Patent Publication Number: US-2023162489-A1

Title: Method of extracting unsuiitable and defective data from plurality of pieces of training data used for learning of machine learning model, information processing device, and non-transitory computer-readable storage medium storing computer program

Description:
The present application is based on, and claims priority from JP Application Serial Number 2021-189881, filed Nov. 24, 2021, the disclosure of which is hereby incorporated by reference herein in its entirety. 
     BACKGROUND 
     1. Technical Field 
     The present disclosure relates to a method of extracting unsuitable and defective data from a plurality of pieces of training data used for learning of a machine learning model, an information processing device, and a non-transitory computer-readable storage medium storing a computer program. 
     2. Related Art 
     US 5,210,798 and WO 2019/083553 each disclose a so-called capsule network as a machine learning model of a vector neural network type using a vector neuron. The vector neuron indicates a neuron where an input and an output are in a vector expression. The capsule network is a machine learning model where the vector neuron called a capsule is a node of a network. The vector neural network-type machine learning model such as a capsule network is applicable to input data classification processing. 
     In general, training data used for learning of the machine learning model may contain unsuitable and defective data such as outlier data and overlap data. The outlier data is data significantly different from characteristics of a normal training data set in general. The overlap data is data having features significantly similar to those of normal training data in a different class. It has been known that, when defective data is present in training data, learning or verification of the machine learning model do not properly proceed. In view of this, there has been demanded a technique of extracting defective data contained in a plurality of pieces of leaning data. 
     SUMMARY 
     According to a first aspect of the present disclosure, there is provided a method for extracting unsuitable and defective data from a plurality of pieces of training data used for learning of a machine learning model for classifying input data into a plurality of classes. The machine learning model is configured as a vector neural network having a plurality of vector neuron layers. The method includes (a) inputting each of the plurality of pieces of training data into the machine learning model that is previously leaned, obtaining a feature spectrum from an output of a specific layer of the machine learning model, and classifying, into classes, the feature spectra corresponding respectively to the plurality of pieces of training data, and (b) selecting target training data from the plurality of pieces of training data, and determining whether the target training data is the defective data. (b) includes (b1) selecting a reference class from the plurality of classes, (b2) calculating a plurality of degrees of similarity between the feature spectrum corresponding to the target training data and a plurality of the feature spectra belonging to the reference class, (b3) applying, to the plurality of degrees of similarity, a defectiveness function that is determined in advance, and calculating a defectiveness index with respect to the target training data, and (b4) determining whether the target training data is the defective data, based on a result of comparison between the defectiveness index and a threshold value. 
     According to a second aspect of the present disclosure, there is provided an information processing device configured to execute processing for extracting unsuitable and defective data from a plurality of pieces of training data used for learning of a machine learning model for classifying input data into a plurality of classes. The information processing device includes a memory configured to store a machine learning model configured as a vector neural network having a plurality of vector neuron layers, and a processor configured to execute an arithmetic operation using the machine learning model. The processor executes processing of (a) inputting each of the plurality of pieces of training data into the machine learning model that is previously leaned, obtaining a feature spectrum from an output of a specific layer of the machine learning model, and classifying, into classes, the feature spectra corresponding respectively to the plurality of pieces of training data, and (b) selecting target training data from the plurality of pieces of training data, and determining whether the target training data is the defective data. (b) includes (b1) selecting a reference class from the plurality of classes, (b2) calculating a plurality of degrees of similarity between the feature spectrum corresponding to the target training data and a plurality of the feature spectra belonging to the reference class, (b3) applying, to the plurality of degrees of similarity, a defectiveness function that is determined in advance, and calculating a defectiveness index with respect to the target training data, and (b4) determining whether the target training data is the defective data, based on a result of comparison between the defectiveness index and a threshold value. 
     According to a third aspect of the present disclosure, there is provided a non-transitory computer-readable storage medium storing a computer program for causing a processor to execute processing of extracting unsuitable and defective data from a plurality of pieces of training data used for learning of a machine learning model for classifying input data into a plurality of classes. The computer program causes the processor to execute processing of (a) inputting each of the plurality of pieces of training data into the machine learning model that is previously leaned, obtaining a feature spectrum from an output of a specific layer of the machine learning model, and classifying, into classes, the feature spectra corresponding respectively to the plurality of pieces of training data, and (b) selecting target training data from the plurality of pieces of training data, and determining whether the target training data is the defective data. (b) includes (b1) selecting a reference class from the plurality of classes, (b2) calculating a plurality of degrees of similarity between the feature spectrum corresponding to the target training data and a plurality of the feature spectra belonging to the reference class, (b3) applying, to the plurality of degrees of similarity, a defectiveness function that is determined in advance, and calculating a defectiveness index with respect to the target training data, and (b4) determining whether the target training data is the defective data, based on a result of comparison between the defectiveness index and a threshold value. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a block diagram illustrating a classification processing system in an exemplary embodiment. 
         FIG.  2    is an explanatory diagram illustrating a configuration example of a machine learning model. 
         FIG.  3    is a flowchart illustrating an overall procedure of processing extracting defective data. 
         FIG.  4    is an explanatory diagram illustrating an example of training data. 
         FIG.  5    is an explanatory diagram illustrating a feature spectrum. 
         FIG.  6    is an explanatory diagram illustrating a configuration of a feature spectrum group. 
         FIG.  7    is a flowchart illustrating a procedure for extracting outlier data. 
         FIG.  8    is an explanatory diagram illustrating a distribution example of a similarity group S q   c,   c  relating to normal training data. 
         FIG.  9    is an explanatory diagram illustrating a distribution example of the similarity group S q   c,   c  relating to the outlier data. 
         FIG.  10    is a flowchart illustrating a procedure for extracting overlap data. 
         FIG.  11    is an explanatory diagram illustrating a distribution example of a similarity group S q   c,   c ′ relating to the normal training data. 
         FIG.  12    is an explanatory diagram illustrating a distribution example of the similarity group S q   c,   c ′ relating to the overlap data. 
         FIG.  13    is an explanatory diagram illustrating a first arithmetic method for obtaining a degree of similarity. 
         FIG.  14    is an explanatory diagram illustrating a second arithmetic method for obtaining a degree of similarity. 
         FIG.  15    is an explanatory diagram illustrating a third arithmetic method for obtaining a degree of similarity. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     A. Exemplary Embodiment 
       FIG.  1    is a block diagram illustrating a classification processing system in an exemplary embodiment. The classification processing system includes an information processing device  100  and a camera  400 . The camera  400  captures an image being training data. A camera that captures a color image may be used as the camera  400 . Alternatively, a camera that captures a monochrome image or a spectral image may be used. In the present exemplary embodiment, an image captured by the camera  400  is used as the training data. Alternatively, data other than an image may be used as the training data. In such a case, a training data reading device selected in accordance with a data type is used in place of the camera  400 . 
     In the present disclosure, the term “training data” is used as a term indicating both training data and verification data. The training data is labeled data used for adjusting an internal parameter of a machine learning model. The verification data is labeled data used for verifying a machine learning model that is previously learned. However, in the exemplary embodiment described below, description is made on a case in which the training data is used as the training data and defective data is extracted or detected from the training data. The “defective data” may contain outlier data and overlap data. The outlier data is data significantly different from characteristics of a normal training data set in general. The overlap data is data having features significantly similar to those of normal training data in a different class. 
     The information processing device  100  includes a processor  110 , a memory  120 , an interface circuit  130 , and an input device  140  and a display device  150  that are coupled to the interface circuit  130 . The camera  400  is also coupled to the interface circuit  130 . Although not limited thereto, for example, the processor  110  is provided with a function of executing processing, which is described below in detail, as well as a function of displaying, on the display device  150 , data obtained through the processing and data generated in the course of the processing. 
     The processor  110  functions as a learning execution unit  112  that executes learning of a machine learning model and a defective data extraction unit  114  that executes processing of extracting defective data from training data. The defective data extraction unit  114  includes a degree of similarity arithmetic unit  310  and a defectiveness index arithmetic unit  320 . Each of the learning execution unit  112  and the defective data extraction unit  114  are implemented when the processor  110  executes a computer program stored in the memory  120 . Alternatively, the learning execution unit  112  and the defective data extraction unit  114  may be implemented with a hardware circuit. The processor in the present disclosure is a term including such a hardware circuit. Further, one or a plurality of processors that execute learning processing or defective data extraction processing may be a processor included in one or a plurality of remote computers that are coupled via a network. 
     In the memory  120 , a machine learning model  200 , a training data group LT, and a feature spectrum group GSp are stored. A configuration example and an operation of the machine learning model  200  are described later. The training data group LT is a group of labeled data used for learning of the machine learning model  200 . In the present exemplary embodiment, the training data group LT is a set of image data as the training data. The feature spectrum group GSp is a set of feature spectra that are obtained by inputting training data being a processing target into the machine learning model  200  that is previously leaned. The feature spectrum is described later. 
       FIG.  2    is an explanatory diagram illustrating a configuration of the machine learning model  200 . The machine learning model  200  has an input layer  210 , an intermediate layer  280 , and an output layer  260 . The intermediate layer  280  includes a convolution layer  220 , a primary vector neuron layer  230 , a first convolution vector neuron layer  240 , and a second convolution vector neuron layer  250 . The output layer  260  is also referred to as a “classification vector neuron layer  260 ”. Among those layers, the input layer  210  is the lowermost layer, and the output layer  260  is the uppermost layer. In the following description, the layers in the intermediate layer  280  are referred to as the “Conv layer  220 ”, the “PrimeVN layer  230 ”, the “ConvVN1 layer  240 ”, and the “ConvVN2 layer  250 ”, respectively. The output layer  260  is referred to as the “ClassVN layer  260 ”. 
     In the example of  FIG.  2   , the two convolution vector neuron layers  240  and  250  are used. However, the number of convolution vector neuron layers is freely selected, and the vector neuron layers may be omitted. However, it is preferred that one or more convolution vector neuron layers be used. 
     An image having a size of 28x28 pixels is input into the input layer  210 . A configuration of each of the layers other than the input layer  210  is described as follows.
     Conv layer  220 : Conv [32, 5, 2]   PrimeVN layer  230 : PrimeVN [16, 1, 1]   ConvVN1 layer  240 : ConvVN1 [12, 3, 2]   ConvVN2 layer  250 : ConvVN2 [6, 3, 1]   ClassVN layer  260 : ClassVN [M, 3, 1]   Vector dimension VD: VD = 16   

