JP5517973B2 - Pattern recognition apparatus and pattern recognition method - Google Patents

Description

  The present invention relates to a pattern recognition apparatus and a pattern recognition method for performing pattern recognition from multidimensional information. The present invention particularly relates to the field of pattern recognition from multidimensional information such as “diagnosis / monitoring” of production line abnormality, “prediction / inspection” of product characteristic values, and “identification” of sensory characteristic values.

  One of the pattern recognition methods for predicting and diagnosing from multidimensional information is the MT system proposed by Dr. Genichi Taguchi. In the MT system, the MT method (a method using the Mahalanobis distance), the MTA method (a method for replacing the correlation coefficient matrix in the MT method with a variance-covariance matrix), and the TS method (a method using orthogonal expansion by feature items) ), The T method (in particular, the T method (1) in which the unit space is the center of the group), and the T method using a standard signal-to-noise ratio (for example, there is no true value as in character recognition and many (Referred to as non-patent documents 1 to 3), and the like. The RS method, the RT method, and the T method (3) are proposed. In addition, devices that apply the above-described MT system to quality control, inspection, and the like have been proposed (see, for example, Patent Documents 1 and 2).

  The unit space means a data set belonging to a homogeneous group for the purpose. For example, a group that is homogeneous for the purpose of health examination (discovery of a disease) is a group of healthy people. A group of healthy persons is considered to form a specific pattern because of a relatively small distribution of characteristic item values related to health. On the other hand, the signal space described later is a standard for evaluating the prediction accuracy. In the above example, a data set belonging to a group having various health states (from health to severe unhealthy states). It is.

  In the T method, only the average value data is used for the unit space. On the other hand, signal space data is generally data for creating a database (see, for example, Non-Patent Document 4).

  These methods in the MT system are divided into (1) MT method and MTA method groups that emphasize correlation between items, and (2) TS method, T method, and RT method groups that emphasize the main effects of items. Divided. One of the groups (1) and (2) is selected according to conditions such as the nature of the unit space, the number of data sets that can be prepared as the unit space, and the presence or absence of multicollinearity. In general, the group (1) is advantageous in terms of prediction accuracy, and the group (2) is considered advantageous in terms of fewer data constraints.

  Hereinafter, the MT method will be representatively taken as a group of (1), and the T method will be taken as a representative of a group of (2) for comparison. The MT method is often used for “diagnosis” such as pass / fail determination. In the MT method, the unit space is at the end of the group. However, in the MT method, in the process of calculating the inverse matrix of the correlation coefficient matrix in the unit space data, (a) there is a combination of two feature items such that the correlation coefficient is 1, or (b) When the value of the feature item is the same between the data sets (σ = 0 of the item), there is a problem that the inverse matrix cannot be calculated.

  For this reason, generally in the case of (a), two feature items are considered to have the same content, and one of the combinations is omitted from the analysis. In general, in the case of (b), since the value of the item does not change in the future, it is considered unnecessary and is omitted from the analysis. However, it is highly possible that the situation such as (a) or (b) occurs only in a unit space where the result is uniform. In signal space data including an abnormal state that is originally desired to be detected, the correlation coefficient between two feature items does not become 1, and the variance (standard deviation) of feature items does not become 0. For this reason, omitting items having abnormal characteristics to be detected in advance from the analysis causes a problem that the pattern recognition accuracy is lowered.

  On the other hand, the T method is used, for example, for quantitative prediction and estimation of an output having a sign. However, unlike the MT method, the T method cannot perform prediction and estimation in consideration of the correlation between two feature items. In order to solve such a problem in the T method, a method of performing prediction and estimation in consideration of the correlation between two feature items has been proposed in the T method (see Non-Patent Document 5).

JP 2009-210445A JP 2009-288100 A

Genichi Taguchi, Handbook of Quality Engineering, Nikkan Kogyo Shimbun, 2007 Genichi Taguchi, prediction and estimation by MT system, standardization and quality control, Vol. 58, no. 8, pp. 68-76, 2005 Taichi Genichi, image recognition, T method using standard S / N ratio, standardization and quality control, Vol. 58, no. 11, pp. 94-101, 2005 Shohei Yoshino, Real Estate Price Prediction with MT System (3), Quality Engineering, Quality Engineering Society, Vol. 14, no. 1,2006 Taro Tadami, Method of Considering Correlation in T Method, 15th Quality Engineering Research Conference Proceedings, Quality Engineering Society, pp. 434-437, 2007

  The method described in Non-Patent Document 5 is to newly create an item considering the correlation between all two items in the unit space, and add the item to the item in the T method for analysis. . However, the method described in Non-Patent Document 5 has the following problems.

FIG. 11 is a diagram for explaining the problems of the method described in Non-Patent Document 5. Referring to FIG. 11, item X _pq indicating the correlation between two items x _p and x _q (p and q represent item numbers) is represented by _scaled items X _p and X _q 2 In the dimension plane, the distance d between the single regression line 2 and the data 30 with respect to the unit space data 1 is expressed as an amount proportional to the distance d. The single regression line 2 is a straight line passing through the data center (origin). According to this definition, X _pq of data on the single regression line 2 is all the same value (X _pq = 0). Here, the point on the plane showing the data is simply referred to as “data”.

Actually, even if a plurality of data is on the single regression line 2, the data may have different characteristics and results. For example, since the two data 31a and 31b are on the single regression line 2, X _pq of the data 31a and 31b is 0 (that is, the distance d = 0). The data 31a is located near the data center (origin), while the data 31b belongs to a signal space far away from the data center. That is, the data 31b is abnormal data.

