is obtained based on the function. I have. Then, a new coefficient value is obtained based on this differential coefficient. Optimization of the coefficient value can be performed by repeating the updating of the coefficient value.

According to the present invention, in order to achieve the above object, a neural network having k coefficients including at least one of discrete coupling coefficients or discrete thresholds, or both. The coefficient determining apparatus for optimizing the coefficient value includes, for each of the coefficients having the discrete values, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and the current coefficient value. Means for calculating an output data group for a predetermined input data group for at least two coefficient values among coefficient values smaller by a predetermined step s2;
One of the at least two coefficient values is set to a new coefficient value with a probability that the smaller the error between the output data group calculated for one coefficient value and the ideal output data group corresponding to the predetermined input data group becomes, the higher the error becomes. And a coefficient value selecting means for selecting a value.

Also in this configuration, an error is calculated for a candidate coefficient value, and the smaller the error is, the higher the probability of obtaining a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeating the updating of the coefficient value.

Further, according to the present invention, in order to achieve the above object, the data conversion apparatus includes k discrete coefficients, discrete thresholds, or k coefficients including at least one of both. A neural network with
For each of the coefficients taking the discrete values, at least one of a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and a coefficient value smaller than the current coefficient value by a predetermined step s2. Means for calculating an output data group for a predetermined input data group for two coefficient values, and an error between the output data group calculated for the at least two coefficient values and an ideal output data group corresponding to the predetermined input data group There is provided a coefficient value selecting means for selecting any one of the at least two coefficient values as a new coefficient value with a probability that the smaller the value, the higher the probability.

Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value having a smaller error has a higher probability as a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeating the updating of the coefficient value.

According to the present invention, in order to achieve the above object, a neural network having k coefficients including at least one of discrete coupling coefficients or discrete thresholds, or both. A coefficient determining device for optimizing a coefficient value, for each of the coefficients having the discrete values, means for calculating an output data group for p kinds of coefficient values in an appropriate section including the current coefficient value; p
Calculating means for calculating an error between the output data group calculated for the coefficient values of the types and the ideal output data group corresponding to the predetermined input data group to obtain p types of errors; Assuming a predetermined function from the coefficient value to an error that is differentiable in the coefficient value of the coefficient value, a differential coefficient calculating unit that calculates a differential coefficient at the current coefficient value, and based on the differential coefficient, stochastically or deterministically A coefficient value updating means for updating the coefficient is provided.

Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on the error, and the differential coefficient of the error function at the current coefficient value is obtained based on the function. I have. Then, a new coefficient value is obtained based on this differential coefficient. Optimization of the coefficient value can be performed by repeating the updating of the coefficient value.

Further, according to the present invention, in order to achieve the above object, the data conversion device includes k coefficients including at least one of a discrete combination coefficient and / or a discrete threshold value. A neural network with
Means for calculating an output data group for p kinds of coefficient values in an appropriate section including a current coefficient value for each of the coefficients having discrete values, and an output data group calculated for the p kinds of coefficient values Calculating means for calculating an error between the ideal output data group corresponding to the predetermined input data group and obtaining p kinds of errors; and a coefficient value differentiable in the current coefficient value from the p kinds of errors. From a predetermined function to an error, a differential coefficient calculating means for calculating a differential coefficient at the current coefficient value, and a coefficient value updating means for stochastically or deterministically updating the coefficient based on the differential coefficient. It is provided.

Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on the error, and the differential coefficient of the error function at the current coefficient value is calculated based on the function. I have. Then, a new coefficient value is obtained based on this differential coefficient. Optimization of the coefficient value can be performed by repeating the updating of the coefficient value.

According to the present invention, in order to achieve the above object, m-dimensional input data is converted to n-dimensional output data in accordance with k coefficients including at least one coefficient having a discrete value. The coefficient determining device that optimizes the coefficient value in the data converting device converts the current coefficient value, the coefficient value that is larger than the current coefficient value by a predetermined step s1 for each of the coefficients having the discrete values, Means for calculating an output data group for a predetermined input data group for at least two coefficient values among coefficient values smaller than the current coefficient value by a predetermined step s2, and an output data group calculated for the at least two coefficient values And the probability that the smaller the difference between the ideal output data group corresponding to the predetermined input data group and the ideal output data group is, the higher the probability is. And a means for calculating an output data group for p kinds of coefficient values in an appropriate section including the current coefficient value for each of the coefficients taking the discrete values. Calculating means for calculating an error between an output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the predetermined input data group to obtain p kinds of errors; A differential coefficient calculating means for calculating a differential coefficient at the current coefficient value, assuming a predetermined function from the coefficient value to an error which is differentiable in the current coefficient value, and a stochastic function based on the differential coefficient. Or coefficient value updating means for deterministically updating the coefficient, and after selecting the coefficient value by the coefficient value selecting means at least once, updating the coefficient value by the coefficient value updating means at least once. like To have.

In this configuration, first, an error is calculated for a candidate coefficient value, and a candidate coefficient value having a smaller error is set as a new coefficient value with a higher probability. Thereafter, an error function is assumed based on the error, and the differential coefficient of the error function at the current coefficient value is determined based on the function. Then, a new coefficient value is obtained based on this differential coefficient. Optimization of the coefficient value can be performed by repeating the updating of the coefficient value.

According to the present invention, in order to achieve the above object, m-dimensional input data is converted to n-dimensional output data in accordance with k coefficients including at least one coefficient having a discrete value. In the method for determining the coefficient value in the data conversion device for converting into a coefficient value, for each of the coefficients having the discrete values, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, Calculating an output data group for a predetermined input data group for at least two coefficient values among coefficient values smaller than the current coefficient value by a predetermined step s2; and calculating the output data group calculated for the at least two coefficient values. The probability that the smaller the error from the ideal output data group corresponding to the predetermined input data group becomes, the higher the error becomes. So that and a step of selecting one as a new coefficient value.

Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error has a higher probability as a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeating the updating of the coefficient value.

According to the present invention, in order to achieve the above object, m-dimensional input data is converted to n-dimensional output data in accordance with k coefficients including at least one coefficient having a discrete value. In the method of determining the coefficient value in the data conversion device for converting to the above, for each of the coefficients having the discrete values, p in an appropriate section including the current coefficient value
Calculating an output data group for the coefficient values of the type; calculating an error between the output data group calculated for the coefficient values of the p types and an ideal output data group corresponding to the predetermined input data group; Calculating means for obtaining an error, and, from the p kinds of errors, assuming a predetermined function from the coefficient value to the error which is differentiable in the current coefficient value, and calculating a differential coefficient in the current coefficient value; And a step of stochastically or deterministically updating the coefficient based on the differential coefficient.

Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on the error, and a differential coefficient of the error function at the current coefficient value is obtained based on the function. I have. Then, a new coefficient value is obtained based on this differential coefficient. Optimization of the coefficient value can be performed by repeating the updating of the coefficient value.

According to the present invention, in order to achieve the above object, m-dimensional input data is converted to n-dimensional output data in accordance with k coefficients including at least one coefficient having a discrete value. In the method for determining the coefficient value in the data conversion device for converting into a coefficient value, for each of the coefficients having the discrete values, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, Calculating an output data group for a predetermined input data group for at least two coefficient values among coefficient values smaller than the current coefficient value by a predetermined step s2; and calculating the output data group calculated for the at least two coefficient values. The probability that the smaller the error from the ideal output data group corresponding to the predetermined input data group becomes, the higher the error becomes. Selecting one as a new coefficient value, and, after the new coefficient value is selected, for each of the coefficients taking the discrete values, the p types of Calculating an output data group for the coefficient value; calculating an error between the output data group calculated for the p types of coefficient values and an ideal output data group corresponding to the predetermined input data group; Calculating a differential coefficient in the current coefficient value, assuming a predetermined function that can be differentiated in the current coefficient value from the p types of errors, and calculating the differential coefficient in the current coefficient value; Updating the coefficient stochastically or deterministically based on the coefficient, executing the selection of the coefficient value at least once, and then updating the coefficient value at least once. .

In this configuration, first, an error is calculated for the candidate coefficient value, and the smaller the error is, the higher the probability that a new coefficient value is obtained with a higher probability. Thereafter, an error function is assumed based on the error, and the differential coefficient of the error function at the current coefficient value is determined based on the function. Then, a new coefficient value is obtained based on this differential coefficient. Optimization of the coefficient value can be performed by repeating the updating of the coefficient value.

According to the present invention, in order to achieve the above object, m-dimensional input data is converted to n-dimensional output data in accordance with k coefficients including at least one coefficient having a discrete value. In the method of setting the coefficient value in the data conversion device to convert, in the standard data conversion device having the same function as the data conversion device main body, for each of the coefficients taking the discrete value, the current coefficient value,
A coefficient value larger than the current coefficient value by a predetermined step s1 and a predetermined step s2 from the current coefficient value
Calculating an output data group for a predetermined input data group with respect to at least two coefficient values among the coefficient values smaller than the above, and an output data group calculated for the at least two coefficient values and an ideal corresponding to the predetermined input data group A step of selecting any one of the at least two coefficient values as a new coefficient value with a probability that the smaller the error from the output data group is, and setting the selected coefficient as a coefficient of the data conversion device body Steps to execute.

Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value having a smaller error is set as a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeating the updating of the coefficient value.

According to the present invention, in order to achieve the above object, m-dimensional input data is converted to n-dimensional output data in accordance with k coefficients including at least one coefficient having a discrete value. In the method of setting the coefficient value in the data conversion device for converting into a data, the reference data conversion device having a data conversion function equivalent to that of the data conversion device main body may be configured such that the current coefficient Calculating an output data group for p kinds of coefficient values in an appropriate section including a numerical value; and calculating an output data group corresponding to the p kinds of coefficient values and an ideal output data group corresponding to the predetermined input data group. Is calculated, and p
Calculation means for obtaining the type of error, and
Assuming a predetermined function from the coefficient value to the error that is differentiable in the current coefficient value, calculating a differential coefficient in the current coefficient value, and based on the differential coefficient, the coefficient is determined stochastically or deterministically. And a step of setting the updated coefficient as a coefficient of the data conversion device main body.

Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on the error, and the differential coefficient of the error function at the current coefficient value is obtained based on the function. I have. Then, a new coefficient value is obtained based on this differential coefficient. Optimization of the coefficient value can be performed by repeating the updating of the coefficient value.

[0071]

Embodiments of the present invention will be described below. [Embodiment 1] FIG. 1 shows the configuration of Embodiment 1 of the present invention. In this figure, a coefficient optimizing system of a data conversion device includes an input buffer 11, a data conversion device 1
2, an output buffer 13, an ideal output memory 14, an error calculation unit 15, an error history memory 16, a random number distribution control unit 17, a step control unit 18, and a coefficient update unit 19.
The input buffer 11 stores m-dimensional input data given from outside. The data conversion device 12 converts m-dimensional input data into n-dimensional output data using coefficients having discrete values. Output buffer 1
Reference numeral 3 stores n-dimensional output data output from the data conversion device 12. The error calculator 15 calculates an error between the output data and the ideal output data, and calculates the error as a coefficient updating unit 19.
And to the error history memory 16. The random number distribution control unit 17 varies the distribution of random numbers according to the error history, and the step control unit 18 also varies the step size according to the error history. Thereby, annealing is performed.
The coefficient updating unit 19 sets a coefficient value that minimizes the sum of the error and the random number as a new coefficient value.

Next, the optimization of the coefficients will be described in detail. A case where j sets of m-dimensional input data and corresponding n-dimensional ideal output data are provided will be described. That is, the input data x and the ideal output data y are
_{{X 1, y 1},} {x 2, y 2}, ..., {x i, y i} ...,
{X _j , y _j }, and each input data x _i has m dimensions,
x _i = (x _i1 , x _i2 ,..., x _im ), and each ideal output data y _i is n-dimensional and y _i = (y _i1 , y _i2 ,..., y _in )
And The k coefficients (w ₁ , w ₂ ,..., W _p ,..., W _k ) of the data converter are predetermined initial values, for example, coefficients determined by a conventional method such as rounding, All are initialized by 0 or the like. This data conversion device, the output when given the m-dimensional data _{x i, f (x i |} w 1, w 2, ..., w p, ..., w k) and.
The error from the ideal output y _{i at} this time is represented by d (y _i , f (x _i
| W ₁ , w ₂ , ..., w _p , ..., w _k )). Where d
Is an appropriate n-dimensional distance, for example, a Euclidean distance. In this embodiment, the error of the data converter is calculated by adding the error of each data.

[0073]

E (w ₁ , w ₂ ,..., W _p ,..., W _k ) = Σ _{i = 1... J} d (y _i , f (x _i | w ₁ , w ₂ ,..., W _p, ..., and w _k)).

Now, of the k coefficients, the p-th coefficient w
Focusing on _p , the error E _{0 with} respect to the current coefficient value, ie,
E ₀ = E (w ₁ , w ₂ ,..., W _p ,..., W _k ), an error E ₊ for a coefficient value larger than the current coefficient value by a predetermined step s, that is, E ₊ = E (w ₁ , w ₁ , w ₂ ,..., w _p + s,
.., W _k ) and an error E ₋ for a coefficient value smaller than the current coefficient value by a predetermined step s, that is, E ₋ =
E (w ₁ , w ₂ ,..., W _p −s,..., W _k ) are calculated. In this embodiment, the predetermined step in the case of addition and the predetermined step in the case of subtraction are both s.
However, the predetermined step in the case of addition and the predetermined step in the case of subtraction do not necessarily have to have the same value.