     In the description for each of the layers, the character string before the brackets indicates a layer name, and the numbers in the brackets indicate the number of channels, a kernel surface size, and a stride in the stated order. For example, the layer name of the Conv layer  220  is “Conv”, the number of channels is 32, the kernel surface size is 5×5, and the stride is two. In  FIG.  2   , such description is given below each of the layers. A rectangular shape with hatching in each of the layers indicates the kernel surface size that is used for calculating an output vector of an adjacent upper layer. In the present exemplary embodiment, input data is in a form of image data, and hence the kernel surface size is also two-dimensional. Note that the parameter values used in the description of each of the layers are merely examples, and may be changed freely. 
     Each of the input layer  210  and the Conv layer  220  is a layer configured as a scholar neuron. Each of the other layers  230  to  260  is a layer configured as a vector neuron. The vector neuron is a neuron where an input and an output are in a vector expression. In the description given above, the dimension of an output vector of an individual vector neuron is 16, which is constant. In the description given below, the term “node” is used as a superordinate concept of the scholar neuron and the vector neuron. 
     In  FIG.  2   , with regard to the Conv layer  220 , a first axis x and a second axis y that define plane coordinates of node arrangement and a third axis z that indicates a depth are illustrated. Further, it is shown that the sizes in the Conv layer  220  in the directions x, y, and z are 12, 12, and 32. The size in the direction x and the size in the direction y indicate the “resolution”. The size in the direction z indicates the number of channels. Those three axes x, y, and z are also used as the coordinate axes expressing a position of each node in the other layers. However, in  FIG.  2   , illustration of those axes x, y, and z is omitted for the layers other than the Conv layer  220 . 
     As is well known, a resolution W1 after convolution is given with the following equation. 
     
       
         
           
             W1 = Ceil 
             
               
                 
                   
                     
                       
                         W0 - Wk + 1 
                       
                     
                   
                   / 
                   S 
                 
               
             
           
         
       
     
     Here, W0 is a resolution before convolution, Wk is the kernel surface size, S is the stride, and Ceil{X} is a function of rounding up digits after the decimal point in the value X. 
     The resolution of each of the layers illustrate in  FIG.  2    is an example while assuming that the resolution of the input data is 28, and the actual resolution of each of the layers is changed appropriately in accordance with a size of the input data. 
     The ClassVN layer  260  has M channels. M is the number of classes distinguished from each other in the machine learning model  200 . In the present exemplary embodiment, M is two, and two class determination values Class_1 and Class_2 are output. The number M of channels of the ClassVN layer  260  can be set to a freely-selected integer equal to or greater than two. 
     In  FIG.  2   , a partial region Rn is further illustrated in each of the layers  220 ,  230 ,  240 ,  250 , and  260 . The suffix “n” of the partial region Rn indicates the reference symbol of each of the layers. For example, the partial region R 220  indicates the partial region in the Conv layer  220 . The “partial region Rn” is a region of each of the layers that is specified with a plane position (x, y) defined by a position in the first axis x and a position in the second axis y and includes a plurality of channels along the third axis z. The partial region Rn has a dimension “Width” x “Height” x “Depth” corresponding to the first axis x, the second axis y, and the third axis z. In the present exemplary embodiment, the number of nodes included in one “partial region Rn” is “1×1× the number of depths”, that is, “1× 1× the number of channels”. 
     As illustrated in  FIG.  2   , a feature spectrum Sp described later is calculated from an output of the ConvVN2 layer  250 . The degree of similarity arithmetic unit  310  uses the feature spectrum Sp, and thus calculates a degree of similarity of the individual training data and other training data. Extraction of the defective data is executed through use of the degree of similarity. 
     In the present disclosure, a vector neuron layer used for calculation of the degree of similarity is also referred to as a “specific layer”. As the specific layer, the vector neuron layers other than the ConvVN2 layer  250  may be used. One or more vector neuron layers may be used, and the number of vector neuron layers is freely selectable. Note that a configuration of the feature spectrum Sp and an arithmetic method of the degree of similarity through use of the feature spectrum Sp are described later. 
       FIG.  3    is a flowchart illustrating an overall procedure of processing of extracting the defective data. In Step S 110 , the learning execution unit  112  uses the training data group LT, and thus executes learning of the machine learning model  200 . After completion of learning, the machine learning model  200  that is previously leaned is stored in the memory  120 . 
       FIG.  4    is an explanatory diagram illustrating an example of the training data. The machine learning model  200  in the present exemplary embodiment utilizes, as an input, an image showing a mounting state of a component on a product, and is configured to output the classification determination values Class_1 and Class_2 indicating a pass and a failure. As the training data, four types of data including pass data LT 1 , failure data LT 2 , outlier data LT 3 , and overlap data LT 4  are used. The pass data LT 1  and the failure data LT 2  are normal training data, and the outlier data LT 3  and the overlap data LT 4  are defective data. 
     The pass data LT 1  is an image of a state in which a mounting angle of the component falls within a normal range. The failure data LT 2  is an image of a state in which the mounting angle of the component falls within an abnormal range, which requires re-fastening. The pass data LT 1  is denoted with a label “1”. The failure data LT 2  is denoted with a label “2”. In the present exemplary embodiment, a plurality of images are prepared for each of the pass data LT 1  and the failure data LT 2 . In the present disclosure, the term “class” and the term “label” are synonyms. 
     The outlier data LT 3  is an image of a state in which the mounting angle of the component falls within the normal range, but the position of the component is deviated from the center of the image. The outlier data LT 3  includes a plurality of images denoted with the label “1” similarly to the pass data LT 1 . The overlap data LT 4  is an image of the mounting angle in a half-done state, which may be classified into the pass data LT 1  and the failure data LT 2 . The overlap data LT 4  includes a plurality of images denoted with the label “1” and a plurality of images denoted with the label “2”. 
     In Step S 120 , the learning execution unit  112  inputs a plurality of pieces of training data, which are subjected to processing of extracting the defective data, into the machine learning model  200  that is previously leaned, and generates the feature spectrum group GSp. The feature spectrum group GSp is a set of feature spectra, which is described later. 
       FIG.  5    is an explanatory diagram illustrating the feature spectrum Sp obtained by inputting freely-selected input data into the machine learning model  200  that is previously leaned. As illustrated in  FIG.  2   , in the present exemplary embodiment, the feature spectrum Sp is generate from an output of the ConvVN2 layer  250 . The horizontal axis in  FIG.  5    indicates positions of vector elements relating to output vectors of a plurality of nodes included in one partial region R 250  of the ConvVN2 layer  250 . Each of the positions of the vector elements is expressed in a combination of an element number ND of the output vector and the channel number NC at each node. In the present exemplary embodiment, the vector dimension is 16 (the number of elements of the output vector being output from each node), and hence the element number ND of the output vector is denoted with 0 to 15, which is sixteen in total. Further, the number of channels of the ConvVN2 layer  250  is six, and thus the channel number NC is denoted with 0 to 5, which is six in total. In other words, the feature spectrum Sp is obtained by arranging the plurality of element values of the output vectors of each of the vector neurons included in one partial region R 250 , over the plurality of channels along the third axis z. 
     The vertical axis in  FIG.  5    indicates a feature value Cv at each of the spectrum positions. In this example, the feature value Cv is a value V ND  of each of the elements of the output vectors. The feature value Cv may be subjected to statistic processing such as centering to the average value 0. Note that, as the feature value Cv, a value obtained by multiplying the value V ND  of each of the elements of the output vectors by a normalization coefficient described later may be used. Alternatively, the normalization coefficient may directly be used. In the latter case, the number of feature values Cv included in the feature spectrum Sp is equal to the number of channels, which is six. Note that the normalization coefficient is a value corresponding to a vector length of the output vector of the node. 
     The number of feature spectra Sp that can be obtained from an output of the ConvVN2 layer  250  with respect to one piece of input data is equal to the number of plane positions (x, y) of the ConvVN2 layer  250 , in other words, the number of partial regions R 250 , which is nine. 
     In Step S 120 , the learning execution unit  112  inputs the training data subjected to process of extracting the defective data, into the machine learning model  200  that is previously leaned, calculates the feature spectra Sp illustrated in  FIG.  5   , and registers the feature spectra Sp as the feature spectrum group GSp in the memory  120 . In the present exemplary embodiment, the training data is subjected to processing of extracting the defective data, and hence the plurality of pieces of training data used in Step S 120  are the same as the plurality of pieces of training data used in Step S 110 . Note that, when the verification data is subjected to processing of extracting the defective data, the plurality of pieces of training data used in Step S 120  are different from the plurality of pieces of training data used in Step S 110 . The following four combinations of first training data that is used in Step S 120  and second training data that is an extraction target of the defective data are considered.
     (1) Both the first training data and the second training data are training data.   (2) The first training data is training data, and the second training data is verification data.   (3) Both the first training data and the second training data are verification data.   (4) The first training data is verification data, and the second training data is training data.   