A similar case is also indicated by data 32a to 32c on a straight line 11 parallel to the single regression line 2. The distance between the straight line 11 and the single regression line 2 is d ′. Accordingly, X _pq for the data 32a to 32c all have the same value (X _pq = d ′). However, of the data 32a to 32c, the data 32a is located closest to the data center (origin). Data 32c is located farthest from the origin, and data 32b is located between data 32a and data 32c.

  In the data expressed by the features of the two items having the correlation, a group having the same degree of abnormality (also called distance) is a group of data represented by points on the concentric ellipse 20 in FIG. It is not an equidistant group from. For this reason, according to the method described in Non-Patent Document 5, there may occur a case where sufficient estimation accuracy cannot be obtained.

  An object of the present invention is to provide a method and apparatus capable of obtaining higher identification accuracy with less restrictions on data formats in the field of pattern recognition based on multidimensional information.

  A pattern recognition device according to an aspect of the present invention is a pattern recognition device that performs pattern recognition based on a plurality of pieces of data each having a plurality of original feature items. An evaluation distance calculation unit that calculates an evaluation distance for all combinations that select two original feature items, and for each data, at least some of the evaluation distances that are calculated corresponding to all combinations are a plurality of A weighting factor that generates a plurality of new feature items by adding to the original feature item and calculates a weighting factor that represents the correlation between the value of each of the plurality of new feature items and the true value of the new feature item A calculation unit, a prediction value calculation unit that calculates a predicted output value using a weighting factor for each new feature item, a comparison between the prediction value and a predetermined threshold value, and a determination for the purpose And a determination unit that performs. The evaluation distance calculation unit calculates the Mahalanobis distance as the evaluation distance.

  A pattern recognition apparatus according to another aspect of the present invention is a pattern recognition apparatus that performs pattern recognition based on a plurality of pieces of data each having a plurality of original feature items. An evaluation distance calculation unit that calculates evaluation distances for all combinations that select two original feature items from, and a plurality of at least some of the evaluation distances calculated for all combinations for each data A weight for generating a plurality of new feature items by adding to the original feature item and calculating a weighting coefficient representing a correlation between each value of the plurality of new feature items and a true value of the new feature item A coefficient calculation unit, a prediction value calculation unit that calculates a predicted output value using a weighting factor for each new feature item, a prediction value and a predetermined threshold value are compared, and a determination for the purpose is made And a determination unit that performs. The evaluation distance calculation unit calculates an evaluation distance used by MTA (Mahalanobis Taguchi Adjoint method) as the evaluation distance.

  A pattern recognition apparatus according to still another aspect of the present invention is a pattern recognition apparatus that performs pattern recognition based on a plurality of data each having a plurality of original feature items, and each of the data includes a plurality of original feature items. An evaluation distance calculation unit that calculates evaluation distances for all combinations that select two original feature items from the inside, and for each data, at least a part of the evaluation distances that are calculated for all combinations A plurality of new feature items are generated by adding to the plurality of original feature items, and a weighting coefficient representing a correlation between each value of the plurality of new feature items and the true value of the new feature item is calculated. The weight coefficient calculation unit, the prediction value calculation unit that calculates the predicted value of the output using the weight coefficient for each new feature item, the predicted value and a predetermined threshold value are compared, and Against And a determination section that performs determination. The evaluation distance calculation unit calculates the product of the normalized value of the first feature item and the normalized value of the second feature item as the evaluation distance.

  A pattern recognition method according to yet another aspect of the present invention is a pattern recognition method for performing pattern recognition based on a plurality of pieces of data each having a plurality of original feature items. A step of calculating evaluation distances for all combinations of selecting two original feature items from the inside, and for each data, at least some of the evaluation distances calculated corresponding to all combinations are converted into a plurality of original distances. Adding to the feature item, generating a plurality of new feature items, and calculating a weighting factor representing a correlation between the value of each of the plurality of new feature items and the true value of the new feature item; , Using a weighting factor for each new feature item, calculating a predicted output value, comparing the predicted value with a predetermined threshold value, and determining the purpose And a step of performing. In the step of calculating the evaluation distance, a Mahalanobis distance is calculated as the evaluation distance.

  A pattern recognition method according to yet another aspect of the present invention is a pattern recognition method for performing pattern recognition based on a plurality of pieces of data each having a plurality of original feature items. A step of calculating evaluation distances for all combinations of selecting two original feature items from the inside, and for each data, at least some of the evaluation distances calculated corresponding to all combinations are converted into a plurality of original distances. Adding to the feature item, generating a plurality of new feature items, and calculating a weighting factor representing a correlation between the value of each of the plurality of new feature items and the true value of the new feature item; , Using a weighting factor for each new feature item, calculating a predicted output value, comparing the predicted value with a predetermined threshold value, and determining the purpose And a step of performing. In the step of calculating the evaluation distance, the evaluation distance used by MTA (Mahalanobis Taguchi Adjoint method) is calculated as the evaluation distance.

  A pattern recognition method according to yet another aspect of the present invention is a pattern recognition method for performing pattern recognition based on a plurality of pieces of data each having a plurality of original feature items. A step of calculating evaluation distances for all combinations of selecting two original feature items from the inside, and for each data, at least some of the evaluation distances calculated corresponding to all combinations are converted into a plurality of original distances. Adding to the feature item, generating a plurality of new feature items, and calculating a weighting factor representing a correlation between the value of each of the plurality of new feature items and the true value of the new feature item; , Using a weighting factor for each new feature item, calculating a predicted output value, comparing the predicted value with a predetermined threshold value, and determining the purpose And a step of performing. In the step of calculating the evaluation distance, a product of the normalized value of the first feature item and the normalized value of the second feature item is calculated as the evaluation distance.

