JPH05143636A - Method and device for discrimination and analysis - Google Patents

Abstract

PURPOSE:To surely separate populations with a linear discrimination function regardless of the nonlinear and complicated boundary form of populations. CONSTITUTION:This method consists or a discrimination function setting device 12 which receives output data of a state setting device 11 and sets a linear discrimination function for separation to plural populations, a separation end discriminating device 13 which discriminates whether sample data is completely separated by the discrimination function obtained by the discrimination function setting device 12 or not, a first discrimination area narrowing-down device 14 which sets a vertical function, which is perpendicular to the obtained discrimination function and equally divides the number of data into two, in the case of a failure of separation and separates sample data of parts divided by this vertical function and inputs these data to the discrimination function setting device, and a discriminating device 15 which receives all discrimination functions obtained by the discrimination function setting device and uses the discrimination function for inputted recollected data W and determines the population to which this data W belongs.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a discriminant analysis method and apparatus for separating a plurality of populations, and more particularly, to improve a method for creating a discriminant function serving as a reference for discriminant analysis, and to perform the method. Of equipment.

[0002]

2. Description of the Related Art Discriminant analysis discriminates to which of a given k population a data having p kinds of variables belongs. First, a boundary which is most easily discriminable from multidimensional sample data in advance, That is, a boundary that minimizes the sum of the probabilities of causing misjudgment is extracted as a discriminant function, and then it is determined by determining to which side of the discriminant function the newly given unknown recall data is located. It is designed to identify the population.

[0003]

However, with the linear discriminant function used in the above-described conventional discriminant analysis, when the boundary shape of the population becomes complicated, the population cannot be separated exactly. Therefore, the reliability in determining which population the recall data belongs to decreases. Further, in recent years, the need for non-linear separation represented by neural networks and fuzzy has increased, and by using such neural networks, it is possible to separate the population having the complicated boundary shape described above. However, when a neural network is used, the more complex the boundary shape and the larger the number of input sample data, the more time it takes for learning, and it is difficult to analyze the obtained calculation results.

The present invention has been made in view of the above background, and an object of the present invention is to make a linear discrimination even if the boundary shape of the population to be separated is non-linear and complicated. It is an object of the present invention to provide a discriminant analysis method and device that can be reliably separated by a function and can process learning time and the like required for the separation in a short time.

[0005]

In order to achieve the above object, in the discriminant analysis method according to the present invention, discriminant analysis is performed on a plurality of populations formed from sample data to obtain a discriminant function, When the population cannot be separated by such a discriminant function, a predetermined vertical function perpendicular to the discriminant function is drawn, and the discriminant function is obtained for each sample data located in the region separated by the vertical function.

Further, when a discriminant function is obtained by performing discriminant analysis on a plurality of populations formed from sample data, and when the populations cannot be separated by such discriminant function, the discriminant function is sandwiched by the non-separable portions. Set two functions parallel to, and for the area surrounded by both functions,
The frequency distribution is taken in the direction parallel to the discriminant function, and it is judged whether the data can be separated from the distribution state. If it can be separated, the partition value for dividing the distribution is obtained. You may make it perform a discriminant function with respect to the sample data located in. Furthermore, the above 2
The two methods may be combined appropriately and executed.

Further, as a discriminant analysis apparatus suitable for implementing the above method, a linear discriminant function that stochastically minimizes misjudgment so as to separate into a plurality of populations based on input sample data is used. When the discriminant function setting device to be set, the separation end determination device that determines whether or not the sample data is completely separated by the discriminant function obtained by the discriminant function setting device, and the sample data is not completely separated In addition, a vertical function perpendicular to the obtained discriminant function is subtracted, and the sample data of the portion divided by the vertical function is separated and input into the discriminant function setting device. That is.

Further, in place of the first discriminant region diaphragm device, a portion which cannot be separated is sandwiched by two functions which are parallel to the discriminant function obtained, and the sandwiched portion is subjected to frequency distribution in a direction parallel to the discriminant function. When the data can be separated from the distribution state, the partition value is set, and when the data cannot be separated, the second discriminant region diaphragm for inputting the sample data belonging to the region sandwiched between the two functions to the discriminant function setting device. A device may be provided.