     In the present exemplary embodiment, the first combination among those combinations is used. 
       FIG.  6    is an explanatory diagram illustrating a configuration of the feature spectrum group GSp. In this example, the feature spectrum group GSp obtained from an output of the ConvVN2 layer  250  is illustrated. Note that registration of a feature spectrum group obtained from an output of at least one vector neuron layer is only required as the feature spectrum group GSp. A feature spectrum group obtained from an output of the ConvVN1 layer  240  or the ClassVN layer  260  may be registered. 
     Each record in the feature spectrum group GSp includes a parameter k indicating the order of the partial region Rn in the layer, a parameter c indicating the class, a parameter q indicating the data number, and the feature spectrum Sp. The feature spectrum Sp is the same as the feature spectrum Sp in  FIG.  5   . 
     The parameter k of the partial region Rn is a value indicating any one of the plurality of partial regions Rn included in the specific layer, in other words, any one of the plane positions (x, y). In a case of the ConvVN2 layer  250 , the number of partial regions R 250  is nine, and hence k = 1 to 9. The parameter c indicating the class is a value indicating any one of the M classes distinguishable in the machine learning model  200 . In the present exemplary embodiment, M = 2, and hence C = 1 to 2. The parameter q of the data number indicates a serial number of the training data belonging to each class. When c = 1, the value is 1 to max1. When c = 2, the value is 1 to max2. In this manner, the feature spectrum Sp is associated with the class c and the data number q of the training data. Further, the feature spectrum Sp is classified into a class. 
     In Step S 130 , the defective data extraction unit  114  uses the feature spectrum group GSp, and thus extracts the defective data from the plurality of pieces of training data. In other words, the defective data extraction unit  114  uses the feature spectrum Sp that is read out from the memory  120 , and extracts or detects the outlier data LT 3  and the overlap data LT 4  from the four types of training data illustrated in  FIG.  4   . The procedure in Step S 130  is described later in detail. 
     In Step S 140 , the defective data extraction unit  114  executes processing of eliminating the defective data. For example, the outlier data can be subjected to elimination processing such as processing of removing the outlier data from the training data group and processing of eliminating the outlier data by subjecting the outlier data to data expansion processing and increasing the number of pieces of data. The overlap data can be subjected to elimination processing such as processing of removing the overlap data from the training data group and processing of adding a new class and allocating the overlap data to the new class. 
     In Step S 150 , the learning execution unit  112  re-executes learning of the machine learning model  200  through use of the training data group after eliminating the defective data. By executing learning with the training data group without the defective data, the machine learning model  200  with high classification accuracy can be obtained. 
       FIG.  7    is a flowchart illustrating a procedure for extracting the outlier data, and illustrates the procedure in Step S 130  in  FIG.  3    in a more detailed manner. In Step S 211 , the defective data extraction unit  114  set the parameter q indicating the data number of the target training data being a determination target and the parameter c indicating the class so that q = 1 and c = 1. The parameters q and c correspond to the data number q and the class c in the feature spectrum group GSp illustrated in  FIG.  5   . In the following description, the target training data is referred to as “target training data  Xq c”, and the class is referred to as a “target class c”. 
     In Step S 212 , the defective data extraction unit  114  sets a parameter c′ indicating a reference class so that c′ = c. The “reference class” indicates a class that is referred to for calculating the degree of similarity with the feature spectrum Sp of the target training data x q   c . In the following description, the reference class is referred to as a “reference class c′”, and training data belonging to the reference class is referred to as “reference training data”. In an arithmetic operation of the degree of similarity, which is described later, a plurality of degrees of similarity between the feature spectrum Sp of the target training data x q   c  and a feature spectrum Sp of a plurality of pieces of reference training data belonging to the reference class c′ are calculated. When the outlier data is extracted as the defective data, the reference class c′ is set to the same value as the target class c. 
     In Step S 213 , the degree of similarity arithmetic unit  310  executes an arithmetic operation for a group by degree of similarity S q   c,   c  between the target training data x q   c  and a reference training data set X c . In the reference symbol S q   c,   c  indicating the degree of similaritygroup by degree of similarity, the subscript “ q ” indicates the data number q of the target training data, the first “c” in the superscript “ c,   c ” indicates the target class, and the second “c” therein indicates the reference class. The reference training data set X c  indicates all pieces of training data belonging to the reference class c′ = c. In example illustrated in  FIG.  6   , when the reference class c′ is set so that c′ = 1, the training data having the data number q of 1 to max1 corresponds to the reference training data set X c . The degree of similaritygroup by degree of similarity S q   c,   c  is a set of degrees of similarity S q   c  between the feature spectrum Sp of the target training data X q   c  and the feature spectrum Sp of the individual reference training data. When c′ = 1, the number of pieces of reference data is max1. Thus, the degree of similaritygroup by degree of similarity S q   c,   c  includes max1 degrees of similarity S q   c . Note that the degree of similarity S q   c  also depends on a data number q′ of the reference training data and the reference class c′. However, in the reference symbols of the degree of similarity S q   c , those parameters q′ and c′ are omitted. The primes “′”given in the parameters q′ and c′ indicate that the parameters are similar to the parameters q and c illustrated in  FIG.  6    described above and are relevant to the reference training data. 
     In Step S 214 , the defective data extraction unit  114  causes a defectiveness function on the degree of similaritygroup by degree of similarity S q   c,   c , and thus obtains a defectiveness index d q . The defectiveness index d q  is an index indicating a state whether the target training data x q   c  is defective. The defectiveness function is a function with the degree of similaritygroup by degree of similarity S q   c,   c  as an input and the defectiveness index d q  as an output. The defectiveness function suitable for extraction of the outlier data is determined in consideration of a difference between distribution of the degree of similaritygroup by degree of similarity S q   c,   c  relating to the normal training data and the degree of similaritygroup by degree of similarity S q   c,   c  and the distribution of the degree of similaritygroup by degree of similarity S q   c,   c  relating to the outlier data. 
       FIG.  8    is an explanatory diagram illustrating a distribution example of the degree of similaritygroup by degree of similarity S q   c,   c  relating to the normal training data. The horizontal axis indicates the degree of similarity S q   C , and the vertical axis indicates frequency. In the procedure in  FIG.  7   , the reference class c′ is the same as the target class c. Thus, most of the degrees of similarity S q   c  included in the degree of similaritygroup by degree of similarity S q   c,   c  relating to the normal training data are close to 1.0. The reason why some of the degrees of similarity S q   c  have significantly small values is that the target class c includes the outlier data. 
       FIG.  9    is an explanatory diagram illustrating a distribution example of the degree of similaritygroup by degree of similarity S q   c,   c  relating to the outlier data. The degree of similaritygroup by degree of similarity S q   c,   c  relating to the outlier data has a tendency that most of the degrees of similarity S q   c  are values significantly smaller than 1.0. This is because, when the target training data x q   c  is the outlier data, the target training data x q   c  has features different from common features of the normal training data belonging to the target class c. 
     As the defectiveness function suitable for processing of extracting the outlier data, any one of the following functions may be used. 
     Defectiveness Function F 1   
     A defectiveness function f 1  is a function for obtaining a statistic representative value of the degree of similaritygroup by degree of similarity S q   c,   c  as the defectiveness index d q . As the statistic representative value, an average value may be used, for example. Note that, in some cases such as processing of extracting the overlap data, which is described later, a maximum value may also be used as the statistic representative value used in the defectiveness function f 1 . 
     Defectiveness Function F 2   
     A defectiveness function f 2  is a function for obtaining a representative value in a histogram of the degree of similaritygroup by degree of similarity S q   c,   c  as the defectiveness index d q . As the representative value in the histogram, a median value or a most frequent value in the histogram may be used. The representative value in the histogram of the degree of similaritygroup by degree of similarity S q   c,   c  is also one of the statistic representative values of the degree of similaritygroup by degree of similarity S q   c,   c . Thus, the second defectiveness function f 2  corresponds to a generic concept of the first defectiveness function f 1 . 
     Defectiveness Function F 3   
     A defectiveness function f 3  is a function for segmenting the histogram of the degree of similaritygroup by degree of similarity S q   c,   c  into one or more unimodal distributions, selecting a representative unimodal from the one or more unimodal distributions in accordance with a predetermined selection condition, and obtaining, as the defectiveness index d q , a representative value in the selected representative unimodal distribution. The third defectiveness function f 3  corresponds to a generic concept of the second defectiveness function f 2 . 
       FIG.  9    illustrates an example of the defectiveness index d q  that is obtained through use of the third defectiveness function f 3  described above. In this example, first, an Expectation-Maximization Algorithm (EM algorithm) is used to subject the histogram of the degree of similaritygroup by degree of similarity S q   c,   c  to fitting in a mixed Gaussian distribution. With this, a plurality of unimodal distributions Ud11 and Ud12 are obtained. Further, as a selection condition for selecting one representative unimodal distribution from the plurality of unimodal distributions Ud11 and Ud12, conditions C1 and C2 given below are used. 
     Condition C1 
     A ratio of an area of one unimodal distribution to an entire area of the histogram of the degree of similaritygroup by degree of similarity S q   c,   c  is equal to or greater than an area threshold value. 
     Condition C2 
     An average value of the degree of similarity S q   c  is the greatest in the unimodal distribution satisfying the condition C1. 