  According to the present invention, in the field of pattern recognition based on multidimensional information, there are few restrictions on the data format, and higher identification accuracy can be obtained.

It is the figure which showed schematic structure of the pattern recognition apparatus which concerns on embodiment of this invention. It is a functional block diagram of the pattern recognition apparatus shown in FIG. 5 is a flowchart for explaining a flow of processing by the pattern recognition apparatus according to the first embodiment. It is the figure explaining the data prepared for the process of step SA in tabular form. 4 is a flowchart for explaining a modification of the process shown in FIG. 3. 10 is a flowchart for explaining a flow of processing by the pattern recognition apparatus according to the second embodiment. Is a diagram showing an example of data when the _S βj -Ve _j <0. It is a figure explaining the data which show the relationship between a feature item and an output, and a simple correlation coefficient at that time, (eta) _j of Embodiments 4-6 compared. It is the figure which showed typically the characteristic value in the normal temperature of a sensor device, and the predicted value in high temperature. It is the figure which showed the comparison result of the T method of Taguchi, the method of nonpatent literature 5, and the method which concerns on each of Embodiment 1-3 of this invention. It is a figure for demonstrating the subject of the method of a nonpatent literature 5. FIG.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The same or corresponding parts are denoted by the same reference numerals, and description thereof will not be repeated.

  FIG. 1 is a diagram showing a schematic configuration of a pattern recognition apparatus according to an embodiment of the present invention. Referring to FIG. 1, the pattern recognition device 50 can be realized by a computer system. The pattern recognition device 50 includes a CPU (Central Processing Unit) 51, a main storage device 52 such as a RAM (Random Access Memory), an auxiliary storage device 53 such as an HDD (Hard Disk Drive), and an input such as a keyboard and a mouse. A device 54, an output device 55 such as a monitor or a printer, and a communication device 56 for exchanging information with external devices are provided.

  The auxiliary storage device 53 stores a program for causing a computer system to execute a pattern recognition method described later. The CPU 51 reads the program from the auxiliary storage device 53 and loads the program into the main storage device 52. The pattern recognition method is executed when the CPU 51 executes the program loaded in the main storage device 52.

  Means for providing a program for causing a computer system to execute the pattern recognition method is not particularly limited. For example, the CPU 51 may read a program recorded on a storage medium such as a CD-ROM and store the program in the auxiliary storage device 53. Alternatively, the CPU 51 may receive a program provided via a communication line via the communication device 56 and store the received program in the auxiliary storage device 53.

  The recording medium on which the program is recorded is not limited to a CD-ROM as long as it is a computer-readable recording medium.

  FIG. 2 is a functional block diagram of the pattern recognition apparatus shown in FIG. With reference to FIG. 2, the pattern recognition device 50 includes a data input unit 61, an evaluation distance calculation unit 62, a weight coefficient calculation unit 63, a predicted value calculation unit 64, a determination unit 65, and an output unit 66. Prepare.

  The data input unit 61 receives necessary data from the outside of the apparatus. The method and means for inputting data to the data input unit 61 are not particularly limited. As a result, a data set having a plurality of feature items as variables is prepared.

  The evaluation distance calculation unit 62 calculates the evaluation distance for each of all combinations for selecting two of the plurality of original feature items for each data. Thereby, a plurality of evaluation distances are calculated for each data.

  The weight coefficient calculation unit 63 generates a plurality of new feature items by adding at least a part of the plurality of evaluation distances to the plurality of original feature items for each data. This new feature item becomes all the feature items of the data. The weighting coefficient calculation unit 63 calculates a weighting coefficient that represents a correlation with the true value corresponding to the feature item for the same feature item of a plurality of data sets.

  The predicted value calculation unit 64 integrates a plurality of new feature items and a plurality of weighting factors for each data, and calculates an output predicted value as an evaluation value.

  The determination unit 65 compares the evaluation value with a predetermined threshold value and makes a determination on the purpose. The output unit 66 outputs the result determined by the determination unit 65 to the outside of the apparatus.

Next, the pattern recognition method according to each embodiment will be described in detail.
[Embodiment 1]
FIG. 3 is a flowchart for explaining the flow of processing by the pattern recognition apparatus according to the first embodiment. 2 and 3, in step S0, data input unit 61 accepts a plurality of data (data sets). Next, in step SA, the evaluation distance calculation unit 62 calculates an evaluation distance for each combination of two combinations selected from the plurality of original feature items for each data. Details of the processing in step SA are as follows.

(Step SA)
FIG. 4 is a diagram illustrating the data prepared for the process of step SA in a table format. Referring to FIG. 4, data sets i = 1, 2,..., N1 (number of data sets: n1) belonging to the unit space and data sets i = n1 + 1, n1 + 2,. , N1 + n2 (number of data sets: n2) is prepared as a data set in the signal space (step S1). The signal space prepared in this way is hereinafter referred to as “new signal space”, and “data set not belonging to unit space” is referred to as “data set belonging to signal space” to distinguish them.

Assume that the true values y ₁ , y ₂ ,..., Y _n of the outputs in the new signal space are known in advance. Further, original feature items x _i1 , x _i2 ,..., X _ik (number of items k) are given to a certain data set i (i = 1, 2,..., N). The lowercase letter “x” represents the value of the original feature item before normalization.

  What is important is that the new signal space used for the analysis includes a data set (signal space data set) corresponding to various output results and not belonging to the unit space. When the correlation coefficient between two items is 1 in a data set that does not belong to the unit space (signal space data set), the two items show exactly the same content. Both items have the same meaning in the future. For this reason, even if one of these two items is deleted, the pattern recognition accuracy does not decrease.