[0009]

A linear discriminant function is set for given sample data, and it is determined whether the population can be separated by the discriminant function. Then, when it is not possible to separate, a vertical vertical function obtained based on the obtained discriminant function,
Alternatively, a new region is formed by a function parallel to the discriminant function, and the discriminant function is obtained for the sample data of the new region. Then, the processes are repeated until the populations are completely separated. As a result, even if the boundary shape of the population is non-linear, they are separated by a linear discriminant function.

If necessary, in addition to the above discriminant function,
By taking the frequency distribution in the direction parallel to the predetermined discriminant function and using the obtained partition value, the population can be separated with a small discriminant function.

[0011]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the discriminant analysis method and apparatus according to the present invention will be described in detail below with reference to the accompanying drawings. FIG. 1 shows a first embodiment of the discriminant analysis apparatus according to the present invention.
As shown in the figure, the state setting device 11 that outputs sample data Xij for multivariate analysis for discriminating the population.
And a discriminant function setting device 1 that receives output data of the state setting device 11 and sets a linear discriminant function that stochastically minimizes misjudgment so as to be separated into a plurality of populations.
2, a separation end determination device 13 that determines whether or not the sample data is completely separated by the discriminant function obtained by the discriminant function setting device 12, and a determination result when the sample data is not completely separated. A dividing line (vertical function) perpendicular to the determined discriminant function is drawn at a position that divides the number of data into two parts, and the sample data of the portion divided by the vertical function is separated and input to the discriminant function setting device 12. First discriminant region diaphragm device 14 and discriminant function setting device 1
The discriminator 15 receives all the discriminant functions obtained in 2 and uses the discriminant function for the input recall data W to determine the population to which the recall data W belongs. Here, the sample data Xij (i is the number of variables (i = 1 to n) set by the state setting device 11 is
The specific data structure of the number of samples (j means the number of samples (j = 1 to N)) is: X1 = [X11, X21, ..., Xn1] X2 = [X12, X22, ..., Xn2] :: Xj = [X1j, X2j, ..., Xnj] :: XN = [X1N, X2N, ..., XnN].

The data structure of the discriminant function Zk (X) formed by the discriminant function setting device 11 is Zk (X) = ak1 * X1 + ak2 * X2 + ... + akn * Xn + bk. Here, aki and bk are constant terms.
In addition, k is a discontinuous natural number and indicates the number of the determined population. The data structure of the dividing line ZT1 (X) perpendicular to the discriminant function formed by the first discriminant device 14 is ZTk (X) = atk1 * X1 + atk2 * X2 + ... atkn * Xn + btk. There is. Here, atki and btk are constant terms.

Furthermore, the population A separated by the discriminant function
Serial numbers are added to k and Bk, respectively, and these numbers are assigned in the order of generation. That is, the population formed from Ak in the sth division is A2s and A (2s +
1), and similarly, Bk becomes B2s and B (2s + 1). Note that s is a continuous natural number starting from 1. The number added to the two divided populations is 2s for the population closer to the origin.

Next, a first embodiment of the discriminant analysis method according to the present invention will be described with reference to the flow chart shown in FIG. First, a procedure for setting a discriminant function for separating a predetermined population will be described. The state setting device 11 inputs all sample data Xij for multivariate analysis to the discriminant function setting device 12 (S101), The discriminant function setting device 12 obtains a linear discriminant function Zk (X) that most efficiently divides the two populations Ak and Bk from the given sample data Xij (S102). Then, the discriminant function Zk (X) is input to the separation end determination device 13, and all the sample data Xij is input to the obtained discriminant function Zk (X), and completely separated into both populations A and B. Then, it is judged whether or not the judgment is possible (S103). If it is possible to determine, all the determination functions Zk (X) are determined by the determination device 15
Is input to end the processing (S104).

On the other hand, when the discrimination cannot be made, the discriminant function and the sample data are sent to the first discriminant region diaphragm device 14 and are perpendicular to the discriminant function Zk (X), and both populations Ak and Bk are constructed. A vertical function ZTk (X) that divides the number of sample data to be halved is obtained. Then, both populations are divided by the obtained dividing line ZTk (X) (S105). It should be noted that, as described above, serial numbers are given to the respective areas divided by this division. That is, for example, two populations obtained by dividing the population A1 by the first division are 2 × 1 = 2, 2 × 1 + 1 = 3.
Therefore, they become A2 and A3, respectively. As a result, four populations A2s, A (2s + 1), B2s, B (2s + 1) are generated.

