JP2022180119A - Data analysis system - Google Patents

Abstract

To provide a data analysis system that solves a problem that learning does not progress with an ArcFace and can generate a machine learning model that enables high-precision prediction while using high prediction accuracy of the ArcFace.SOLUTION: A data analysis system 1 includes: a loss function calculation unit 25 that calculates, when an angle θ between a feature vector x' and a weight vector W of a correct answer class is smaller than a predetermined value θTh, a loss function value Lossarc by applying margin addition processing by an ArcFace using the feature vector x' and the weight vector W, and calculates, when the formed angle θ is equal to or greater than a predetermined value θTh, a loss function value Losscos by applying the margin addition processing by a CosFace using the feature vector x' and the weight vector W; and a learning processing unit 26 that learns, on the basis of the loss function values Lossarc, Losscos, a machine learning model 11 by a gradient method.SELECTED DRAWING: Figure 2

Description

The present invention relates to data analysis systems.

Patent Literature 1 describes a visual inspection apparatus that inspects the presence or absence of defects in a visual image using a discriminator configured by a neural network. In general, machine learning models that perform class classification, such as inspection of the presence or absence of defects in appearance images, are desired to have clear class classification boundaries.

Various methods of learning a machine learning model consisting of a neural network for performing class classification are known. For example, there is a method of learning using distances in feature space, such as Euclidean distance, Manhattan distance, and Chebyshev distance. In this case, for example, a loss function for distance learning such as Center Loss is used.

ArcFace, CosFace, SphereFace, etc. are known as distance learning using angles. These distance learning methods are methods of learning by adding a margin in the case of the correct class to the inner product of the feature vector and the weight vector of the correct class. These distance learning methods are methods of learning so as to reduce the angle θ between the feature vector and the weight vector of the correct class. These distance learning methods differ in how to give a margin. Also, in general, ArcFace has the best prediction accuracy, followed by CosFace, and then SphereFace.

Japanese Patent Application Laid-Open No. 2020-106461

The inventors found that, as distance learning using angles, when margin addition processing by ArcFace is applied and learning is performed using the gradient method, the initial cos distance (cos similarity ) is small, learning may not progress.

The present invention has been made in view of this problem, and solves the problem that learning does not progress with ArcFace while utilizing the high prediction accuracy of ArcFace, and generates a machine learning model that enables highly accurate prediction. It is intended to provide a data analysis system capable of

One aspect of the present invention is
A data analysis system configured by a computer device comprising an arithmetic processing device and a storage device,
The storage device is composed of a neural network, and outputs a feature vector using the weight vector of the fully connected layer at the final stage. store a machine learning model for classifying,
The arithmetic processing unit is
a machine learning model execution unit that outputs the feature vector by executing the machine learning model when learning data is input;
a weight vector acquisition unit that acquires the weight vector when the machine learning model execution unit outputs the feature vector;
when the angle θ between the feature vector and the weight vector of the correct class is smaller than a predetermined value, applying margin addition processing by ArcFace using the feature vector and the weight vector to calculate the value of the loss function; a loss function calculation unit that calculates a loss function value by applying margin addition processing by CosFace using the feature vector and the weight vector when the formed angle θ is equal to or greater than the predetermined value;
a learning processing unit that learns the machine learning model by a gradient method based on the value of the loss function;
in a data analysis system comprising

The learning of the machine learning model uses both ArcFace and CosFace as distance learning using angles. Specifically, when the angle θ formed by the feature vector and the weight vector is smaller than a predetermined value, the loss function calculation unit applies margin addition processing by ArcFace, and when the angle θ formed is greater than or equal to a predetermined value, , Margin addition processing by CosFace is applied.

Therefore, margin addition processing by CosFace is applied to areas where there is a possibility that learning will not progress if only margin addition processing by ArcFace is performed. Therefore, as a whole, there is no region where learning is not progressed with ArcFace, and a state can be established in which learning is reliably progressed with CosFace.