Next, a predetermined interval [0,
T], a random number N based on a uniform distribution is added to each,

[0076]

[Number 2] _{e 0 = E 0 + N e} + = E + + N e - = E - + obtain N. Here, if e ₀ is the minimum among e ₀ , e ₊ , and e ₋ , w _p is not updated. If e ₊ is minimum, then s for w _p
Add and update. If e _- is minimum, subtract s from w _p and update.

This operation is performed by using each coefficient w _p (p = 1, 2,...,
Apply for k). When this optimization operation has completed one round, the error of the data conversion device is obtained, and the error is reduced to a value equal to or less than a predetermined value, substantially converges, or repeated a predetermined number of times. At that time, if the error is the minimum,
The coefficient is recorded as “optimal coefficient”, and T is increased by multiplying T for determining the above-mentioned predetermined section by a predetermined value larger than 1. On the other hand, if the error has increased compared to before performing one round of optimization, 1 is added to T.
Multiplying by a predetermined value smaller than T reduces T. The same operation is performed for the predetermined step s, but the value is not smaller than the minimum step.

As described above, when the learning is completed, the finally recorded “optimum coefficient” is output.

Next, a specific procedure of coefficient determination will be described using the simplest example of this embodiment shown in FIG. A data conversion device according to the following equation having one input and one output and having _two integer coefficients w ₁ and w ₂ will be described.

[0080]

Y = x · w ₁ + w ₂ where x is the input of the data converter and y is the output of the data converter. Assuming that predetermined steps are s ₁ = s ₂ = 1, the following values are supplied to the data converter as an input group and a corresponding ideal output group.

[0081]

[Table 1] The method for determining the coefficients according to the present embodiment, both the w ₁ and w ₂ and the initial value is 0. In this case, the error is
Use the total Euclidean distance. First, w _1, and calculates the error, the plus uniform random interval [0 ... 2] to the error. As a result, it is assumed that it is calculated as shown in the following table.

[0082]

[Table 2] Based on this result, w ₁ is not updated. Next, w _2, likewise, to calculate the error, the plus random Id to the error. As a result, it is assumed that it is calculated as shown in the following table.

[0083]

[Table 3] Based on this result, w ₂ also does not update. This situation is an example of a minimal situation where no variable is changed and the error is smaller. In this embodiment, since an error is added, the calculation is continuously repeated to escape from such a minimum with a predetermined probability.

At this point, the error is evaluated to obtain 2. Since the error is large, it continues for w _1, calculates the error, the plus a random number error. As a result, it is assumed that it is calculated as shown in the following table.

[0085]

[Table 4] Based on this result, w ₁ is updated to 1. Furthermore, for w _2, likewise, to calculate the error, the plus a random number error. As a result, it is assumed that it is calculated as shown in the following table.

[0086]

[Table 5] Based on this result, w ₂ is updated to -1. At this point, the error is evaluated and 0 is obtained. Since the error is sufficiently small, the optimization of the coefficient ends.

As described above, according to the present embodiment, the error gradually decreases, and the error is minimized by adding a predetermined random number. Can be obtained.

In the simple example described above, the optimization has been completed at the point of time when the optimization has been performed twice, but it is generally necessary to determine a more complicated coefficient in a realistic coefficient determination. . In this case, if the optimization is performed while the random number is large, even if the optimization is almost completed, it is difficult to converge to the final coefficient. Therefore, the size of the random number is reduced and convergence is advanced so that a coefficient having a small error is selected with a higher probability. On the other hand, if the random number is too small, it may not be possible to escape from the minimum. In the present embodiment, this problem has been solved by controlling the probability based on the error history.

In the simple example described above, the predetermined step uses 1 for both s ₁ and s _2. However, in order to speed up the processing and to escape from a minimum to a higher probability,
A predetermined step is controlled based on the error history. Moreover, using different values for s _1, s _2, substantially smaller steps, namely s _1, s _2, | to allow optimization of the greatest common divisor | s ₁ -s _2.

The operation has been described with a simple example.
According to this embodiment, the same operation is performed in a complicated data conversion device.

In this method, the error of the data conversion device is evaluated based on the error including rounding and accuracy in the device. Therefore, it is possible to calculate a coefficient having a smaller error at a higher speed than the full search, including such an error.

[Second Embodiment] Next, a second embodiment in which color conversion is performed using a neural network that takes discrete coefficients as a data conversion device will be described. FIG. 3 shows the configuration of the present embodiment. In this figure, portions corresponding to those in FIG. 1 are denoted by corresponding reference numerals, and detailed description thereof is omitted. In FIG. 3, an input buffer 11 stores a print C as input data.
(Sian), M (Magenta), Y (Yellow), K
(Ink) area ratio is maintained. The color conversion device 21 using a neural network converts the area ratio of C, M, Y, and K into CIE L ^* a ^* b ^* (D50) color coordinates. The coefficients of the neural network are discrete,
The optimization is performed by the coefficient updating unit 19. The converted color coordinate data is stored in the output buffer 13, and the color difference calculator 22 calculates the color difference between the output color coordinate data and the ideal color coordinate data. The color difference root mean square calculator 23 calculates the root mean square of the color difference, which is regarded as an error.

Next, the optimization of the coefficients of the color conversion device 21 will be described in detail. As described above, the color conversion device 21
Indicates the area ratio of C, M, Y, and K of the printing, and the CI of the printing result.
EL ^* a ^* b ^* (D50) is converted into color coordinates. To determine the coefficients of the color conversion device 21, 928 sets of CMYK area ratios based on IT8 / 7.3 extended set are input and the ideal output is printed based on each area ratio. The color is measured with a D50 light source, and CIE L ^* a ^* b ^* color coordinates are used. That is, the input data x and the ideal output data y are
_{{X 1, y 1},} {x 2, y 2}, ..., {x i, y i} ...,
{X ₉₂₈ , y ₉₂₈ }, each input data x _i is four-dimensional, x _i = (C _i , M _i , Y _i , K _i ), and each ideal output data y _i is three-dimensional Let y _i = (L _i , a _i , b _i ). The k coefficients (w ₁ ,
_{w 2, ..., w p,} ..., w k) is, it keeps initialized to all pre-0. This data conversion device, the output when given the data _{x i, g (x i |} w 1, w 2, ..., w p, ..., w k) and. The error from the ideal output y _{i at} this time is represented by ΔE color difference, that is, the Euclidean distance ΔE (y _i , g (x _i | w ₁ , w ₂ ,..., W _p) in the CIEL ^* a ^* b * color space. …, W _k ))
And In the present embodiment, the error of the color conversion device is calculated as the root mean square error of each color, that is,

[0094]

(Equation 4) And

Now, of the k coefficients, the p-th coefficient w
Focusing on _p , the error E _{0 with} respect to the current coefficient value, ie,
E ₀ = E (w ₁ , w ₂ ,..., W _p ,..., W _k ) and an error E ₊ for a coefficient value larger than the current coefficient value by a predetermined step s ₁ , that is, E ₊ = E (w _{1, w 2, ..., w} p +
s ₁ ,..., w _k ) and an error E for a coefficient value smaller than the current coefficient value by a predetermined step s ₂ , that is, E ₋
= E (w ₁ , w ₂ ,..., W _p −s ₂ ,..., W _k ) are calculated. In this embodiment, the predetermined step in the case of addition has a different value, but the predetermined step in the case of addition and the predetermined step in the case of subtraction do not necessarily have to have different values.