     For example, the area threshold value in the above-mentioned condition C1 is set to a value from approximately 5% to approximately 10%. As illustrated in  FIG.  9   , the condition C1 is used to exclude a unimodal distribution including the degrees of similarity S q   c  close to 1.0. This is because the degree of similaritygroup by degree of similarity S q   c,   c  of the outlier data includes a few degrees of similarity S q   c  close to 1.0. In the example of  FIG.  9   , the second unimodal distribution Ud12 of the two unimodal distributions Ud11 and Ud12 does not satisfy the condition C1 given above. In view of this, the first unimodal distribution Ud11 is selected as a representative unimodal distribution, and a most frequent value being its representative value is determined as the defectiveness index d q . When the target training data x q   c  is the outlier data, the defectiveness index d q  is a significantly small value. 
     A condition other than the above-mentioned conditions C1 and C2 may be used a selection condition for selecting one representative unimodal distribution from the plurality of unimodal distributions Ud11 and Ud12. For example, a unimodal distribution with the largest area in the plurality of unimodal distributions may be selected as a representative unimodal distribution. As described above, the histogram of the degree of similaritygroup by degree of similarity S q   c,   C  is segmented into one or more unimodal distributions, and one representative unimodal distribution is selected therefrom. With this, even when the histogram of the degree of similaritygroup by degree of similarity S q   c,   c  has a plurality of peaks, the defectiveness index d q  can be obtained appropriately. 
     In Step S 215  to Step S 217 , the defective data extraction unit  114  determines whether the target training data X q   c  is the outlier data, based on a result of comparison between the defectiveness index d q  and a first threshold value Th1. Specifically, when d q ≤Th1, it is determined that the target training data x q   c  is the outlier data in Step S 216 . Meanwhile, when Th1&lt;d q , it is determined that the target training data x q   c  is the normal training data in Step S 217 . As illustrated in  FIG.  9   , the first threshold value Th1 is set to be a value that is significantly greater than the defectiveness index d q  obtained when the target training data x q   c  is the outlier data. 
     In Step S 218 , the defective data extraction unit  114  increments the target training data number q by one. In Step S 219 , the defective data extraction unit  114  determines whether the target training data number q exceeds the maximum value, in other words, whether the processing from Step S 213  to Step S 217  is completed for all the pieces of training data in the target class c. When the processing is not completed for all the pieces of training data in the target class c, the procedure returns to Step S 213 . Meanwhile, when the processing is completed for all the pieces of training data in the target class c, the procedure proceeds to Step S 220 . 
     In Step S 220 , the defective data extraction unit  114  increments the target class c by one, and sets the target training data number q to 1. In Step S 221 , the defective data extraction unit  114  determines whether the processing from Step S 212  to S 219  is completed for all the classes. When the processing is not completed for all the classes, the procedure returns to Step S 212 . Meanwhile, when the processing is completed for all the classes, the processing in  FIG.  7    is completed. 
     When the processing is executed by following the procedure in  FIG.  7    as described above, the outlier data can be extracted or detected from the plurality of pieces of training data. 
       FIG.  10    is a flowchart illustrating a procedure for extracting the overlap data, and illustrates the procedure in Step S 130  in  FIG.  3    in a more detailed manner. The procedure in  FIG.  10    is executed independently from the procedure in  FIG.  7    described above. In the present exemplary embodiment, the processing of extracting the outlier data in the procedure in  FIG.  7    and the processing of extracting the overlap data in the procedure in  FIG.  10    can be executed separately as the processing in Step S 130  in  FIG.  3   . Those two types of the extraction processing may be executed in a freely-selected order. However, only one of the processing in  FIG.  7    and the processing in  FIG.  10    may be executed. 
     Step S 311  to Step S 321  in  FIG.  10    substantially correspond to Step S 211  to Step S 221  in  FIG.  7   . More specifically, Step S 311  and Step S 318  to Step S 321  are similar to Step S 211  and Step S 218  to Step S 221 , and Step S 312  to Step S 317  are different from Step S 212  to Step S 217 . In the following description, the contents in Step S 312  to Step S 317  are described. 
     In Step S 312 , the defective data extraction unit  114  sets the reference class c′ to {all the classes other than c}. Here, “c” indicates the target class. In the example illustrated in  FIG.  6   , when c = 1, c′ = 2. Note that, when the number of classes is three or more, it is assumed that the reference class c′ includes a plurality of classes. 
     In Step S 313 , the degree of similarity arithmetic unit  310  executes an arithmetic operation for the degree of similaritygroup by degree of similarity S q   c,   c ′ between the target training data X q   c  and the reference training data set X c ′. In the example illustrated in  FIG.  6   , when c = 1 and c′ = 2, the training data of max2 belonging to the class 2 corresponds to the reference training data set X c ′. Therefore, the degree of similaritygroup by degree of similarity S q   c,   c ′ includes max2 degrees of similarity S q   c′  . 
     In Step S 314 , the defective data extraction unit  114  causes the defectiveness function to act on the degree of similaritygroup by degree of similarity S q   c,   c ′, and thus obtains the defectiveness index d q . The defectiveness function suitable for extraction of the overlap data is determined in consideration of a difference between the distribution of the degree of similaritygroup by degree of similarity S q   c,   c ′ relating to the normal training data and the distribution of the degree of similaritygroup by degree of similarity S q   c,   c ′ relating to the overlap data. 
       FIG.  11    is an explanatory diagram illustrating a distribution example of the degree of similaritygroup by degree of similarity S q   c,   c ′ relating to the normal training data. The reference class c′ is set for a class other than the target class c, and hence most of the degrees of similarity S q   c  included in the degree of similaritygroup by degree of similarity S q   c,   c′  relating to the normal training data are values that are significantly smaller than 1.0. The reason why a few degrees of similarity S q   c  close to 1.0 are present is that the reference class c′ includes the overlap data. 
       FIG.  12    is an explanatory diagram illustrating a distribution example of the degree of similaritygroup by degree of similarity S q   c,   c ′ relating to the overlap data. In the degree of similaritygroup by degree of similarity S q   c,   c ′ relating to the overlap data, a number of degrees of similarity S q   c  are values close to 1.0. This is because, when the target training data X q   c  is the overlap data, the target training data x q   c  has features similar to features of a class other than the target class c. 
     The defectiveness function suitable for processing extracting the overlap data, functions that are substantially the same as the defectiveness functions f 1  to f 3  described with processing of extracting the outlier data may be used. In other words, as the defectiveness function, a function for obtaining a statistic representative value of the degree of similaritygroup by degree of similarity S q   c,   c ′ as the defectiveness index d q  may be used. In the example of  FIG.  12   , the third defectiveness function f 3  described above is used, and a second unimodal distribution Ud22 of two unimodal distributions Ud21 and Ud22 is selected as a representative unimodal distribution. Further, the most frequent value being a representative value in the representative unimodal distribution Ud22 is determined as the defectiveness index d q . Note that the defectiveness function used for processing of extracting the overlap data and the defectiveness function used for processing of extracting the outlier data may be functions that are different from each other. 
     In Step S 315  to Step S 317 , the defective data extraction unit  114  determines whether the target training data X q   c  is the overlap data, based on a result of comparison between the defectiveness index d q  and the second threshold value Th2. Specifically, when Th2≤d q , it is determined that the target training data x q   c  is the overlap data in Step S316. Meanwhile, when d q &lt;Th2, it is determined that the target training data x q   c  is the normal training data in Step S 317 . As illustrated in  FIG.  12   , the second threshold value Th2 is set to a value that is sufficiently smaller than the defectiveness index d q  obtained when the target training data x q   c  is the overlap data. Note that the first threshold value Th1 used for processing of extracting the outlier data and the second threshold value Th2 used for processing of extracting the overlap data may be set to the same value, or may be set to values different from each other. 
     When the processing is executed by following the procedure in  FIG.  10    as described above, the overlap data can be extracted or detected from the plurality of pieces of training data. 
     Note that, in the processing in  FIG.  10   , the reference class c′ is set as {all the classes other than the target class c}, and the defectiveness index d q  is obtained once with respect to {all the classes other than the target class c}. Instead, the reference class c′ may be set as {one class other than the target class c}, and the defectiveness index d q  may be obtained with respect to the individual reference class c′. In the latter case, when the defectiveness index d q  is equal to or greater than the second threshold value Th2 in at least one class other than the target class c, it is determined that the target training data x q   c  is the overlap data. Further, when the defectiveness index d q  is less than the second threshold value Th2 in all the classes other than the target class c, it is determined that the target training data x q   c  is not the overlap data. 
     As described, in the above-mentioned exemplary embodiment, the defective data can be extracted from the training data through use of the defectiveness index d q  calculated based on the degree of similarity. 
     B. Method of Calculating Degree of Similarity 
     For example, any one of the following methods may be employed as the arithmetic method of the degree of similarity described above. 
     (1) A first arithmetic method M1 for obtaining a degree of similarity without considering correspondence of partial region Rn in the feature spectrum Sp of the target training data x q   c  and the feature spectrum Sp of the reference training data x q′   c′     (2) A second arithmetic method M2 for obtaining a degree of similarity in the partial region Rn corresponding to the feature spectrum Sp of the target training data X q   c  and the feature spectrum Sp of the reference training data x q′   c′     (3) A third arithmetic method M3 for obtaining a degree of similarity without considering the partial region Rn at all   