Furthermore, as the learning progresses, the angle θ between the feature vector and the weight vector of the correct class becomes smaller. At the beginning of learning, when the angle θ between the feature vector and the weight vector of the correct class is greater than a predetermined value, CosFace margin addition processing is applied. After that, as the learning progresses, the formed angle θ becomes smaller. Then, the formed angle θ reaches a predetermined value, and the area of CosFace shifts to the area of ArcFace. After that, as learning by ArcFace progresses, a machine learning model capable of making highly accurate predictions is generated.

It is a functional block block diagram in the learning phase of a data-analysis system. It is a figure which shows the detailed structure in the learning phase of a data-analysis system. In the graph showing the relationship between the cos distance and the value of the loss function, the solid line indicates the first combined pattern of ArcFace and CosFace, and the dashed line indicates the pattern of ArcFace only. In the graph showing the relationship between the cos distance and the value of the loss function, the solid line indicates the second combined pattern of ArcFace and CosFace, and the dashed line indicates the pattern of ArcFace alone.

(1. Machine learning model)
A machine learning model is composed of a neural network. The term "neural network" as used herein includes the case where the number of hidden layers is one or the case where the number of hidden layers is multiple. In other words, when there are multiple hidden layers, it is called a so-called deep neural network. Of course, the machine learning model can apply, for example, a convolutional neural network as a neural network. Since the machine learning model is composed of a neural network, it outputs a feature vector corresponding to input data.

The machine learning model of this embodiment performs processing using weights, biases, activation functions, etc. in each neuron. Weights and biases are mainly learned. In the machine learning model, the output of the fully connected layer at the final stage becomes the feature vector. The fully connected layer at the final stage outputs the feature vector using the weight vector.

In this embodiment, the machine learning model is a model for classifying target data. For example, it is possible to determine to which class the target data belongs by determining whether or not the feature vector relating to the target data is close to the feature vector relating to the representative data of each class. In this embodiment, the machine learning model is a model for performing class classification of target data based on feature vectors relating to target data, feature vectors relating to class representative data, and cos distances.

For example, the machine learning model can be a model that targets image data and is used for classifying image data. In this case, the machine learning model performs class classification of the target image data based on the cos distance between the feature vector relating to the target image data and the feature vector relating to the class representative image data.

In particular, the machine learning model is exemplified by a model used for visual inspection of industrial products. In this case, by inputting image data of the appearance of the industrial product, it is determined whether the target industrial product is a non-defective product or a defective product. Specifically, a feature vector that is output when external image data of a target is input to the machine learning model is acquired. Also, a feature vector that is output when the representative image data of a non-defective product is input to the machine learning model is acquired. Furthermore, the feature vector output when the representative image data of the defective product is input to the machine learning model is acquired.

Then, based on the cos distance between the feature vector related to the target appearance image data and the feature vector related to the non-defective representative image data, it is determined whether the target appearance image data is classified into the non-defective product class. On the other hand, it is determined whether the target appearance image data is classified into the defective product class from the cos distance between the feature vector relating to the target appearance image data and the feature vector relating to the representative image data of the defective product. In this way, it is possible to determine whether an industrial product is good or bad based on the cos distance between the feature vector and the representative image data of each class.

If there are multiple types of defective products, the cos distance between the feature vector related to the target external image data and the feature vector related to the representative image data of each defective product determines which class of defective product the target external image data belongs to. It is also possible to determine whether it is classified into Here, as industrial products, various parts such as vehicle parts, industrial machine parts, and consumer equipment parts can be targeted.

(2. Outline of learning phase of data analysis system 1)
An overview of the configuration of the data analysis system 1 in the learning phase will be described with reference to FIG. A data analysis system 1 is composed of a computer device having a storage device 2 and an arithmetic processing device 3 .

The storage device 2 stores the machine learning model 11 described above. Furthermore, the storage device 2 stores learning data 12 used in the learning phase of the machine learning model. The learning data 12 is, for example, appearance image data of industrial products, and includes image data of non-defective products and image data of defective products. Further, the learning data 12 includes information indicating whether each image data is good or bad, that is, a correct label 12a.