Next, based on these errors, one of the ones with a lower error is selected by an appropriate function selected with a higher probability. If E ₀ is selected, w _p is not updated. If E ₊ is selected, s _{1 for} w _p
Add and update. If E _- is selected, w _p to s ₂
And update.

This operation is repeated for each weight w _p (p = 1, 2,...,
Apply for k). When this optimization operation has completed one round, the error of the color conversion apparatus is obtained, and the error is reduced to a value equal to or less than a predetermined value, substantially converged, or repeated a predetermined number of times. At this time, when the error becomes the minimum, the coefficient is recorded as the “optimal coefficient”, and the above-described predetermined step s is performed.
Is multiplied by a predetermined value greater than 1 to obtain s
Increase. On the other hand, the error is compared before cormorants 1 cruise optimization, if you happen to increase, multiplied by the smaller predetermined value than 1 to s ₁ and S _2, to reduce the s ₁ and S ₂ Is not less than the minimum step.

As described above, when the learning is completed, the finally recorded “optimum coefficient” is output.

[Third Embodiment] Next, a third embodiment using a color conversion apparatus using a table in which coefficients take discrete values and interpolation will be described. FIG. 4 shows a configuration of the third embodiment.
In this figure, parts corresponding to those in FIG. 1 are denoted by corresponding reference numerals, and detailed description is omitted. In FIG. 4, the input buffer 11 receives CIE L ^* a ^* b ^* as input data ^.
(D50) Stores color coordinate data. The color conversion device 31 inputs CIE L ^* a ^* b ^* (D50) color coordinates using a table in which coefficients take discrete values and interpolation,
This is to calculate the area ratio of C, M, Y, K of a predetermined printing device. In this embodiment, the value stored at each grid point is a discrete value. Details of the conversion device 31 will be described later. C,
The area ratios of M, Y, and K are stored in the output buffer 13,
Based on this, the printing device 32 is driven to obtain a print output. After that, the print output is measured and CIE L ^* a ^* b
^* (D50) Obtain color coordinate data. The color coordinate data is stored in the measurement value buffer 33. The input data itself is stored in the ideal output data memory 14, the color difference between the input data and the color coordinate data of the measured value buffer 33 is calculated by the color difference calculation unit 22, and the average color difference is calculated by the average color difference calculation unit 3.
It is calculated in 4 and is regarded as an error.

Next, the optimization of the coefficients of the conversion device 31 will be described in detail. The conversion device 31 calculates L ^{* in the} input space ^.
Each area ratio of CMYK after conversion is recorded in advance in a three-dimensional table composed of 10 points on each axis, a ^* axis and b ^* axis, for example, 10 points on each axis. The interpolation value of the grid point corresponding to each vertex of the rectangular parallelepiped including, according to the position in the rectangular parallelepiped, to obtain a conversion result,
Interpolation methods include tetrahedral interpolation, prism interpolation, c
Ubic interpolation and the like are known. The present embodiment can be applied to any of these interpolation methods.

Generally, the conversion value stored at each grid point is a value obtained by rounding the conversion value at each representative point according to the accuracy of the table. Occurs.

The error of the color conversion device at a predetermined coefficient is defined as an average color difference obtained by the following procedure. Color conversion is performed by a predetermined coefficient at a sufficiently fine predetermined interval, for example, at an interval of 1/16 of the interval between the representative values of the grid points in each dimension, and each area ratio of CMYK is calculated. Printing is performed based on this calculation result, the color difference between the colorimetric values and the color coordinates before conversion is calculated, and the average color difference over the entire input range is used as an error. At this time, instead of actually performing printing and performing colorimetry, a predicted value after printing may be estimated using a modeled printer.

The present embodiment aims at optimizing the value of each grid point so as to minimize the average color difference after interpolation, and performs the following optimization.

First, for all grid points, the coefficient of discrete value ｛C stored in the table of each grid point (L, A, B)
(L, A, B), M (L, A, B), Y (L, A,
B), K (L, A, B)} are initialized by values obtained by rounding the corresponding converted values according to the precision of the table. T and s
Is an appropriate initial value. Each grid point is assigned a serial number in ascending order of color saturation within the color reproduction range, and subsequently, with respect to grid points outside the color reproduction range, serial numbers are assigned in ascending order of color difference before and after conversion. Next, the following processing is performed. Process (1): The grid point values of K are calculated in ascending order of the serial number,
Optimization is performed by the operations of the processes (1.1) to (1.3). Process (1.1): A predetermined step s is added to the current value of K to calculate an error of the color conversion device. Process (1.2): A predetermined step s and a minimum unit of the step are subtracted from the current value of K to calculate an error of the color conversion device.

At this time, instead of the entire input range, the average of the color differences may be obtained only in a range where this coefficient has an influence. For example, in the tetrahedron interpolation method, the prism interpolation method, and the cubic interpolation method, the average may be obtained only for the portions included in the tetrahedron, the triangular prism, and the rectangular parallelepiped each having the lattice point at the vertex. Process (1.3): A random number based on a uniform distribution is added to a predetermined section [0, T] to the error of the process (1.1) and the error of the process (1.2), respectively. If the sum of the error of 1.1) and the random number is smaller than the sum of the error of step (1.2) and the random number, a predetermined step s is added to the current value of K to update. If not, a predetermined step s and the minimum unit of the step are subtracted from the current value of K and updated. Process (2): The operation of process (1) is applied to K at all grid points. When this optimization operation has completed one round, the error of the color conversion apparatus is obtained, and the error is reduced to a value equal to or less than a predetermined value, substantially converged, or repeated a predetermined number of times.
At this time, when the error becomes the minimum, the coefficient is recorded as “K is the optimal coefficient”, and T for determining the predetermined section is multiplied by a predetermined value larger than 1.
Increase T. On the other hand, if the error increases before performing one round of optimization, T is reduced by multiplying T by a predetermined value smaller than 1. The same operation is performed for the predetermined step s, but the value is not smaller than the minimum step.