Further, in order to discriminate later recall data, it is necessary to clarify the association of each population.
Therefore, the table of Tai and Tbi as shown below is created.

Tai: [(Ai, AL, AL + 1), (F), (dui, doi)] Tbi: [(Bi, BL, BL + 1), (F), (dui, doi)] where i, L = 1, 2, 3, ... Here, the meaning of each table is that from the first term to the third term, the Tree relationship of the population, that is, Ai (Bi) is defined by the vertical function orthogonal to the discriminant function. AL, AL + 1 (BL, B
L + 1). When there is no branch destination, that is, when the paired populations Ak and Bk are separated, the first to third terms are set to (0,0,0). The fourth item F is the population Ak
And Bk are flags indicating whether or not they have been separated, and are "1" or "-1" when they are separated, and "0" when they are not separated. As a specific calculation method, all the data of the population Ai are substituted into the discriminant function Zi, and if all Zi (X)> 0, then F = 1. If all Zi (X) <0, then set F = -1. Otherwise (Ai data exists on both sides of the discriminant function), F = 0. It should be noted that the fifth and sixth terms are provided for the purpose of sharing with Tree used in the methods and apparatuses in the second and third embodiments described later, and in this example, all (0, 0) Becomes Therefore, if only this embodiment is used, the items up to item 4 may be used.

Then, the above-mentioned first discrimination area diaphragm device 1
The sample data included in the population divided by the vertical function ZTk (X) generated in 4 is sent to the discriminant function setting device 12 in a state of being separated separately (S106).
That is, A2s and B2s are paired, and A (2s + 1) and B2
Send (2s + 1) as a pair. Then, the process returns to step 102 and the above process is repeated. The discriminant analysis performed in step 102 is performed from the smaller serial number assigned to the population.

Here, a concrete example of the above-mentioned learning method is shown in FIG.
Will be explained. First, it is assumed that two populations A1 and B1 are constituted by given sample data as shown in FIG. Then, the discriminant function setting device 12 subtracts the discriminant function Z1 from the sample data.
Then, since the discriminant function Z1 cannot separate the two populations A1 and B1 from each other, a predetermined vertical function ZT1 orthogonal to the discriminant function Z1 is drawn, and the two populations A1 and B1 are respectively separated by A2 and A3, B2, B
Divide into 3 (Fig. (B)). Then, the sample data belonging to the divided populations A2 and B2 and the sample data belonging to A3 and B3 are input to the discriminant function setting device 12 in a state where they are separately separated. Then, in the discriminant function setting device 12, a discriminant analysis is performed on the sample data of the population having a small serial number, that is, sample data of A2 and B2, and the discriminant function Z2 is drawn ((C) in the same figure). Then, the separation end determination device 13 determines that the two populations A2 and B2 have been separated by the discriminant function Z2.
The discrimination process for A2 and B2 is completed for this population.

Then, a discriminant analysis is performed on the sample data of a large population, that is, sample data of A3 and B3, and a discriminant function Z3 is drawn. However, since the discriminant function Z3 cannot separate the two populations A3 and B3, a predetermined vertical function ZT3 orthogonal to the discriminant function Z3 is drawn, and the two vertical populations Z3 and A3 are used to divide the two populations A3 and B3, respectively. , A5, B4, B5 (FIG. 7 (D)).

Then, similarly to the above, the discriminant analysis is performed on the sample data of A4 and B4, and the discriminant function Z4 is drawn ((E) in the same figure). In addition, the discriminant analysis is performed on the sample data of A5 and B5, and the discriminant function Z5 is drawn ((F) of the same figure). As a result, the two populations Ak and Bk are completely separated, and all the above discriminant functions Z1, Z2, Z3, Z
Discriminating device 1 for table data of 4, Z5 and Tree
5, and the process is terminated. The table data and the Tree structure in the above-described specific example are as shown in FIGS. 4 and 5, respectively. The description of the population B side is omitted because it is similar to that of the population A.

Next, a method of discriminating which population the unknown recall data belongs to based on the discriminant function formed by the above method will be described with reference to the flowchart of FIG.