  Similarly, an item with σ = 0 means that the value of the item does not change in any state. An item for which σ = 0 does not contribute to the recognition accuracy at all. Therefore, even if the item is deleted, the pattern recognition accuracy is not affected. Therefore, in the data set shown in FIG. 4, the correlation coefficient between two items is not 1, and the standard deviation σ of a certain item is not 0.

Next, evaluation distances are calculated for all combinations that combine two items selected from the original feature items x _i1 , x _i2 ,..., X _ik of the data set i of the new signal space (step S3). , S4). In the first embodiment, the Mahalanobis distance including the signal space is used as the evaluation distance. Hereinafter, a method for calculating the evaluation distance will be described in detail.

First, the average value μ _j (j = 1, 2,..., K) and the standard deviation σ _j (j = 1, 2,..., K) of the data values x _ij of the original feature items are obtained ( Step S3). The average value μ _j is expressed according to the equation (1). The standard deviation σ _j is expressed according to equation (2).

Returning to FIG. 3, in step S3, X _ij is obtained by normalizing the value x _ij of the original feature item. The normalized value X _ij is expressed according to the following equation (3).

Subsequently, in step S4, an evaluation distance X _pq for a combination (p, q) of two items p, q out of k original feature items is obtained. X _pq is given by the Mahalanobis distance in the two-dimensional space of the two items p and q. When the single correlation coefficient of items p and q is r _pq , the correlation coefficient matrix R _pq is expressed according to the following equation (4).

Evaluation distance X _pq (Mahalanobis distance in the first embodiment) is expressed according to the following equation (5) using an inverse matrix of correlation coefficient matrix R _pq and a two-item vector (T represents transposition).

Note that whether the right side of equation (5) is divided by the number of items of 2 is not related to the pattern recognition accuracy. Further, the square root of the right side of Expression (5) may be taken as the value of the evaluation distance X _pq . Furthermore, the square root of the value obtained by dividing the right side of Equation (5) by 2 of the number of items may be used as the value of the evaluation distance X _pq .

Evaluation distances are calculated according to the above method for all combinations of two items selected from a plurality (k) of original feature items. As a result, in addition to the _k original feature items, new items of _k C ₂ = {k · (k−1) / 2} items (hereinafter referred to as “correlation feature items”) are obtained.

(Step SB)
In step SB, the weight coefficient calculation unit 63 (see FIG. 2) generates a plurality of new feature items by adding at least a part of the plurality of evaluation distances to the plurality of original feature items for each data. Details of the processing in step SB are as follows.

  First, the weight coefficient calculation unit 63 adds the k original feature items and {k · (k−1) / 2} correlation feature items to generate a new feature item (all feature items) ( Step S5). The total number of feature items in this case is k + {k · (k−1) / 2} = k · (k + 1) / 2. The weight coefficient calculation unit 63 sets k · (k + 1) / 2 = K, and assigns serial numbers 1, 2,..., K to the K feature items.

  In the above example, all correlation feature items are used to generate all feature items. However, all the feature items may be generated by some of the plurality of correlation feature items and k original feature items. Whether to use all or some of the plurality of correlation feature items is selected depending on a known method for diagnosing the importance of the item after analysis, and limits the embodiment of the present invention. It is not a thing.

Subsequently, the weighting factor calculation unit 63 calculates the value (standardized value) X of the feature item j for each feature item j (j = 1, 2,..., K) prepared by the process of step SA. _1j, X _2j, ..., the true value y _1, y ₂ of X _nj and output, ..., weighting factors w _1, w ₂ which corresponds to the magnitude of the correlation between y _n, ... , W _K are calculated (step S6).

(Step SC)
In step SC, the predicted value calculation unit 64 obtains an output predicted value ^ Y using the weighting factors w ₁ , w ₂ ,..., W _K calculated for each feature item (to avoid complexity). The data set number shall be omitted). Predicted value ^ Y is, for example, the weighting factor w _1, w _2, · · ·, is calculated according to equation (6) below the apportioning of w _K.

If the feature item value and the output value are standardized (for example, the average value is subtracted) when calculating the weighting factor, the feature item value and the output value in Equation (6) are respectively calculated. Also, the normalized value shall be used. In order to distinguish from the standardized feature items used in Equation (3), the standardized feature items are expressed as Z ₁ , Z ₂ ,..., Z _K in Equation (6).

β _j is a coefficient for correcting the unit of the feature item Z _j after normalization. Further, since the predicted value ^ Y is a standardized value, it is needless to say that an operation (for example, adding an average value) to return the predicted value ^ Y to a value before standardization is necessary.

(Step SD)
The process of calculating the predicted value in step SC can be performed on a signal space data set whose true value is known, or can be performed on an unknown data set whose true value is not known. it can. When the predicted value ^ Y is obtained for the signal space data set, the correlation between the predicted value ^ Y and the corresponding true value y (correlation coefficient, SN ratio of Taguchi's dynamic characteristics, etc.) is evaluated. To evaluate the prediction accuracy. It is also possible to optimize the combination of feature items to be used. Since this operation is publicly known, detailed description thereof will not be repeated here.

On the other hand, when the predicted value ^ Y is obtained for an unknown data set, the predicted value ^ Y (return to the original value if ^ Y is a normalized value) is determined in advance. Compare with threshold y _th . Thereby, for example, determination and determination, such as pass / fail, pass / fail, normal or abnormal, health or unhealthy, are executed. In step S10, the determination result is output.