Next, the following processing is executed with “K is the optimal coefficient” as an initial value and T and s as appropriate initial values. Process (3): CMY lattice point values are optimized by the operations of processes (3.1) to (3.5) in ascending order of serial numbers. Process (3.1): A predetermined step s is added to the current value of C to calculate an error of the color conversion device. Process (3.2): A predetermined step s and a minimum unit of the step are subtracted from the current value of C to calculate an error of the color conversion device. Process (3.3): A random number based on a uniform distribution is added to the error of the above process (3.1) and the error of the process (3.2) in a predetermined section [0, T], respectively. When the sum of the error of 3.1) and the random number is smaller than the sum of the error of the process (3.2) and the random number, a predetermined step s is added to the current value of C and updated. If not, a predetermined step s and the minimum unit of the step are subtracted from the current value of C and updated. Process (3.4): The operations of processes (3.1) to (3.3) are applied to M instead of C. Process (3.5): The operations of processes (3.1) to (3.3) are applied to Y instead of C. Process (4): The operation of process (3) is applied to all grid points. When this optimization operation has completed one round, the error of the color conversion apparatus is obtained, and the error is reduced to a value equal to or less than a predetermined value, substantially converged, or repeated a predetermined number of times. At this time, if the error becomes the minimum, the coefficient is recorded as the “optimal coefficient”, and 1 is set to T for determining the aforementioned predetermined section.
T is increased by multiplying by a predetermined value greater than. On the other hand, when the error is compared before performing one round of optimization,
If it has increased, T is reduced by multiplying T by a predetermined value smaller than one. The same operation as T is performed for the predetermined step s, but the value is not smaller than the minimum step.

As described above, when the learning is completed, the finally recorded “optimal coefficient” is output.

[Fourth Embodiment] Next, a fourth embodiment for optimizing coefficients by introducing a continuous function that can be assumed between discrete coefficient values and errors will be described. FIG. 5 shows the configuration of the fourth embodiment. In FIG. 5, portions corresponding to those in FIG. 3 are denoted by corresponding reference numerals, and detailed description thereof is omitted.
In FIG. 5, a quadratic function determining unit 41 determines a quadratic function based on the errors of E ₀ , E ₋ and E ₊ , and a differential coefficient calculating unit 42 calculates a differential coefficient of the quadratic function at E ₀ . . The coefficient updating unit 43 determines a coefficient according to the temperature (temperature during annealing) and the differential coefficient. This will be described later in detail.

Next, the color conversion device 21 according to this embodiment will be described.
The optimization of the coefficient will be described in detail. Color conversion device 2
1 may perform the optimization according to the present embodiment alone, or may perform the optimization according to the present embodiment after optimizing the number of times as appropriate according to the second embodiment prior to the present embodiment. Various definitions such as errors are the same as in the second embodiment.

Now, of the k coefficients, the p-th coefficient w
Focusing on _p , the error E _{0 with} respect to the current coefficient value, ie,
E ₀ = E (w ₁ , w ₂ ,..., W _p ,..., W _k ) and an error E ₊ for a coefficient value larger than the current coefficient value by a predetermined step s ₁ , that is, E ₊ = E (w _{1, w 2, ..., w} p +
s ₁ ,..., w _k ) and an error E for a coefficient value smaller than the current coefficient value by a predetermined step s ₂ , that is, E ₋
= E (w ₁ , w ₂ ,..., W _p −s ₂ ,..., W _k ) are calculated. Than the error of the three points, to estimate the quadratic function, calculates a differential coefficient E _'p in w _p.

According to the temperature t, if the differential coefficient E ′ _p is large, the probability variable X becomes 1 with high probability (0 otherwise).
₊ (E ′ _p ; t) and a random variable X ₋ (E ′ _p ; t) which becomes 1 with a high probability if the derivative E ′ _p is small (0 otherwise).
Updates the coefficient w _p with the following values. Here, it is assumed that the random variables X ₊ and X _- are uncertainly influenced by the differential coefficient as the temperature is higher, and deterministically as the temperature is lower.

[0112]

## EQU5 ## wp ← w _p + s ₁ .X ₊ (E ′ _p ; t) −s ₂ .X ₋
(E ′ _p ; t) In this embodiment, the predetermined step in the case of addition has a different value, but the predetermined step in the case of addition and the predetermined step in the case of subtraction do not necessarily have to have different values. .

This operation is repeated for each weight w _p (p = 1, 2,...,
Apply for k). When this optimization operation has completed one round, the error of the color conversion apparatus is obtained, and the error is reduced to a value equal to or less than a predetermined value, substantially converged, or repeated a predetermined number of times. At this time, when the error becomes the minimum, the coefficient is recorded as the “optimal coefficient”, and the above-described predetermined step s is performed.
To _1, s ₂ and the temperature t, by multiplying a predetermined value greater than 1 increases the step and temperature. On the other hand, if the error increases before performing one round of optimization, s ₁ , s ₂ and the temperature t are multiplied by a predetermined value smaller than 1, and the step and the temperature are calculated. Decrease. However, each step is not set to a value smaller than the minimum step.

As described above, when the learning is completed, the finally recorded “optimum coefficient” is output.

In this embodiment, three points are taken and the differential coefficient is calculated by a quadratic function. However, if two or more points are taken, the differential coefficient can be determined by an appropriate function.

In the above description, three points were obtained.
It is possible to calculate the p type coefficients using different appropriate function _{f 1 (w), f 2} (w) ... f p (w).

Here, as an example, when p = 4,

[0118]

F ₁ (w) = w + 1 f ₂ (w) = w + 2 f ₃ (w) = w + 3 f ₄ (w) = w + 4 When calculating the differential coefficient, since the differential coefficient of the current value can be estimated even in a section that does not include the current coefficient, the function value does not have to be in the section that includes the current coefficient.

As another example, when p = 5,

[0120]

F ₁ (w) = floor (w × 0.98) f ₂ (w) = floor (w × 0.99) f ₃ (w) = w f ₄ (w) = ceil (w / 0) .99) f ₅ (w) = it may be as ceil (w / 0.98). Where floor is truncated and cei
l is rounding up. Here, as an example of the operation of rounding to a discrete value that can take a coefficient, an example using truncation or round-up has been shown, but the rounding operation can take any method.

[Application Example] Next, an application example of the present invention will be described.

FIG. 6 shows an electronic device using the data conversion apparatus of the present invention.
00 has a data conversion device 110. The data conversion device 110 is the same as the above-described embodiment, and takes a discrete value as a conversion coefficient. Data converter 1
10 is optimized by the coefficient optimizing unit 111 in the same manner as in the above-described embodiment.

In this case, the coefficient may be optimized in advance by the reference data converter, and the coefficient may be installed in the data converter 110 of the electronic device 100.
Thereafter, the coefficient optimizing unit 111 may further perform a final optimizing process.