     In the following description, description is sequentially made on methods of calculating a degree of similarity from an output of the ConvVN2 layer  250  while following those arithmetic methods M1, M2, and M3. 
       FIG.  13    is an explanatory diagram illustrating the first arithmetic method M1 for obtaining a degree of similarity. In the first arithmetic method M1, first, a local degree of similarity SL q   c (k) of a partial region k is calculated from an output of the ConvVN2 layer  250  being the specific layer, in accordance with an equation described below. In the machine learning model  200  in  FIG.  2   , the number of partial regions R 250  of the ConvVN2 layer  250  is nine, and hence the parameter k indicating the partial region is 1 to 9. Note that  FIG.  13    illustrates an example in which c = 1 and c′ = 2. Any one of three types of the degrees of similarity S q   c , which are illustrated on the right side of  FIG.  13   , is calculated from the local degree of similarity SL q   c (k) . 
     In the first arithmetic method M1, the local degree of similarity SL q   c (k) is calculated through use of the following equation. SL q   c (k) = max[G{Sp(k, c, q), Sp(k′ = all, c′, q′)}] ••• (B1), where 
     k and k′ are parameters indicating the partial region Rn;   c and c′ are parameters indicating the target class and the reference class;   q and q′ are parameters indicating the data number of the target training data and the data number of the reference training data;   G{a, b} is the function for obtaining a degree of similarity between a and b;   Sp(k, c, q) is the feature spectrum obtained from an output of the specified partial region k of the specific layer in accordance with the target training data x q   c ;   Sp(k′ = all, c′, q′) is the feature spectrum obtained from an output of all the partial regions k′ of the specific layer in accordance with the reference training data X q′   c′ ; and   max [X] is a logical operation for obtaining a maximum value of the values X.   