According to the method according to the first embodiment, the Mahalanobis distance is calculated as the evaluation distance by the process of step SA. As a result, it is possible to avoid a problem such as a problem in the method according to Non-Patent Document 5 (calculation is not possible when σ = 0 in the unit space, or the item X _pq does not correctly indicate the correlation between the two items).

  According to the first embodiment, there is multicollinearity (when the number of items k> the number of data sets n, the correlation between two feature items is 1, the standard deviation of unit space items is 0, etc.) Since the correlation between items can be taken into consideration even in the data, restrictions on the data format caused by the correlation between feature items being 1 or the standard deviation of the item being 0 can be removed, and more accurate than the conventional method. Correlation feature items can be introduced. Therefore, according to the first embodiment, the accuracy of pattern recognition can be improved.

(Modification)
In the above embodiment, the correlation item is calculated using both the unit space data set and the signal space data set. However, in some cases, it is also possible to employ a method of calculating a correlation item using only a unit space data set.

In general, when a correlation item is created only from unit space data, when R _pq = 1 (the correlation coefficient between items p and q is 1), σ _p = 0 (the variance of item p is 0) In other words, a special situation occurs such as the case where the value does not change in the unit space), so that it is considered that the calculation cannot be performed or a part of the item cannot be deleted carelessly. However, if R _pq ≠ 1 or σ _p ≠ 0 in the unit space, there are cases where the pattern recognition accuracy is better when the correlation item is created from the unit space data alone. In such a case, it is possible to employ a method of calculating correlation items using only a unit space data set in step S1.

  FIG. 5 is a flowchart for explaining a modification of the process shown in FIG. Referring to FIG. 5, in step S1, only a unit space data set is used. Since the processing of the other steps is the same as the processing of the corresponding steps in FIG. 3, the following description will not be repeated.

Further, when R _pq = 1 or σ _p = 0 occurs in the unit space, a very small random number with an average of 0 may be added to the values X _p and X _q of the original feature item. . Thereby, it is possible to remove the data restriction (R _pq = 1 or σ _p = 0) without reducing the number of items. “Very small” means, for example, that the fluctuation range of the random number is, for example, about 1/100 of the average value of the signal space data of the corresponding item.

[Embodiment 2]
In the second embodiment, the distance in the MTA method (Mahalanobis Taguchi Adjoint method) is used as the evaluation distance. In this respect, the second embodiment is different from the first embodiment.

  FIG. 6 is a flowchart for explaining the flow of processing by the pattern recognition apparatus according to the second embodiment. 3 and 6, the second embodiment is different from the flowchart of FIG. 3 in that the processes of steps S2 and S3 are omitted. Further, the second embodiment differs from the first embodiment in the point of the evaluation distance calculation method in step S4. Hereinafter, a method for calculating the evaluation distance will be described in detail.

First, evaluation distance calculation unit 62 shown in FIG. 2, the dispersion V _p of the original characteristic item p dataset variance V _q of the current characteristic item q, items p, the covariance V _pq = V _qp of q formula ( 7) to (9), and a variance-covariance matrix V is created according to equation (10). p = 1, 2,..., k, q = 1, 2,..., k, and p ≠ q.

  Next, the evaluation distance calculation unit 62 obtains a cofactor matrix A of the variance-covariance matrix V according to Expression (11).

Subsequently, the evaluation distance calculation unit 62 uses the cofactor matrix A to calculate the correlation feature item X _pq between the two feature items p and q according to the following equation (12).

The right side of equation (12) may be divided by the number of items 2. Further, the square root of the right side of Expression (12) may be taken as the value of X _pq . Furthermore, the right side of Expression (12) may be divided by the number of items 2 to obtain the square root of the value. In either case, the pattern recognition accuracy is not affected.

  According to the second embodiment, as in the first embodiment, since the correlation between items can be taken into account even in data having multicollinearity, when the correlation between feature items is 1 or when the standard deviation of the items is 0 In addition to removing restrictions on the data format due to the above, it is possible to introduce more accurate correlation feature items than in the conventional method. Therefore, according to the second embodiment, the accuracy of pattern recognition can be improved.

  Furthermore, the evaluation distance calculated by the above method can be obtained without going through the standardization of feature items and the inverse matrix of the correlation coefficient matrix. Therefore, in the second embodiment, the processing of steps S2 and S3 shown in FIG. 3 can be made unnecessary.

  Furthermore, according to the second embodiment, when the variance of the feature items p and q is very close to 0, or when the correlation coefficient of the feature items p and q is very close to 1, the calculation items are lost. A decrease in pattern recognition accuracy can be prevented.

The above method has been described on the assumption that a new signal space data set is used. However, if R _pq ≠ 1 or σ _p ≠ 0 in the unit space, there are cases where the pattern recognition accuracy is better if the correlation item is created from the unit space data alone. Therefore, in such a case, as in the first embodiment, the correlation item may be calculated from the unit space data set by using only the unit space data set in the process of step S1 shown in FIG.

[Embodiment 3]
In the third embodiment, the product (= X _p · X _q ) of the standardized value of the item X _{p and} the standardized value of the item X _q is used as the evaluation distance. In this respect, the third embodiment is different from the first and second embodiments.

  Note that the flowchart for explaining the flow of processing by the pattern recognition apparatus according to the third embodiment is basically the same as the flowchart shown in FIG. 3, and differs in a specific method for calculating the evaluation distance.

  Similarly to the first and second embodiments, in the method according to the third embodiment, a data set of a new signal space can be used, or only a data set belonging to a unit space can be used.