FIG. 7 shows a color image forming apparatus (color copying machine or color printing machine) using the data conversion apparatus of the present invention. In this figure, an image forming apparatus 200 has two colors of data conversion apparatuses. Conversion devices 210, 220
have. The color data input from the input unit 230 is sequentially color-converted by the color conversion units 210 and 220,
0 and printed out. In this example, both or one of the color conversion devices 210 and 220 can optimize the coefficient of the data conversion device of the present invention.

FIG. 8 shows a robot device using the data conversion device of the present invention. In this figure, the robot 300 has a data conversion device 310 and responds to a position input from a position input section 320. The posture and the like are controlled. The error detection unit 330 detects an error,
Accordingly, the optimization of the coefficients of the data conversion device is performed.

[0126]

As described above, according to the present invention,
Even when data conversion is performed using coefficients having discrete values, the values of the coefficients can be easily and stably learned.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating a configuration of a first exemplary embodiment of the present invention.

FIG. 2 is a diagram specifically explaining the details of the above embodiment.

FIG. 3 is a diagram illustrating a configuration of a second exemplary embodiment of the present invention.

FIG. 4 is a diagram showing a configuration of a third embodiment of the present invention.

FIG. 5 is a diagram illustrating a configuration of a fourth embodiment of the present invention.

FIG. 6 is a diagram illustrating an application example of the present invention.

FIG. 7 is a diagram illustrating an application example of the present invention.

FIG. 8 is a diagram illustrating an application example of the present invention.

[Explanation of symbols]

 REFERENCE SIGNS LIST 11 input buffer 12 data conversion device 13 output buffer 14 ideal output memory 15 error calculation unit 16 error history memory 17 random number distribution control unit 18 step control unit 19 coefficient update unit 100 electronic device 200 color image forming device 300 robot

──────────────────────────────────────────────────の Continued on front page (51) Int.Cl. ⁶ Identification code FI H04N 9/64 H04N 1/46 Z

Claims (36)