     Note that, as the function G{a, b} for obtaining the degree of similarity, for example, an equation for obtaining a cosine degree of similarity or a degree of similarity corresponding to a distance may be used. 
     The three types of the degrees of similarity S q   c , which are illustrated on the right side of  FIG.  13   , are obtained by obtaining a maximum value, an average value, or a minimum value of the local degree of similarity SL q   c (k) of the plurality of partial regions k. An arithmetic operation to be used for obtaining the maximum value, the average value, or the minimum value is set in advance through experimental or empirical observation of a user. 
     As described above, in the first arithmetic method M1 for obtaining a degree of similarity,
     (1) the local degree of similarity SL q   c (k) being a degree of similarity between the feature spectrum Sp(k, c, q) and the feature spectrum Sp(k′ = all, c′, q′) is obtained, the feature spectrum Sp(k, c, q) being obtained from an output of the specified partial region k of the specific layer in accordance with the target training data x q   c , the feature spectrum Sp(k′ = all, c′, q′) being obtained form an output of all the partial regions k′ of the specific layer in accordance with the reference training data x q′   c′ , and   (2) the degree of similarity S q   c  is obtained by obtaining the maximum value, the average value, or the minimum value of the local degree of similarity SL q   c (k) for the plurality of partial regions k.   

     With the first arithmetic method M1, the degree of similarity S q   c  can be obtained in an arithmetic operation and a procedure that are relatively simple. 
       FIG.  14    is an explanatory diagram illustrating the second arithmetic method M2 for obtaining a degree of similarity. In the second arithmetic method M2, the local degree of similarity SL q   c (k) is calculated through use of the following equation in place of Equation (B1) given above. 
     
       
         
           
             
               
                 SL 
               
               q 
             
             
                 
               c 
             
             
               k 
             
              = G 
             
               
                 Sp 
                 
                   
                     k, c, q 
                   
                 
                 , 
                  Sp 
                 
                   
                     k′ = k, c′, q′ 
                   
                 
               
             
           
         
       
     
      where 
     Sp(k′ = k, c′, q′) is the feature spectrum obtained by an output of the specified partial region k′ = k of the specific layer in accordance with the reference training data X q′   c ′. 
     In the first arithmetic method M1 described above, the feature spectrum Sp(k′ = all, c′, q′) obtained form an output of all the partial regions k′ of the specific layer in accordance with the reference training data x q ′ c′  is used. In contrast, the second arithmetic method M2 only uses the feature spectrum Sp(k′ = k, c′, q′) of the partial region k′ = k that is the same as the partial region k of the feature spectrum Sp(k, c, q) obtained in accordance with the target training data x q   c . Other contents of the second arithmetic method M2 are similar to those of the first arithmetic method M1. 
     In the second arithmetic method M2 for obtaining a degree of similarity,
     (1) the local degree of similarity SL q   c (k) being a degree of similarity between the feature spectrum Sp(k, c, q) and the feature spectrum Sp(k′ = all, c′, q′) is obtained, the feature spectrum Sp(k, c, q) being obtained from an output of the specified partial region k of the specific layer in accordance with the target training data x q   c , the feature spectrum Sp(k′ = all, c′, q′) being obtained form an output of the corresponding partial region k′ = k of the specific layer in accordance with the reference training data x q′   c′ , and   (2) the degree of similarity S q   c  is obtained by obtaining the maximum value, the average value, or the minimum value of the local degree of similarity SL q   c (k) for the plurality of partial regions k.   

     With the second arithmetic method M2, the degree of similarity S q   c  can also be obtained in an arithmetic operation and a procedure that are relatively simple. 
       FIG.  15    is an explanatory diagram illustrating the third arithmetic method M3 for obtaining a degree of similarity. In the third arithmetic method M3, the degree of similarity S q   c  is calculated from an output of the ConvVN2 layer  250  being the specific layer, without obtaining the local degree of similarity SL q   c  (k) . 
     The degree of similarity S q   c  obtained in the third arithmetic method M3 is calculated through use of the following equation. 
     
       
         
           
             
               S 
               q 
             
             
                 
               c 
             
             E 
             = 
             max 
             
               
                 
                   
                     G 
                     
                       
                         Sp 
                         
                           
                             k = all, c, q 
                           
                         
                         , 
                          Sp 
                         
                           
                             k′ = all, c′, q′ 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
      where
     Sp(k = all, c, q) is the feature spectrum obtained from an output of all the partial regions k of the specific layer in accordance with the target training data X q   c ; and   Sp(k′ = all, c′, q′) is the feature spectrum obtained from an output of all the partial regions k′ of the specific layer in accordance with the reference training data X q′   c′ .   

     As described above, in the third arithmetic method M3 for obtaining a degree of similarity, 
     the degree of similarity S q   c  between the feature spectrum Sp(k = all, c, q) and the feature spectrum Sp(k′ = all, c′, q′) is obtained, the feature spectrum Sp(k = all, c, q) being obtained from an output of all the partial regions k of the specific layer in accordance with the target training data x q   c , the feature spectrum Sp(k′ = all, c′, q′) being obtained form an output of all the partial regions k′ of the specific layer in accordance with the reference training data x q′   c′ . 
     With the third arithmetic method M3, the degree of similarity S q   c  can be obtained in an arithmetic operation and a procedure that are further simple. 
     Each of the three arithmetic methods M1 to M3 described above is a method for executing an arithmetic operation for a degree of similarity through use of an output of one specific layer. However, an arithmetic operation for a degree of similarity can be executed while one or more of the plurality of vector neuron layers  240 ,  250 , and  260  illustrated in  FIG.  2    is regarded as the specific layer. For example, when the plurality of specific layers are used, it is preferred that the minimum value of the plurality of degrees of similarity obtained from the plurality of specific layers be used as a final degree of similarity. 
     C. Arithmetic Method of Output Vector in Each Layer of Machine Learning Model 
     Arithmetic methods for obtaining an output of each of the layers illustrated in  FIG.  2    are as follows. 
     For each of the nodes of the PrimeVN layer  230 , a vector output of the node is obtained by regarding scholar outputs of 1×1×32 nodes of the Conv layer  220  as 32-dimensional vectors and multiplying the vectors by a transformation matrix. In the transformation matrix, a surface size is a 1×1 kernel element. The transformation matrix is updated by learning of the machine learning model  200 . Note that processing in the Conv layer  220  and processing in the PrimeVN layer  230  may be integrated so as to configure one primary vector neuron layer. 
     When the PrimeVN layer  230  is referred to as a “lower layer L”, and the ConvVN1 layer  240  that is adjacent on the upper side is referred to as an “upper layer L+1”, an output of each node of the upper layer L+1 is determined through use of the following equations. 
     [Mathematical Expression 1] 
     
       
         
           
             
               v 
               
                 i 
                 j 
               
             
             = 
             
               W 
               
                 i 
                 j 
               
               L 
             
             
               M 
               i 
               L 
             
           
         
       
     
     
       
         
           
             
               u 
               j 
             
             = 
             
               
                 ∑ 
                 i 
               
               
                 
                   v 
                   
                     i 
                     j 
                   
                 
               
             
           
         
       
     
     
       
         
           
             
               a 
               j 
             
             = 
             F 
             
               
                 
                   
                     
                       u 
                       j 
                     
                   
                 
               
             
           
         
       
     
     
       
         
           
             
               M 
               j 
               
                 L 
                 + 
                 1 
               
             
             = 
             
               a 
               j 
             
             × 
             
               1 
               
                 
                   
                     
                       u 
                       j 
                     
                   
                 
               
             
             
               u 
               j 
             
           
         
       
     
      where 
     M L   i  is an output vector of an i-th node in the lower layer L; M L+1   j  is an output vector of a j-th node in the upper layer L+1;   v ij  is a predicted vector of the output vector M L+1   j ;   W L   ij  is a predicted matrix for calculating the predicted vector v ij  from the output vector M L   i  of the lower layer L;   U j  is a sum vector being a sum of the predicted vector v ij , that is, a linear combination;   a j  is an activation value being a normalization coefficient obtained by normalizing a norm | u j  | of the sum vector u j ; and   F(X) is a normalization function for normalizing X.   