The storage device 2 further stores a loss function calculation program 13 . The loss function calculation program includes a program for applying margin addition processing by ArcFace to calculate the value of the loss function, and a program for applying margin addition processing by CosFace to calculate the value of the loss function.

The arithmetic processing device 3 includes a machine learning model execution unit 21 , a feature vector normalization processing unit 22 , a weight vector acquisition unit 23 , a weight vector normalization processing unit 24 , a loss function calculation unit 25 and a learning processing unit 26 .

When image data is input to the machine learning model 11, the machine learning model execution unit 21 outputs a feature vector related to the input image data. In the learning phase, the machine learning model execution unit 21 inputs learning data 12 of appearance images stored in the storage device 2 and outputs a feature vector related to the input learning data 12 . The feature vector normalization processing unit 22 performs L2 normalization on the feature vectors output by the machine learning model execution unit 21 .

The weight vector acquisition unit 23 acquires the weight vector of the final fully connected layer when the machine learning model execution unit 21 outputs the feature vector. The weight vector normalization processing unit 24 performs L2 normalization on the weight vector acquired by the weight vector acquisition unit 23 .

The loss function calculation unit 25 executes the loss function calculation program 13 stored in the storage device 2 to apply margin addition processing by ArcFace to calculate the loss function value Loss. Further, the loss function calculation unit 25 executes the loss function calculation program 13 to apply margin addition processing by CosFace to calculate the value Loss of the loss function. An overview of the application of the two margin addition processes is as follows.

When the angle θ between the feature vector and the weight vector of the correct class is smaller than a predetermined value, the loss function calculation unit 25 applies margin addition processing by ArcFace using the feature vector and the weight vector to obtain the loss function value Loss Calculate On the other hand, when the formed angle θ is equal to or greater than a predetermined value, the loss function calculator 25 applies margin addition processing by CosFace using the feature vector and the weight vector to calculate the loss function value Loss. In calculating the loss function value Loss, the correct label 12a included in the learning data 12 stored in the storage device 20 is used.

The learning processing unit 26 learns the machine learning model 11 by the gradient method based on the loss function value Loss calculated by the loss function calculation unit 25 . The learning processing unit 26 learns the weights and biases of the machine learning model 11 stored in the storage device 2 . In this embodiment, the learning processing unit 26 learns by applying the gradient descent method so that the loss function value Loss becomes the minimum value or the minimum value.

(3. Detailed configuration of learning phase of data analysis system 1)
A detailed configuration of the learning phase of the data analysis system 1 will be described with reference to FIG. The machine learning model execution unit 21 receives the image data included in the learning data 12 and executes the machine learning model. Then, the machine learning model execution unit 21 outputs feature vectors. Here, when the image data included in the input learning data 12 is x, and the feature vector to be output is x', the expression (1) is obtained. f( ) is a function representing the machine learning model 11 .

The feature vector normalization processing unit 22 L2-normalizes the feature vector x′ to output a normalized feature vector x″. ). The normalized feature vector x″ is a vector with the length of the feature vector x′ set to one.

The weight vector acquisition unit 23 acquires the weight vector W of the final fully connected layer in the machine learning model 11 executed by the machine learning model execution unit 21 . The weight vector normalization processing unit 24 performs L2 normalization on the weight vector W to output a normalized weight vector W'. The weight vector W and the normalized weight vector W' are expressed as in Equation (3). The normalized weight vector W' is a vector having the length of the weight vector W set to one.

The loss function calculator 25 includes an ArcFace application unit 30 and a CosFace application unit 40 . The ArcFace application unit 30 includes an inner product calculation unit 31 , an ArcFace calculation unit 32 , a logit calculation unit 33 , a softmax function calculation unit 34 and a loss calculation unit 35 . The CosFace application unit 40 includes an inner product calculation unit 41 , a CosFace calculation unit 42 , a logit calculation unit 43 , a softmax function calculation unit 44 and a loss calculation unit 45 . However, since the inner calculation section 31 of the ArcFace application section 30 and the inner calculation section 41 of the CosFace application section 40 perform the same processing, they may execute a common program.