  As described in the first embodiment, when obtaining the standardized value of the feature item, the average value is subtracted from the value of the original feature item. When only the unit space data set is used, the average value of the feature items is obtained for the unit space data set. On the other hand, when using data in the unit space and data that does not belong to the unit space, the average value of the feature items is obtained by including the data in the unit space and the data that does not belong to the unit space.

  In the case of the standardized value, the data center of the items p and q is near the origin of (0, 0). For this reason, when the correlation coefficient between the item p and the item q is positive, a deviation in the direction of the regression line is indicated when the reference value product is positive, and a deviation perpendicular to the regression line is indicated when the reference value product is negative (the correlation coefficient is negative). In the case of, the result is corrected by the sign of the coefficient β). The normalized product has properties similar to the Mahalanobis distance and the MTA method distance, and is easy to calculate. Therefore, in some cases, it can be expected that the pattern recognition accuracy is highest when the method according to the third embodiment is used.

[Embodiment 4]
In the fourth embodiment, the weighting coefficient is calculated using the T method (Taguchi method) in the process of step SB of the pattern recognition method according to the first to third embodiments.

  The flowchart for explaining the flow of processing by the pattern recognition apparatus according to the fourth embodiment is basically the same as the flowchart shown in FIG. Hereinafter, the calculation method of the weighting coefficient will be described in detail.

First, the weight coefficient calculation unit 63 shown in FIG. 2 performs normalization on the feature items X ₁ , X ₂ ,..., X _K (original feature item + correlated feature item) and the output value y. In the case of standardization of an item value, the average value of the item is subtracted from the item value. On the other hand, when the output value is normalized, the average value of the output values is subtracted from the output value. For distinction from the first embodiment, the item value after normalization is expressed as Z _{ij in the} fourth embodiment. Also, the normalized output value is denoted as Y _i .

The normalized item value Z _ij and the normalized output value Y _i are expressed according to the following equations (13) and (14), respectively.

Taguchi shown in the following equations (15) and (16) as scales indicating the correlation between the feature item Z _ij and the output Y _{i in the} item j (j = 1, 2,..., K) calculating a proportionality constant beta _j of the SN ratio eta _j, and Z _ij and Y _i of the dynamic characteristics.

here,

It is.
For example, since the single correlation coefficient asymptotically approaches ± 1, there is almost no difference in the weighting coefficient in the vicinity of ± 1. However, since η _j can take as large a value as possible in principle, the sensitivity of weighting is increased, and a more accurate prediction relational expression can be created.

In the method of Non-Patent Document 5, the value of η is not used. As a result, η = 0 in the case of S _β <V _e , so that usable items are reduced. Since the method according to Embodiment 4 uses the value of η, such a problem can be prevented. Therefore, according to the fourth embodiment, weighting with higher sensitivity can be performed, so that the accuracy of pattern recognition can be improved.

[Embodiment 5]
In the fifth embodiment, η _j of the evaluation formula in the T method used in the pattern recognition method of the fourth embodiment is expressed by the average variation S _βj shown in the formula (20) and the formula (21). It is the ratio to the residual S _ej . η _j is expressed according to the following equation (23).

In the equation (15), when S _βj −V _ej <0, it is defined as η _j ≡0. This is because it is inappropriate that the weight coefficient for obtaining the estimated value of the output becomes negative.

When η _j ≡0, the weight coefficient w _j is w _j = 0. Therefore, as is clear from the equation (6), the feature item j is not used for the analysis.

FIG. 7 is a diagram illustrating an example of data in the case of S _βj −V _ej <0. In the case of data as shown in FIG. 7, in the calculation in equation (15), Sβ ₁ = 0.245, Ve ₁ = 0.251 and the numerator of the SN ratio η ₁ becomes negative. However, when the significance of the single correlation coefficient is tested with this data, it becomes significant at a risk rate of 5%.

In this way, even if η _j <0, the correlation coefficient may be significant. However, the reason for not adding such feature items to the prediction from the beginning is that the possibility of improving the prediction accuracy is discarded. become.

In the present embodiment, by using η _j defined by Expression (23), while maintaining the monotonicity between the output and the correlation coefficient of the feature item (the larger the single correlation coefficient, the larger the SN ratio), Η _j (S / N ratio) that does not become negative can be defined.

FIG. 8 is a diagram for explaining the comparison between the data representing the relationship between the feature item and the output, the single correlation coefficient at that time, and η _{j in the} fourth to sixth embodiments. As shown in FIG. 8, the SN ratio, that is, η _j may be negative in the fourth embodiment, whereas η _j is always positive in the fifth embodiment. Note that η _j according to the sixth embodiment will be described later.

Further, from the relationship between the single correlation coefficient and η _j shown in FIG. 8, it is understood that the monotonicity between the output and the correlation coefficient of the feature item is secured in the fifth embodiment.

  Therefore, according to Embodiment 5, since all the feature items can be used for the estimation formula (Formula (6)), the prediction accuracy can be improved.

[Embodiment 6]
In the sixth embodiment, in the pattern recognition method according to the fourth embodiment, the evaluation formula η _j in the T method is given according to the following formula (24). Here, r _j is a single correlation coefficient between the item x _j and the output.

Ρ (= r _j ² ), which is the square of the single correlation coefficient r _j , is a scale representing the contribution ratio of two variables (item x _j and output y). Therefore, the ratio of the contribution ratio ρ and its residual 1−ρ takes a positive value without an upper limit. That is, the above ratio has the same property as η _{j in the} fifth embodiment.

As shown in FIG. 7, in the sixth embodiment, η _j is always positive. Furthermore, it can be seen from the relationship between the simple correlation coefficient and η _j that the monotonicity between the output and the correlation coefficient of the feature item is secured in the sixth embodiment.