That is, the recall mode is activated and the recall data W is input to the discriminator 15 (S110). Then, the discrimination device 15 discriminates which population the given recall data W belongs to (S111). Specifically, the recall data W is substituted into the vertical function ZT1 which is perpendicular to the first discriminant function Z1, and whether the value is positive or negative (A2, B2) or (A3, B3). To determine if they belong to the population. Here, since the serial number of the population near the origin is made smaller, if ZT1 (W) is negative, the recall data W belongs to (A2, B2), and if it is positive, it belongs to (A3, B3). ..

If it is found that the recall data W belongs to Ak or Bk, the table of Tak and Tbk is referred to, and it is checked whether each population is divided. If divided, the table is divided. The four populations described above are examined and substituted into the vertical function ZTk of the discriminant function in the same manner as above, and it is determined which side of the population the positive or negative of the obtained value belongs to. That is, if ZTk (W) is negative, recall data W
Belongs to (A2s, B2s), and if positive, it belongs to (A2s + 1, B2s + 1).

When the populations Ae and Be containing the recall data are finally specified by repeating the above operation, it is finally determined which of the populations Te belongs to.
Judgment is made based on F included in the ae and Tbe tables. Then, the analysis result is output (S113), and the recall process ends.

In the apparatus and method according to the first embodiment described above, when narrowing down the discriminant region, the vertical function perpendicular to the discriminant function is drawn at a position that divides the target sample data number into two equal parts. However, the present invention is not limited to this, and for example, the sum of distances from the vertical function to each sample data is equal on both sides, the sum of squares of the distances is equal, or the area of the population is equal. It is possible to take various methods such as drawing a vertical function at a position where B is divided into two.

FIG. 6 shows a second embodiment of the discriminant analysis apparatus according to the present invention. As shown in the figure, the basic structure is the same as that of the first embodiment, and therefore the description thereof is omitted by giving the same reference numeral. Here, in this example, unlike the above-described embodiment, the first determination area diaphragm device 14 is replaced by a second
A discrimination area diaphragm device 14a is provided. When the sample data cannot be completely separated by the discriminant function Zk (X), the second discriminant area diaphragm device 14a sandwiches a portion which cannot be separated by two functions parallel to the obtained discriminant function Zk (X). , The sandwiched portion is the discriminant function Zk (X)
Takes a frequency distribution in the direction parallel to, and when the data can be separated from the distribution state (when there is no overlapping part in the frequency distribution), it is used for separation (determination). Data belonging to a region sandwiched between two functions parallel to is input to the discriminant function setting device 12. Further, the present device 14a also has a function of setting the partition value S indicating the boundary of the distribution at that time to the discriminating device 15 when the frequency distribution can be separated.

In addition, 2 which is parallel to the discriminant function Zk (X)
The distances between the two functions and the discriminant function Zk (X), that is, the margin amounts are dui and doi. However, the function-side margin amount near the origin is dui. Further, one of the functions separates the population Ai into AL and AL + 1, and the other function separates the population Bi into BL and BL + 1. The serial numbers assigned to the separated populations are larger within the margin, that is, within the area surrounded by the two functions. Further, the table of Trees among the respective populations is: Tai: (Ai, AL, AL + 1), (F), (dui, doi) Tbi: (Bi, BL, BL +) as in the first embodiment. 1), (F), (dui, doi) However, in the fourth item F, in addition to "-1, 0, 1" used in the first embodiment, there is "2" when it has a partition value. The margin amounts are input to the fifth and sixth terms, but they can be separated by a discriminant function, that is, if there is no branch destination population, both the fifth and sixth terms are 0. Become.

Next, a second embodiment of the discriminant analysis method according to the present invention will be described with reference to the flow chart shown in FIG. First, a procedure of setting a discriminant function for separating a predetermined population will be described. The state setting device 10 inputs all sample data Xij for multivariate analysis to the discriminant function setting device 12 (S201). The discriminant function setting device 12 obtains a linear discriminant function Zk (X) that most efficiently divides the two populations Ak and Bk from the given sample data Xij (S202). Then, the discriminant function Zk (X) is input to the separation end determination device 13, and all the sample data Xij is input to the obtained discriminant function Zk (X), and completely separated into both populations A and B. Then, it is judged whether or not the judgment is possible (S203). If it is possible to determine, all the determination functions Zk (X) are determined by the determination device 15
Is input to end the processing (S204).