     For example, as the normalization function F(X), Equation (E3a) or Equation (E3b) given below may be used. 
     [Mathematical Expression 2] 
     
       
         
           
             
               a 
               j 
             
             = 
             F 
             
               
                 
                   
                     
                       u 
                       j 
                     
                   
                 
               
             
             = 
             s 
             o 
             f 
             t 
             m 
             a 
             x 
             
               
                 
                   
                     
                       u 
                       j 
                     
                   
                 
               
             
             = 
             
               
                 e 
                 x 
                 p 
                 
                   
                     β 
                     
                       
                         
                           u 
                           j 
                         
                       
                     
                   
                 
               
               
                 
                   
                     ∑ 
                     k 
                   
                   
                     e 
                     x 
                     p 
                     
                       
                         β 
                         
                           
                             
                               u 
                               k 
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     
       
         
           
             
               a 
               j 
             
             = 
             F 
             
               
                 
                   
                     
                       u 
                       j 
                     
                   
                 
               
             
             = 
             
               
                 
                   
                     
                       u 
                       j 
                     
                   
                 
               
               
                 
                   
                     ∑ 
                     k 
                   
                   
                     
                       
                         
                           u 
                           k 
                         
                       
                     
                   
                 
               
             
           
         
       
     
      where 
     k is an ordinal number for all the nodes in the upper layer L+1; and   β is an adjustment parameter being a freely-selected positive coefficient, for example, β = 1.   

     In Equation (E3a) given above, the activation value a j  is obtained by normalizing the norm | u j  | of the sum vector u j  with the softmax function for all the nodes in the upper layer L+1. Meanwhile, in Equation (E3b), the norm | u j  | of the sum vector u j  is divided by the sum of the norm | u j  | of all the nodes in the upper layer L+1. With this, the activation value a j  is obtained. Note that, as the normalization function F(X), a function other than Equation (E3a) and Equation (E3b) may be used. 
     For sake of convenience, the ordinal number i in Equation (E2) given above is allocated to each of the nodes in the lower layer L for determining the output vector M L+1   j  of the j-th node in the upper layer L+1, and is a value from 1 to n. Further, the integer n is the number of nodes in the lower layer L for determining the output vector M L+1   j  of the j-th node in the upper layer L+1. Therefore, the integer n is provided in the equation given below. 
     
       
         
           
             n = Nk  
             × 
              Nc 
           
         
       
     
     Here, Nk is a kernel surface size, and Nc is the number of channels of the PrimeVN layer  230  being a lower layer. In the example of  FIG.  2   , Nk = 9 and Nc = 16. Thus, n = 144. 
     One kernel used for obtaining an output vector of the ConvVN1 layer  240  has 144 (3×3×16) elements, each of which has a surface size being a kernel size of 3x3, and has a depth being the number of channels in the lower layer of 16. Each of the elements is a prediction matrix W L   ij . Further, in order to generate output vectors of 12 channels of the ConvVN1 layer  240 , 12 kernel pairs are required. Therefore, the number of predication matrices W L   ij  of the kernels used for obtaining output vectors of the ConvVN1 layer  240  is 1,728 (144 × 12). Those prediction matrices W L   ij  are updated by learning of the machine learning model  200 . 
     As understood from Equation (E1) to Equation (E4) given above, the output vector M L+1   j  of each of the nodes in the upper layer L+1 is obtained by the following arithmetic operation. 
     (A) the predicted vector v ij  is obtained by multiplying the output vector M L   i  of each of the nodes in the lower layer L by the prediction matrix W L   ij ;   (b) the sum vector U j  being a sum of the predicted vectors v ij  of the respective nodes in the lower layer L, which is a linear combination, is obtained;   (c) the activation value a j  being a normalization coefficient is obtained by normalizing the norm | u j  | of the sum vector u j ; and   (d) the sum vector u j  is divided by the norm | u j  |, and is further multiplied by the activation value a j .   