[Claims] 1. A data conversion apparatus for converting m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient which takes a discrete value, wherein said discrete value is taken For each of the coefficients, a predetermined coefficient value is determined for at least two of the current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and a coefficient value smaller than the current coefficient value by a predetermined step s2. Means for calculating an output data group for the input data group, and a probability that the smaller the error between the calculated output data group for the at least two coefficient values and the ideal output data group corresponding to the predetermined input data group is, the higher the probability is; Coefficient value selecting means for selecting any one of the at least two coefficient values as a new coefficient value. . 2. The apparatus according to claim 1, wherein said coefficient value selecting means includes means for adding a random number according to a predetermined distribution to each error in said at least two coefficient values, and selecting a coefficient value giving a minimum value of the sum. The coefficient determining apparatus according to claim 1, wherein 3. The degree of the gradual decrease of the probability with respect to the magnitude of the error, or the predetermined steps s1 and s2
3. A coefficient determining apparatus according to claim 1, further comprising: means for controlling (a) or (b) based on an error history. 4. The coefficient determination method according to claim 3, wherein the means for controlling the degree of the gradual decrease of the probability with respect to the magnitude of the error in accordance with the history of the error is a means for controlling the predetermined distribution. apparatus. 5. The at least one coefficient having a discrete value is a discrete value corresponding to n outputs for each representative point in a table of m-dimensional representative points corresponding to m-dimensional input data. Is recorded in advance, and a value corresponding to the output of the representative point of the data conversion apparatus that obtains an n-dimensional output by interpolating a value corresponding to the output. And means for updating the coefficient by defining
The coefficient determination device according to 2, 3, or 4. 6. A data conversion means for converting m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient taking a discrete value, and taking the discrete value For each of the coefficients, a current coefficient value, a coefficient value greater than the current coefficient value by a predetermined step s1,
Means for calculating an output data group for a predetermined input data group for at least two coefficient values among coefficient values smaller than the current coefficient value by a predetermined step s2, and an output data group calculated for the at least two coefficient values And coefficient value selecting means for selecting any one of the at least two coefficient values as a new coefficient value with a probability that the smaller the error between the ideal output data group corresponding to the predetermined input data group and the ideal output data group is, the higher the error becomes. A data conversion device, comprising: 7. An m-dimensional first color data is represented by n in accordance with k coefficients including at least one coefficient taking a discrete value.
Color conversion means for converting to a second dimension of color data; a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1 for each of the coefficients having the discrete values, Means for calculating a second color data group for a predetermined first color data group for at least two coefficient values among coefficient values smaller than the coefficient value by a predetermined step s2, and calculating for the at least two coefficient values. With the probability that the smaller the error between the second color data group and the ideal second color data group corresponding to the predetermined first color data group becomes, the higher one of the at least two coefficient values is, A coefficient value selecting means for selecting a new coefficient value. 8. The color conversion device according to claim 7, wherein the error is a color difference. 9. A means for receiving m-dimensional first color data; and converting the m-dimensional first color data into n-dimensional data according to k coefficients including at least one coefficient taking a discrete value. Second
Color conversion means for converting into color data; output means for performing a predetermined output operation based on the second color data output from the color conversion means; and for each of the coefficients taking discrete values, Predetermined first color data for at least two of a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and a coefficient value smaller than the current coefficient value by a predetermined step s2; Means for calculating a second color data group for a group; a second color data group calculated for the at least two coefficient values; and an ideal second color data group corresponding to the predetermined first color data group A coefficient value selecting means for selecting any one of the at least two coefficient values as a new coefficient value with a probability that the error becomes higher as the error from the color image becomes smaller. Forming apparatus. 10. The color image forming apparatus according to claim 9, wherein said output means receives said second color data via a subsequent color conversion means. 11. A means for receiving m-dimensional input data, and data for converting said m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient taking a discrete value. Conversion means, output means for performing a predetermined output operation based on the n-dimensional output data output from the data conversion means, for each of the coefficients taking the discrete value, the current coefficient value, the current Means for calculating an output data group with respect to a predetermined input data group for at least two coefficient values among a coefficient value larger than the coefficient value by a predetermined step s1 and a coefficient value smaller than the current coefficient value by a predetermined step s2; The smaller the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the predetermined input data group, the higher the error. Probability, the electronic device characterized by having a coefficient selecting means for selecting one of the at least two coefficient values as a new coefficient value that. 12. A data conversion device for converting m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient taking a discrete value, wherein said discrete value is taken. Means for calculating, for each of the coefficients, an output data group for p types of coefficient values in an appropriate section including the current coefficient value; an output data group calculated for the p types of coefficient values; and the predetermined input data group Calculating means for calculating an error from an ideal output data group corresponding to the above, and obtaining p kinds of errors; and a predetermined function from the p kinds of errors, which can be differentiated in the current coefficient value, from a coefficient value to an error. And differential coefficient calculating means for calculating a differential coefficient in a current coefficient value, and coefficient value updating means for stochastically or deterministically updating the coefficient based on the differential coefficient. Number determining device. 13. At least one of a current coefficient value, a coefficient value obtained by adding a predetermined step s1 to the current coefficient value, and a coefficient value obtained by subtracting a predetermined step s2 from the current coefficient value.
13. The coefficient determining apparatus according to claim 12, wherein one of the coefficients is included in the p kinds of coefficients. 14. A method for controlling a degree of a gradual decrease of the probability with respect to a magnitude of the derivative and one or both of the predetermined steps s1 and s2 in accordance with an error history. Item 14. The coefficient determination device according to item 12 or 13. 15. The at least one coefficient taking a discrete value is a discrete value corresponding to n outputs for each representative point in a table of m-dimensional representative points corresponding to m-dimensional input data. Is recorded in advance, and a value corresponding to the output of the representative point of the data conversion apparatus that obtains an n-dimensional output by interpolating a value corresponding to the output. 2. A means for updating a coefficient by defining the following.
The coefficient determining apparatus according to 2, 13, or 14. 16. Data conversion means for converting m-dimensional input data into n-dimensional output data according to k coefficients including at least one coefficient taking a discrete value, and taking the discrete value Means for calculating, for each of the coefficients, an output data group for p types of coefficient values in an appropriate section including the current coefficient value; an output data group calculated for the p types of coefficient values; and the predetermined input data group Calculating means for calculating an error from an ideal output data group corresponding to the above, and obtaining p kinds of errors; and calculating a function from an appropriate count value differentiable in the current coefficient value to the error from the p kinds of errors. A data transformation method comprising: a differential coefficient calculating means for calculating a differential coefficient at an assumed and current coefficient value; and a coefficient value updating means for stochastically or deterministically updating the coefficient based on the differential coefficient. Apparatus. 17. Color conversion means for converting m-dimensional first color data into n-dimensional second color data in accordance with k coefficients including at least one coefficient having a discrete value, Means for calculating a second color data group for p kinds of coefficient values in an appropriate section including the current coefficient value for each of the coefficients having discrete values, Calculating means for calculating an error between the second color data group and an ideal second color data group corresponding to the predetermined first color data group to obtain p kinds of errors; A differential coefficient calculating means for calculating a differential coefficient at the current coefficient value, assuming a predetermined function from the coefficient value to an error, which is differentiable at the current coefficient value; and Coefficient value updating means for periodically updating the coefficient The color conversion apparatus according to claim and. 18. The color conversion apparatus according to claim 17, wherein said error is a color difference. 19. means for receiving m-dimensional first color data; and converting the m-dimensional first color data into n-dimensional data according to k coefficients including at least one coefficient taking discrete values. Second
Color conversion means for converting into color data; output means for performing a predetermined output operation based on the second color data output from the color conversion means; and for each of the coefficients taking discrete values, Means for calculating a second color data group for p kinds of coefficient values in an appropriate section including the current coefficient value; a second color data group calculated for the p kinds of coefficient values; Calculating means for calculating an error from an ideal second color data group corresponding to the color data group of the above, and obtaining p kinds of errors; Assuming a predetermined function from a numerical value to an error, a differential coefficient calculating means for calculating a differential coefficient at the current coefficient value, and a coefficient value updating means for stochastically or deterministically updating the coefficient based on the differential coefficient. A color characterized by having Image forming apparatus. 20. The color image forming apparatus according to claim 19, wherein said output means receives said second color data via a subsequent color conversion means. 21. A means for receiving m-dimensional input data, and data for converting said m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient taking a discrete value. Conversion means, output means for performing a predetermined output operation based on the n-dimensional output data output from the data conversion means, and appropriate coefficients including a current coefficient value for each of the coefficients having discrete values. Means for calculating an output data group for p kinds of coefficient values in the section; calculating an error between the output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the predetermined input data group , Calculating means for obtaining p kinds of errors, and assuming a predetermined function from the coefficient values to the errors that can be differentiated in the current coefficient values from the p kinds of errors, A differential coefficient calculating means for calculating, based on the differential coefficient, the electronic device characterized by having a coefficient updating means for updating the probabilistic or deterministic manner coefficient. 