On the other hand, when the discrimination cannot be made, the discriminant function and the sample data are set to the second discriminant area diaphragm device 14a.
Then, a predetermined margin is taken in parallel from the discriminant function Zk (X), and two parallel functions are drawn so as to include a region that cannot be discriminated (S205). Then, the region surrounded by the two parallel functions is subjected to frequency distribution in the direction parallel to the discriminant function Zk (X), and it is determined whether or not each population can be separated (S206). Then, if it is possible to separate, a partition value S (value on a parallel function) that separates adjacent populations is obtained (S207), the partition value S is set in the discrimination device 15 (S204), and the process is ended. ..

If the data cannot be separated, the data in the area surrounded by the two parallel functions is set in the discriminant function setting device 12 (S208), the process returns to step 202, and the data is extracted. After setting the discriminant function, the above process is repeated until the population can be separated.

Here, a concrete example of the above-mentioned learning method is shown in FIG.
Will be explained. First, it is assumed that two populations A1 and B1 are constituted by given sample data as shown in FIG. Then, the discriminant function setting device 12 subtracts the discriminant function Z1 from the sample data.
Then, the discriminant function Z1 cannot separate the two populations A1 and B1. Therefore, two functions parallel to the discriminant function Z1 and separated by predetermined margins do1 and du1 are drawn. Then, in both functions, both populations A1 and B1 are A2 and
It is divided into A3, B2, and B3 (FIG. 7B). As a result, the discriminant function Z1 separates the populations A2 and B2.

On the other hand, the population A3 which cannot be separated and which exists in the area surrounded by both functions (shown by hatching in the figure)
, B3 has a frequency distribution in the direction parallel to the discriminant function Z1 ((C) in the figure). In this example, since the populations A3 and B3 are partially overlapped, the populations cannot be separated. Therefore, the sample data belonging to the populations A3 and B3 are taken out, the discriminant function Z3 is subtracted therefrom, and two functions parallel to the discriminant function Z3 and separated by predetermined margins do3 and du3 are drawn in the same manner as described above ( The same figure (D)). Then, both populations A3 and B3 are divided into A4, A5, B4, and B5 by both functions ((E) in the same figure). Therefore, this discriminant function Z3 is 2
Two populations A4 and B4 are separated. Then, the discriminant function Z is applied to the populations A5 and B5 existing in the area (indicated by hatching in the figure) surrounded by both functions that cannot be separated.
The frequency distribution is taken in the direction parallel to 3 (Fig. (F)). Then, as is clear from the figure, the distributions of the two populations A5 and B5 have no overlapping portions, and the two populations A5 and B5 have no overlap.
Are separated by partition values S1 and S2. That is, the discriminant function Z1 separates the populations A2 and B2, the discriminant function Z3 separates the populations A4 and B4, and the partition values S1 and S2 associated with the frequency distribution form the populations A5 and B5. It is separated and the separation work is completed.

Then, all of the above discriminant functions Z1 and Z3
, All the partition values S1, S2 and the table data of Tree are supplied to the discriminator 15, and the process is terminated.
The table data and T in the above-mentioned specific example
The ree structure is as shown in FIGS. 9 and 10, respectively. The description of the population B side is omitted because it is similar to that of the population A.

Next, a method for determining which population the unknown recall data belongs to based on the discriminant function formed by the above method will be described with reference to the flowchart of FIG.

That is, the recall mode is activated and the recall data W is input to the discriminator 15 (S210). Then, the discrimination device 15 discriminates which population the given recall data W belongs to (S211). Specifically, first look at the flag F in the table of Ta1 and Tb1, and if the value is 1 or -1, it means that the population is separated by one discriminant function Z1. Data W
Is assigned to the first discriminant function Z1 (W), it is determined whether the population is A1 or B1 depending on whether the value is positive or negative, and the recall process ends. Where Z1
If (W) is positive, it belongs to the population of F = 1, and if it is negative, the recall data W belongs to the population of F = -1.

On the other hand, when Ta1 and Tb2 are not 1 or -1 (this case is common), the recall data W is substituted into the first discriminant function Z1 (W), and the obtained value and margin du1 , Do1 and (A2, B2) or (A3, B3) to determine which pair of populations they belong to. Here, the serial numbers assigned to the population are parallel 2
Since the area surrounded by the two functions is enlarged, if Z1 (X) <du1 or do1 <Z1 (X), the recall data W can be located outside the area, that is, by this discriminant function Z1. Since it means that it is located at A2 or B2, the value obtained as above and T
From the flag F of the ai and Tbi table, A2 and B2
It is determined which of the two populations belong to, and the recall process is terminated. If Z1 (X)> du1 and do1> Z1 (X), the recall data W is located in the area, that is,
It can be seen that it is located at A3 or B3.