     Note that the activation value a j  is a normalization coefficient that is obtained by normalizing the norm | u j  | for all the nodes in the upper layer L+1. Therefore, the activation value a j  can be considered as an index indicating a relative output intensity of each of the nodes among all the nodes in the upper layer L+1. The norm used in Equation (E3), Equation (E3a), Equation (E3b), and Equation (4) is an L2 norm indicating a vector length in a general example. In this case, the activation value a j  corresponds to a vector length of the output vector M L+1   j . The activation value a j  is only used in Equation (E3) and Equation (E4) given above, and hence is not required to be output from the node. However, the upper layer L+1 may be configured so that the activation value a j  is output to the outside. 
     A configuration of the vector neural network is substantially the same as a configuration of the capsule network, and the vector neuron in the vector neural network corresponds to the capsule in the capsule network. However, the arithmetic operation with Equation (E1) to Equation (E4) given above, which are used in the vector neural network, is different from an arithmetic operation used in the capsule network. The most significant difference between the two arithmetic operations is that, in the capsule network, the predicted vector v ij  in the right side of Equation (E2) given above is multiplied by a weight and the weight is searched by repeating dynamic routing for a plurality of times. Meanwhile, in the vector neural network of the present exemplary embodiment, the output vector M L+1   j  is obtained by calculating Equation (E1) to Equation (E4) given above once in a sequential manner. Thus, there is no need of repeating dynamic routing, and the arithmetic operation can be executed faster, which are advantageous points. Further, the vector neural network of the present exemplary embodiment has a less memory amount, which is required for the arithmetic operation, than the capsule network. According to an experiment conducted by the inventor of the present disclosure, the vector neural network requires approximately ⅓ to ½ of the memory amount of the capsule network, which is also an advantageous point. 
     The vector neural network is similar to the capsule network in that a node with an input and an output in a vector expression is used. Therefore, the vector neural network is also similar to the capsule network in that the vector neuron is used. Further, in the plurality of layers  220  to  260 , the upper layers indicate a feature of a larger region, and the lower layers indicate a feature of a smaller region, which is similar to the general convolution neural network. Here, the “feature” indicates a feature included in input data to the neural network. In the vector neural network or the capsule network, an output vector of a certain node contains space information indicating information relating to a spatial feature expressed by the node. In this regard, the vector neural network or the capsule network are superior to the general convolution neural network. In other words, a vector length of an output vector of the certain node indicates an existence probability of a feature expressed by the node, and the vector direction indicates space information such as a feature direction and a scale. Therefore, vector directions of output vectors of two nodes belonging to the same layer indicate positional relationships of the respective features. Alternatively, it can also be said that vector directions of output vectors of the two nodes indicate feature variations. For example, when the node corresponds to a feature of an “eye”, a direction of the output vector may express variations such as smallness of an eye and an almond-shaped eye. It is said that, in the general convolution neural network, space information relating to a feature is lost due to pooling processing. As a result, as compared to the general convolution neural network, the vector neural network and the capsule network are excellent in a function of distinguishing input data. 
     The advantageous points of the vector neural network can be considered as follows. In other words, the vector neural network has an advantageous point in that an output vector of the node expresses features of the input data as coordinates in a successive space. Therefore, the output vectors can be evaluated in such a manner that similar vector directions show similar features. Further, even when features contained in input data are not covered in teaching data, the features can be interpolated and can be distinguished from each other, which is also an advantageous point. In contrast, in the general convolution neural network, disorderly compaction is caused due to pooling processing, and hence features in input data cannot be expressed as coordinates in a successive space, which is a drawback. 
     An output of each of the node in the ConvVN2 layer  250  and the ClassVN layer  260  are similarly determined through use Equation (E1) to Equation (E4) given above, and detailed description thereof is omitted. A resolution of the ClassVN layer  260  being the uppermost layer is 1x1, and the number of channels thereof is M. 
     An output of the ClassVN layer  260  is converted into the plurality of class determination values Class_1 and Class_2 for the plurality of classes. In general, those class determination values are values obtained through normalization with the softmax function. Specifically, for example, a vector length of an output vector is calculated from the output vector of each of the nodes in the ClassVN layer  260 , and the vector length of each of the nodes is further normalized with the softmax function. By executing this arithmetic operation, a determination value for each of the classes can be obtained. As described above, the activation value a j  obtained by Equation (E3) given above is a value corresponding to a vector length of the output vector M L+1   j , and is normalized. Therefore, the activation value a j  of each of the nodes in the ClassVN layer  260  may be output, and may be used directly as a determination value of each of the classes. 
     In the exemplary embodiment described above, as the machine learning model  200 , the vector neural network that obtains an output vector by an arithmetic operation with Equation (E1) to Equation (E4) given above is used. Instead, the capsule network disclosed in each of US 5,210,798 and WO 2019/083553 may be used. 
     Other Aspects: 
     The present disclosure is not limited to the exemplary embodiment described above, and may be implemented in various aspects without departing from the spirits of the disclosure. For example, the present disclosure can also be achieved in the following aspects. Appropriate replacements or combinations may be made to the technical features in the above-described exemplary embodiment which correspond to the technical features in the aspects described below to solve some or all of the problems of the disclosure or to achieve some or all of the advantageous effects of the disclosure. Additionally, when the technical features are not described herein as essential technical features, such technical features may be deleted appropriately. 
     (1) According to a first aspect of the present disclosure, there is provided a method of extracting unsuitable and defective data from a plurality of pieces of training data used for learning of a machine learning model for classifying input data into a plurality of classes. The machine learning model is configured as a vector neural network having a plurality of vector neuron layers. The method includes (a) inputting each of the plurality of pieces of training data into the machine learning model that is previously leaned, obtaining a feature spectrum from an output of a specific layer of the machine learning model, and classifying, into classes, the feature spectra corresponding respectively to the plurality of pieces of training data, and (b) selecting target training data from the plurality of pieces of training data, and determining whether the target training data is the defective data. (b) includes (b1) selecting a reference class from the plurality of classes, (b2) calculating a plurality of degrees of similarity between the feature spectrum corresponding to the target training data and a plurality of the feature spectra belonging to the reference class, (b3) applying, to the plurality of degrees of similarity, a defectiveness function that is determined in advance, and calculating a defectiveness index with respect to the target training data, and (b4) determining whether the target training data is the defective data, based on a result of comparison between the defectiveness index and a threshold value. 
     With this method, through use of the defectiveness index calculated based on the degree of similarity, the defective data can be extracted from the training data. 
     (2) In the method described above, the defectiveness function may be a function for obtaining, as the defectiveness index, a statistic representative value of the plurality of degrees of similarity. 
     With this method, the defectiveness index can be obtained as appropriate. 
     (3) In the method described above, the defectiveness function may be a function for obtaining, as the defectiveness index, an average value or a maximum value of the plurality of degrees of similarity. 
     With this method, the defectiveness index can be obtained as appropriate. 
     (4) In the method described above, the defectiveness function may be a function for obtaining, as the defectiveness index, a representative value in a histogram of the plurality of degrees of similarity. 
     With this method, the defectiveness index can be obtained as appropriate. 
     (5) In the method described above, (b3) may include segmenting the histogram of the plurality of degrees of similarity into one or more unimodal distributions, and obtaining, as the defectiveness index, a representative value in a representative unimodal distribution that is selected from the one or more unimodal distributions in accordance with a selection condition that is determined in advance. 
     With this method, the defectiveness index can be obtained as appropriate from the histogram having a plurality of peaks. 
     (6) In the method described above, the selection condition may include a first condition that a ratio of one unimodal distribution area to an entire area of the histogram is equal to or greater than an area threshold value, and a second condition that, in the unimodal distribution satisfying the first condition, the average value of the plurality of degrees of similarity is the greatest. 
     With this method, the unimodal distribution for obtaining the defectiveness index can be selected as appropriate. 
     (7) In the method described above, the defective data may include outlier data, the reference class may be a class corresponding to a target class to which the target training data belongs, and (b4) may include determining the target training data is the outlier data when the defectiveness index is equal to or less than the threshold value, and determining the target training data is not the outlier data when the defectiveness index exceeds the threshold value. 
     With this method, the outlier data can be extracted as the defective data. 
     (8) In the method described above, the defective data may include overlap data approximating to training data in another class different from a class to which the defective data belongs, the reference class may be a class different from a target class to which the target training data belongs, and (b4) may include 
     determining the target training data is the overlap data when the defectiveness index is equal to or greater than the threshold value, and determining the target training data is not the overlap data when the defectiveness index is less than the threshold value. 
     With this method, the overlap data can be extracted as the defective data. 
     (9) In the method described above, the specific layer may have a configuration in which a vector neuron arranged in a plane defined with two axes including a first axis and a second axis is arranged as a plurality of channels along a third axis being a direction different from the two axes. The feature spectrum may be any one of (i) a first type of a feature spectrum obtained by arranging a plurality of element values of an output vector of a vector neuron at one plane position in the specific layer, over the plurality of channels along the third axis, (ii) a second type of a feature spectrum obtained by multiplying each of the plurality of element values of the first type of the feature spectrum by an activation value corresponding to a vector length of the output vector, and (iii) a third type of a feature spectrum obtained by arranging the activation value at one plane position in the specific layer, over the plurality of channels along the third axis. 
     With this method, the feature spectrum can easily be obtained. 
     (10) According to a second aspect of the present disclosure, there is provided an information processing device configured to execute processing for extracting unsuitable and defective data from a plurality of pieces of training data used for learning of a machine learning model for classifying input data into a plurality of classes. The information processing device includes a memory configured to store a machine learning model configured as a vector neural network having a plurality of vector neuron layers, and a processor configured to execute an arithmetic operation using the machine learning model. The processor executes processing of (a) inputting each of the plurality of pieces of training data into the machine learning model that is previously leaned, obtaining a feature spectrum from an output of a specific layer of the machine learning model, and classifying, into classes, the feature spectra corresponding respectively to the plurality of pieces of training data, and (b) selecting target training data from the plurality of pieces of training data, and determining whether the target training data is the defective data. (b) includes (b1) selecting a reference class from the plurality of classes, (b2) calculating a plurality of degrees of similarity between the feature spectrum corresponding to the target training data and a plurality of the feature spectra belonging to the reference class, (b3) applying, to the plurality of degrees of similarity, a defectiveness function that is determined in advance, and calculating a defectiveness index with respect to the target training data, and (b4) determining whether the target training data is the defective data, based on a result of comparison between the defectiveness index and a threshold value. 
     (11) According to a third aspect of the present disclosure, there is provided a non-transitory computer-readable storage medium storing a computer program for causing a processor to execute processing of extracting unsuitable and defective data from a plurality of pieces of training data used for learning of a machine learning model for classifying input data into a plurality of classes. The computer program causes the processor to execute processing of (a) inputting each of the plurality of pieces of training data into the machine learning model that is previously leaned, obtaining a feature spectrum from an output of a specific layer of the machine learning model, and classifying, into classes, the feature spectra corresponding respectively to the plurality of pieces of training data, and (b) selecting target training data from the plurality of pieces of training data, and determining whether the target training data is the defective data. (b) includes (b1) selecting a reference class from the plurality of classes, (b2) calculating a plurality of degrees of similarity between the feature spectrum corresponding to the target training data and a plurality of the feature spectra belonging to the reference class, (b3) applying, to the plurality of degrees of similarity, a defectiveness function that is determined in advance, and calculating a defectiveness index with respect to the target training data, and (b4) determining whether the target training data is the defective data, based on a result of comparison between the defectiveness index and a threshold value. 
     The present disclosure may be achieved in various forms other than the above-mentioned aspects. For example, the present disclosure can be implemented in forms including a computer program for achieving the functions of the defective data extraction device, and a non-transitory storage medium storing the computer program.