In the sixth embodiment, by calculating η _j using Expression (24), as in the fifth embodiment, η _j that is not negative is maintained while maintaining the monotonicity between the output and the correlation coefficient of the feature item. Can be defined. Therefore, according to the sixth embodiment, as in the fifth embodiment, since all feature items can be used in the estimation formula (formula (6)), the prediction accuracy can be improved.

[Embodiment 7]
The seventh embodiment is a specific application of the pattern recognition apparatus and method. In addition, the following description shows an example which can demonstrate the effect by this invention concretely, and does not limit the scope of the present invention.

  In this embodiment, in the sensor device, the characteristic value at high temperature is predicted using the characteristic value at room temperature as the current feature item. In this case, the high-temperature characteristic value of the signal data is previously determined by measurement, and this is used as the true value of the analysis. When the pattern recognition apparatus and method according to the present embodiment are used for prediction, a high-temperature characteristic value is predicted from a normal-temperature characteristic value in a sample whose high-temperature characteristic value is unknown. Such prediction can omit the online high-temperature characteristic value measurement in the manufacturing process. Therefore, it contributes to man-hour reduction such as adjustment and inspection, and to productivity improvement.

  Here, the characteristic value is a main management item that has specifications (standard values) in the adjustment process and the inspection process and is managed in good or bad. For example, in the case of a pressure sensor, the output voltage value corresponding to the input pressure is the main characteristic value. In another example, since it is important for optical products to obtain the required light intensity distribution at the irradiation position, the main characteristics are the amount of light at each irradiation position, or the uniformity of the light intensity. Value.

  Note that the number of characteristic values at high temperatures and the number of main characteristic values at low temperatures to be predicted is not limited, and may be any number. For example, in the case of a light amount distribution which is a characteristic value in an optical system product, it is necessary to manage the characteristic value for each light irradiation position (coordinate) as shown in FIG.

  Here, it is assumed that a prediction relational expression for predicting each of the plurality of possible characteristic values is created. One of the predicted characteristic values is described here as output y.

Referring to FIG. 9, as an original feature item, the measured value at the normal temperature at each input coordinate (p ₁ , p ₂ ,..., P _l ) of the characteristic value curve, the value at the peak of the characteristic value curve, and its Input coordinates, values at the bottom of the characteristic value curve and their input coordinates, the difference between the peak and bottom values, the difference between the input coordinates at the peak of the characteristic value curve and the input coordinates at the bottom of the characteristic value curve, etc. Selected feature items. As a characteristic other than the above, for example, a method of adopting the number of intersections when a plurality of horizontal lines are drawn on a curve or the sum of distances between the intersections can be used.

  In addition, what should be adopted as the original feature item is a problem similar to each technology, and therefore is a problem to be studied and judged individually. That is, the present invention is not limited by the type of original feature item.

  Next, the selected 24 items were fixed, and a plurality of methods were compared. Specifically, 20 types of data sets having various output characteristics whose true values (characteristic values at high temperature) are known are prepared as signal space data. Since the number of data sets is smaller than the number of original items, it is not possible to use a known multiple regression analysis method, or the MT method or MTA method in the MT system. For this reason, (a) when using Taguchi's T method, (b) when using the method of Non-Patent Document 5, (c) when using the method according to each of Embodiments 1 to 3 of the present invention Compared.

In the methods (b) and (c), 24 original feature items (k = 24) to 276 (= _k C ₂ = {k · (k−1) / 2) are used using signal space data. } = 24 × 23/2) correlation feature items were created and added to the original feature items (a total of 300 feature items). In (c), the weighting factor in the fifth embodiment is used as the weighting factor.

  As a result of the comparative evaluation, in the process of calculating the weighting coefficient η, 2 out of 24 items in the method (a) and 34 out of 300 items in the method (b) are η <0, and these items are used for the analysis. I couldn't. On the other hand, in the method (c), that is, the method according to the embodiment of the present invention, there was no item satisfying η <0.

  Using items for which η> 0 (22 items in the method (a), 266 items in the method (b), 300 items in the method (c)), the predicted value of the characteristic value at high temperature in the signal space data And the correlation coefficient of true values were compared in the total of multiple input cases.

  FIG. 10 is a diagram showing a comparison result of the Taguchi T method, the method of Non-Patent Document 5, and the method according to each of Embodiments 1 to 3 of the present invention. As shown in FIG. 10, the correlation coefficient obtained by the method according to (c) was the highest. Thus, according to the embodiment of the present invention, it is shown that the true value can be predicted more accurately.

  The embodiment disclosed this time must be considered as illustrative in all points and not restrictive. The scope of the present invention is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.

  1 unit space data, 2 single regression line, 11 line, 20 concentric ellipse, 50 pattern recognition device, 51 CPU, 52 main storage device, 53 auxiliary storage device, 54 input device, 55 output device, 56 communication device, 61 data input Unit, 62 evaluation distance calculation unit, 63 weight coefficient calculation unit, 64 predicted value calculation unit, 65 determination unit, 66 output unit.