22. In a neural network having k coefficients including at least one discrete coupling coefficient or a discrete threshold value, or both, a current value of each of the discrete value coefficients is determined by a current value. An output data group corresponding to a predetermined input data group for at least two of a coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1 and a coefficient value smaller than the current coefficient value by a predetermined step s2 Means for calculating the at least two coefficient values with a probability that the smaller the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the predetermined input data group is, the higher the error is. A coefficient value selecting means for selecting any one as a new coefficient value. Coefficient determining apparatus of the work. 23. A neural network having k coefficients including at least one discrete combination coefficient or a discrete threshold value, or both, and a current value of each of the discrete value coefficients. An output data group corresponding to a predetermined input data group for at least two of a coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1 and a coefficient value smaller than the current coefficient value by a predetermined step s2 Means for calculating the at least two coefficient values with a probability that the smaller the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the predetermined input data group is, the higher the error is. A coefficient value selecting unit for selecting any one as a new coefficient value. 24. In a neural network having k coefficients including at least one discrete combination coefficient or a discrete threshold value or both, a current value of each of the discrete value coefficients is determined by a current value. Means for calculating an output data group for p kinds of coefficient values in an appropriate section including a coefficient value; an output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the predetermined input data group Calculation means for calculating an error with respect to the current coefficient value, and a predetermined function which is differentiable in the current coefficient value from the p type error and which is assumed to be a function from the coefficient value to the error. A differential coefficient calculating means for calculating a differential coefficient in a numerical value; and a coefficient value updating means for stochastically or deterministically updating the coefficient based on the differential coefficient. Coefficient determiner Le networks. 25. A neural network having k coefficients including at least one discrete combination coefficient or a discrete threshold value or both, and a current value of each of the discrete value coefficients. Means for calculating an output data group for p kinds of coefficient values in an appropriate section including a coefficient value; an output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the predetermined input data group Calculation means for calculating an error with respect to the current coefficient value, and a predetermined function which is differentiable in the current coefficient value from the p type error and which is assumed to be a function from the coefficient value to the error. A neural network comprising: differential coefficient calculating means for calculating a differential coefficient in a numerical value; and coefficient value updating means for stochastically or deterministically updating the coefficient based on the differential coefficient. Coefficient determining device and a neural network data conversion device according to the network. 26. A data conversion device for converting m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient that takes a discrete value, wherein said discrete value is taken For each of the coefficients, a predetermined coefficient value is determined for at least two of the current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and a coefficient value smaller than the current coefficient value by a predetermined step s2. Means for calculating an output data group for the input data group, and a probability that the smaller the error between the calculated output data group for the at least two coefficient values and the ideal output data group corresponding to the predetermined input data group is, the higher the probability is; Coefficient value selecting means for selecting any one of the at least two coefficient values as a new coefficient value, and each of the coefficients taking the discrete values Means for calculating an output data group for p kinds of coefficient values in an appropriate section including the current coefficient value; and for the output data group calculated for the p kinds of coefficient values and the predetermined input data group. Calculation means for calculating an error from the ideal output data group to obtain p kinds of errors, and assuming a predetermined function which can be differentiated in the current coefficient value from the p kinds of errors and which is differentiable from the coefficient value to the error. A differential coefficient calculating means for calculating a differential coefficient in a current coefficient value; and a coefficient value updating means for stochastically or deterministically updating the coefficient based on the differential coefficient. A coefficient determination device that executes updating of a coefficient value by the coefficient value updating unit one or more times after executing a numerical value selection at least once. 27. A method for determining a coefficient value in a data conversion device for converting m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient taking a discrete value. For each of the coefficients having discrete values, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and a coefficient value smaller than the current coefficient value by a predetermined step s2 Calculating an output data group for a predetermined input data group for at least two coefficient values; and an error between the output data group calculated for the at least two coefficient values and an ideal output data group corresponding to the predetermined input data group Selecting one of the at least two coefficient values as a new coefficient value with a probability that the smaller the Coefficient determination method characterized by. 28. A method for determining a coefficient value in a data conversion device for converting m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient having a discrete value. Calculating, for each of the coefficients having discrete values, an output data group for p types of coefficient values in an appropriate section including the current coefficient value; and output data calculated for the p types of coefficient values. Calculating means for calculating an error between a group and an ideal output data group corresponding to the predetermined input data group to obtain p kinds of errors; and a differential means capable of differentiating the current coefficient value from the p kinds of errors. Assuming a predetermined function from a numerical value to an error, calculating a differential coefficient at the current coefficient value; and, based on the differential coefficient, stochastically or deterministically updating the coefficient. Coefficient determination method characterized by comprising. 29. A method for determining a coefficient value in a data conversion device for converting m-dimensional input data into n-dimensional output data according to k coefficients including at least one coefficient taking a discrete value. For each of the coefficients having discrete values, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and a coefficient value smaller than the current coefficient value by a predetermined step s2 Calculating an output data group for a predetermined input data group for at least two coefficient values; and an error between the output data group calculated for the at least two coefficient values and an ideal output data group corresponding to the predetermined input data group Selecting one of the at least two coefficient values as a new coefficient value with a probability that the smaller the is, After the new coefficient value is selected, for each of the coefficients taking the discrete values, calculating an output data group for p kinds of coefficient values in an appropriate section including the current coefficient value; calculating means for calculating an error between an output data group calculated for p kinds of coefficient values and an ideal output data group corresponding to the predetermined input data group to obtain p kinds of errors; Assuming a predetermined function from the coefficient value to the error that is differentiable in the current coefficient value, calculating a differential coefficient in the current coefficient value, based on the differential coefficient, stochastically or deterministically calculating the coefficient. Updating the coefficient value one or more times, and then performing the update of the coefficient value one or more times. 30. A method for setting a coefficient value in a data conversion device for converting m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient taking a discrete value. In a standard data conversion device having a function equivalent to that of the data conversion device main body, for each of the coefficients having the discrete values, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, And calculating an output data group for a predetermined input data group with respect to at least two coefficient values among coefficient values smaller than the current coefficient value by a predetermined step s2; and an output data group calculated for the at least two coefficient values. And the probability that the smaller the difference between the ideal output data group corresponding to the predetermined input data group and the ideal output data group becomes, Coefficient setting method characterized by also comprising the steps of selecting one of the two coefficient values as a new coefficient value, and setting the selected coefficient as the coefficient of the data conversion apparatus. 31. A method for setting a coefficient value in a data conversion device for converting m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient taking a discrete value. In a reference data conversion device having a data conversion function equivalent to that of the data conversion device body, for each of the coefficients having discrete values, output is performed for p types of coefficient values in an appropriate section including a current coefficient value. Calculating a data group; calculating an error between the output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the predetermined input data group to obtain p kinds of errors; From the p kinds of errors, assuming a predetermined function from the coefficient value to the error, which is differentiable in the current coefficient value, calculating a differential coefficient in the current coefficient value. A coefficient setting method, comprising: a step; a step of stochastically or deterministically updating a coefficient based on the differential coefficient; and a step of setting the updated coefficient as a coefficient of the data conversion device main body. 32. A data conversion apparatus for converting m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient which takes a discrete value, wherein said discrete value is taken Coefficient calculating means for calculating p kinds of coefficient values by applying p kinds of predetermined functions to the current coefficient values for at least one of the coefficients, and p kinds of coefficient values given by the coefficient calculating means Output data calculating means for calculating an output data group corresponding to the predetermined input; calculating an error between the output data group and an ideal output data group corresponding to the predetermined input to obtain p kinds of errors Error calculating means, calculating a differential coefficient in the current coefficient value from the p kinds of errors, assuming a predetermined function that is differentiable in the current coefficient value and from the coefficient value to the error. Coefficient determination apparatus characterized by having a coefficient calculating means. 33. A data conversion device for converting m-dimensional input data into n-dimensional output data in accordance with k coefficients including at least one coefficient that takes a discrete value, wherein said discrete value is taken. Coefficient calculating means for calculating p kinds of coefficient values by applying p kinds of predetermined functions to the current coefficient values for at least one of the coefficients, and p kinds of coefficient values given by the coefficient calculating means Output data calculating means for calculating an output data group corresponding to the predetermined input; calculating an error between the output data group and an ideal output data group corresponding to the predetermined input to obtain p kinds of errors Error calculating means, calculating a differential coefficient in the current coefficient value from the p kinds of errors, assuming a predetermined function that is differentiable in the current coefficient value and from the coefficient value to the error. A coefficient calculating means, based on the coefficient, the coefficient determination apparatus characterized by having a coefficient updating means for updating the probabilistic or deterministic manner coefficient. 34. The coefficient determining apparatus according to claim 32, further comprising means for controlling the number of said p and said predetermined p kinds of functions according to an error history. 35. The predetermined function is a method in which an appropriate discrete value is
35. The coefficient determining apparatus according to claim 32, wherein the coefficient value is a function value in addition to the current coefficient value. 36. The predetermined function multiplies an appropriate value by a current coefficient value, or divides the current coefficient value by an appropriate value, and rounds the resulting product or quotient to a discrete value. 35. The coefficient determining apparatus according to claim 32, wherein the calculated value is a function value.