Then, the recall data W is A3 or B3.
(Hereinafter, as general data, the numerical value to be given will be described as k (Ak or Bk))
The flag F is set to 2 by referring to the table of Tak and Tbk.
If it is 2, it is possible to separate by the partition value. Therefore, the recall data W is projected in the parallel direction of the discriminant function, and it is determined which population is included from the partition value Sm. , The recall process ends.

On the other hand, when it is not possible to separate from the partition value, the recall data is substituted into the next discriminant function Zk (W), and the obtained values and the four populations branched from the margins dul, dol and Bk. (A2s, B2s) or (A2s +
1, B2s + 1) to determine where it belongs. The specific determination method is as described above. In this way, the population Ae including the recall data W in the discriminant function or the partition value
Alternatively, Be is required. Then, the obtained analysis result is output, and the recall process ends (S212).

FIG. 11 shows a third embodiment of the discriminant analysis apparatus of the present invention. As shown in the figure, the basic configuration is the same as that of the first embodiment described above (denoted by the same reference numeral), and its features are the separation end determination device 13 in the first embodiment and the first determination. A third discrimination area limiting device 16 is inserted and arranged between the area limiting device 14 and the area determining device 14. The third discrimination area diaphragm device 16 has a function similar to that of the second discrimination area diaphragm device 14a in the second embodiment. That is, a part that cannot be separated is sandwiched by two functions that are parallel to the obtained discriminant function, a frequency distribution is taken in the direction parallel to the discriminant function for the sandwiched part, and when the data can be separated from the distribution state, the partition is created. In terms of obtaining a value and setting it in the discriminator 15, the second discriminant area diaphragm device 14
The same as a. However, this third discrimination area diaphragm device 16
In the case of data that cannot be separated, the input discriminant function is output as it is, and it is supplied to the first discriminant area diaphragm device 14.

The discriminant analysis method performed by using such an apparatus is a combination of the methods of the first and second embodiments described above. The first embodiment is executed and the second step is executed in the final step. A discrimination method using an example frequency distribution is incorporated. As a result, the number of discriminant functions used can be reduced, and the system can be simplified.

A specific method will be described below.
A discriminant function is obtained from the given sample data as in each of the above-described embodiments, and the separation end determination device 13 determines whether or not the separation is completed by the discriminant function. And
If the separation has not been completed, a discriminant function is input to the third discriminant region diaphragm device 16, a function parallel to the discriminant function is drawn therein, and a frequency distribution is obtained. Is determined, and if possible, the partition value S is determined and set in the determination device 15.

On the other hand, if the frequency distribution cannot be separated, the discriminant function is substituted into the first discriminant region diaphragm device 14 as in the first embodiment, and a predetermined vertical function perpendicular to the discriminant function is drawn. , The area (sample data) is divided into two parts by the vertical function, and the divided area is supplied to the discriminant function setting device 12, and the discriminant function is performed for each. After that, by repeating the above-mentioned operation, all the required discriminant functions and partition values as necessary are set in the discriminator 15, and the recall process is terminated.

[0044]

As described above, in the discriminant analysis method and apparatus according to the present invention, even if the boundary shapes of the populations to be separated are non-linear, they can be separated by a linear discriminant function. Therefore, compared to neural networks,
The learning time is short and the analysis of the calculation result is easy. Then, when unknown recall data is input, the population can be easily specified based on the obtained discriminant function and, if necessary, the partition value.

[Brief description of drawings]

FIG. 1 is a block configuration diagram showing a first embodiment of a discriminant analysis apparatus according to the present invention.

FIG. 2 is a flowchart showing a first embodiment of the discriminant analysis method according to the present invention.

FIG. 3 is a diagram showing an example of processing steps of the present invention.

4 is a diagram showing a configuration of a table for a population A. FIG.

5 is a diagram showing a Tree structure for a population A. FIG.

FIG. 6 is a block configuration diagram showing a second embodiment of the discriminant analysis apparatus according to the present invention.

FIG. 7 is a flowchart showing a second embodiment of the discriminant analysis method according to the present invention.