Claims (16)

A pattern recognition device for performing pattern recognition based on a plurality of data each having a plurality of original feature items,
For each of the data, an evaluation distance calculation unit that calculates an evaluation distance for all combinations of selecting two original feature items from the plurality of original feature items;
For each of the data, a plurality of new feature items are generated by adding at least some of the evaluation distances calculated corresponding to all the combinations to the plurality of original feature items, A weighting factor calculating unit that calculates a weighting factor representing a correlation between each value of the new feature item and the true value of the new feature item;
A predicted value calculation unit that calculates a predicted value of output using the weighting factor for each new feature item;
A judgment unit that compares the predicted value with a predetermined threshold value and makes a judgment on a purpose;
The evaluation distance calculation unit is a pattern recognition device that calculates a Mahalanobis distance as the evaluation distance. A pattern recognition device for performing pattern recognition based on a plurality of data each having a plurality of original feature items,
For each of the data, an evaluation distance calculation unit that calculates an evaluation distance for all combinations of selecting two original feature items from the plurality of original feature items;
For each of the data, a plurality of new feature items are generated by adding at least a part of the evaluation distance calculated corresponding to all the combinations to the plurality of original feature items, and A weighting factor calculating unit that calculates a weighting factor representing a correlation between each value of the new feature item and the true value of the new feature item;
A predicted value calculation unit that calculates a predicted value of output using the weighting factor for each new feature item;
A judgment unit that compares the predicted value with a predetermined threshold value and makes a judgment on a purpose;
The said evaluation distance calculation part is a pattern recognition apparatus which calculates the evaluation distance used by MTA (Maharanobis Taguchi Adjoint) method as said evaluation distance. A pattern recognition device for performing pattern recognition based on a plurality of data each having a plurality of original feature items,
For each of the data, an evaluation distance calculation unit that calculates an evaluation distance for all combinations of selecting two original feature items from the plurality of original feature items;
For each of the data, a plurality of new feature items are generated by adding at least a part of the evaluation distance calculated corresponding to all the combinations to the plurality of original feature items, and A weighting factor calculating unit that calculates a weighting factor representing a correlation between each value of the new feature item and the true value of the new feature item;
A predicted value calculation unit that calculates a predicted value of output using the weighting factor for each new feature item;
A judgment unit that compares the predicted value with a predetermined threshold value and makes a judgment on a purpose;
The said evaluation distance calculation part is a pattern recognition apparatus which calculates the product of the normalized value of a 1st feature item, and the normalized value of a 2nd feature item as said evaluation distance.   4. The pattern recognition apparatus according to claim 1, wherein the plurality of data includes both unit space data and signal space data. 5.   The pattern recognition apparatus according to claim 1, wherein the plurality of data includes only unit space data.   The pattern recognition apparatus according to claim 1, wherein the weighting factor calculation unit calculates an SN ratio in a T method (Taguchi method) as the weighting factor. Wherein the SN ratio as eta, the average of the variation and S _beta, when the residual and S _e, the SN ratio is defined by η = S β _/ S _e, the pattern recognition apparatus according to claim 6. When the SN ratio is η and the single correlation coefficient between the value of the new feature item and the true value of the new feature item is r, the SN ratio is η = r ² / (1−r ^2). The pattern recognition device according to claim 6, defined by: A pattern recognition method for performing pattern recognition based on a plurality of data each having a plurality of original feature items,
Calculating an evaluation distance for all combinations of selecting two original feature items from the plurality of original feature items for each of the data;
Generating a plurality of new feature items by adding at least a part of the evaluation distance calculated corresponding to all the combinations to the plurality of original feature items for each of the data;
Calculating a weighting coefficient representing the correlation between the value of each of the plurality of new feature items and the true value of the new feature item;
Using the weighting factor for each new feature item to calculate a predicted output value;
Comparing the predicted value with a predetermined threshold value and making a determination on the purpose,
The pattern recognition method of calculating a Mahalanobis distance as the evaluation distance in the step of calculating the evaluation distance. A pattern recognition method for performing pattern recognition based on a plurality of data each having a plurality of original feature items,
Calculating an evaluation distance for all combinations of selecting two original feature items from the plurality of original feature items for each of the data;
Generating a plurality of new feature items by adding at least a part of the evaluation distance calculated corresponding to all the combinations to the plurality of original feature items for each of the data;
Calculating a weighting coefficient representing the correlation between the value of each of the plurality of new feature items and the true value of the new feature item;
Using the weighting factor for each new feature item to calculate a predicted output value;
Comparing the predicted value with a predetermined threshold value and making a determination on the purpose,
A pattern recognition method, wherein, in the step of calculating the evaluation distance, an evaluation distance used by an MTA (Mahalanobis Taguchi Adjoint) method is calculated as the evaluation distance. A pattern recognition method for performing pattern recognition based on a plurality of data each having a plurality of original feature items,
Calculating an evaluation distance for all combinations of selecting two original feature items from the plurality of original feature items for each of the data;
Generating a plurality of new feature items by adding at least a part of the evaluation distance calculated corresponding to all the combinations to the plurality of original feature items for each of the data;
Calculating a weighting coefficient representing the correlation between the value of each of the plurality of new feature items and the true value of the new feature item;
Using the weighting factor for each new feature item to calculate a predicted output value;
Comparing the predicted value with a predetermined threshold value and making a determination on the purpose,
The pattern recognition method, wherein, in the step of calculating the evaluation distance, a product of a normalized value of the first feature item and a normalized value of the second feature item is calculated as the evaluation distance.   The pattern recognition method according to claim 9, wherein the plurality of data includes both unit space data and signal space data.   The pattern recognition method according to claim 9, wherein the plurality of data includes only unit space data.   The pattern recognition method according to claim 9, wherein, in the step of calculating the weighting factor, an SN ratio in a T method (Taguchi method) is calculated as the weighting factor. Wherein the SN ratio and eta, the variation of the average and S _beta, when the residual and S _e, the SN ratio is defined by η = S β _/ S _e, the pattern recognition method according to claim 14. When the SN ratio is η and the single correlation coefficient between the value of the new feature item and the true value of the new feature item is r, the SN ratio is η = r ² / (1−r ^2). The pattern recognition method according to claim 14, defined by:

Images