FIG. 8 is a diagram showing an example of processing steps of the present invention.

9 is a diagram showing a configuration of a table for a population A. FIG.

10 is a diagram showing a Tree structure for a population A. FIG.

FIG. 11 is a block diagram showing a third embodiment of the discriminant analysis apparatus according to the present invention.

[Explanation of symbols]

 11 State Setting Device 12 Discriminant Function Setting Device 13 Separation End Determination Device 14 First Discrimination Area Diaphragm Device 14a Second Discrimination Area Diaphragm Device 15 Discrimination Device 16 Third Discrimination Area Diaphragm Device

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Yasuhiro Tsutsumi 10 Hanazono Dodo-cho, Ukyo-ku, Kyoto City, Kyoto Prefecture Omron Co., Ltd. Within the corporation

Claims (8)

[Claims] 1. A discriminant function is obtained by performing discriminant analysis on a plurality of populations formed from sample data, and when the discriminant function cannot separate the populations, a predetermined vertical function perpendicular to the discriminant function. And a discriminant analysis method is obtained for each sample data located in a region separated by the vertical function. 2. A discriminant function setting device that sets a linear discriminant function that stochastically minimizes misjudgment so as to separate into a plurality of populations based on input sample data.
A separation end determining device that determines whether or not the sample data is completely separated by the discriminant function obtained by the discriminant function setting device, and a discriminant function that is obtained when the sample data is not completely separated. A discriminant analysis device, comprising: a first discriminant region diaphragm device that draws a vertical vertical function and separates sample data of portions divided by the vertical function into the discriminant function setting device. 3. A discriminant function is obtained by performing discriminant analysis on a plurality of populations formed from sample data, and when the populations cannot be separated by the discriminant function, the discriminant function is sandwiched by the non-separable portions. And two functions parallel to each other are set, a frequency distribution is taken in a direction parallel to the discriminant function with respect to a region surrounded by both functions, and it is determined whether or not the data can be separated from the distribution state, and the data can be separated. In this case, a partition value for dividing the distribution is obtained, and when the partition values cannot be separated, a discriminant analysis method is performed on the sample data located in the area. 4. A discriminant function setting device that sets a linear discriminant function that stochastically minimizes misjudgment so as to separate into a plurality of populations based on input sample data.
A discriminant termination determination device that determines whether or not the sample data is completely separated by the discriminant function obtained by the discriminant function setting device, and a part that cannot be separated by two functions that are parallel to the determined discriminant function are sandwiched, A frequency distribution is taken in the sandwiched part in a direction parallel to the discriminant function, and when the data can be separated from the distribution state, the partition value is set, and when the data cannot be separated, the region sandwiched between the two functions is set. A discriminant analysis device, comprising: a second discriminant region diaphragm device for inputting belonging sample data to the discriminant function setting device. 5. When a population function cannot be separated by the obtained discriminant function at a predetermined timing during the execution of the discriminant analysis method according to claim 1, the non-separable portion is sandwiched so as to be parallel to the discriminant function. Two functions are set, a frequency distribution is taken in a direction parallel to the discriminant function for the area surrounded by both functions, and it is judged whether or not the data can be separated from the distribution state. A discriminant analysis method, wherein a value is obtained, and when the values cannot be separated, the method according to claim 1 is continued. 6. A discriminant function setting device that sets a linear discriminant function that stochastically minimizes erroneous discrimination so as to separate into a plurality of populations based on input sample data.
A discriminant termination determination device that determines whether or not the sample data is completely separated by the discriminant function obtained by the discriminant function setting device, and a part that cannot be separated by two functions that are parallel to the determined discriminant function are sandwiched, A third discriminant region diaphragm device that takes a frequency distribution in the sandwiched portion in a direction parallel to the discriminant function and sets the partition value when data can be separated from the distribution state, and the third discriminant region diaphragm device. When the partition value cannot be obtained, a vertical function perpendicular to the discriminant function is drawn, and sample data of portions divided by the vertical function are separated and input to the discriminant function setting device. And a discriminant analysis device. 7. When unknown recall data is input,
A discriminant analysis method comprising discriminating which one of the plurality of populations belongs using a discriminant function set by the method of claim 1. 8. When unknown recall data is input,
A discriminant analysis method, comprising discriminating which one of the plurality of populations belongs using the discriminant function and the partition value set by the method according to claim 3 or 5.