The inner product calculation unit 31 of the ArcFace application unit 30 acquires the normalized feature vector x″ and the normalized weight vector W′. A cos distance (cos θ), which is the inner product of the normalized feature vector x″ and the normalized weight vector W′, is calculated. The same applies to the inner calculation section 41 of the CosFace application section 40 .

If the angle θ between the normalized feature vector x″ and the normalized weight vector W′ of the correct class j is smaller _than a predetermined value θTh, the ArcFace calculator 32 calculates the normalized feature Using the angle θ between the vector x″ and the normalized weight vector W′, the angle θ′ is calculated by ArcFace. The ArcFace calculation unit 32 executes a process (margin addition process) of adding a margin _ma by ArcFace when it corresponds to the correct class j. The ArcFace calculator 32 uses the angle θ formed by the normalized feature vector x″ and the normalized weight vector W′ without adding the margin _ma when it does not correspond to the correct class j.

Here, the predetermined value θ _Th is represented by Equation (6).

When the formed angle θ is smaller than the predetermined value _θTh , the ArcFace calculator 32 uses the angle _θ'j calculated by the formula (5) to calculate the cos distance ( cos θ' _j ). In other words, the ArcFace calculator 32 calculates the cos distance (cos θ′ _j ) when the margin _ma is added when it corresponds to the correct class j. On the other hand, the ArcFace calculator 32 uses the cos distance (cos θ′ _j ) calculated by the inner product calculator 31 as it is without adding the margin _ma when it does not correspond to the correct class j.

The CosFace calculation unit 42 performs CosFace processing when the angle θ between the normalized feature vector x″ and the normalized weight vector W′ of the correct class j is equal to _or greater than a predetermined value θTh according to Equation (8). The CosFace calculation unit 42 executes a process (margin addition process) for adding _a margin _mc by CosFace when it corresponds to the correct class j, and calculates the cos distance (cos θ On the other hand, the CosFace calculation unit 42 calculates the cos distance (cos θ' _j ) calculated by the inner product calculation unit 31 without adding the margin m _c when it does not correspond to the correct _class j. is used as is.

Here, the margin _mc by CosFace is represented by Equation (9).

The logit calculation unit 33 of the ArcFace application unit 30 calculates the logit logit by multiplying the cos distance (cos θ' _j ) calculated by the ArcFace calculation unit 32 by the scale parameter s according to equation (10). The logit calculation unit 43 of the CosFace application unit 40 also performs similar processing. That is, the logit calculator 43 calculates the logit logit by multiplying the cos distance (cos θ′ _j ) calculated by the CosFace calculator 42 by the scale parameter s according to Equation (10).

The softmax function calculation unit 34 of the ArcFace application unit 30 converts the logit logit calculated by the logit calculation unit 33 using the softmax function according to equation (11). Similarly, the softmax function calculation unit 44 of the CosFace application unit 40 converts the logit logit calculated by the logit calculation unit 43 using the softmax function according to equation (11).

The loss calculation unit 35 of the ArcFace application unit 30 calculates the value Loss _arc of the loss function by ArcFace according to Equation (12). The loss calculator 35 applies cross entropy as a loss function to the logit logit calculated by the logit calculator 33 to calculate a cross entropy error as a loss function value Loss _arc . In calculating the cross-entropy error, the correct label 12a in the learning data 12 is used.

That is, the loss function by ArcFace shown in Equation (12) estimates the cos distance between the weight vector _Wyi of the correct answer class j and the feature vector _x'i smaller than the actual value by adding the margin _ma , and the incorrect answer class This corresponds to overestimating the cos distance between the weight vector W and the feature vector x'. That is, since the loss function value Loss _arc is given so as to be closer to the weight vector _Wyi of the correct class j than the weight vector W of other classes, the weight vector of the correct class and the weight vector of the incorrect class are divided into It has a pulling effect.

The loss calculation unit 45 of the CosFace application unit 40 calculates the value Loss _cos of the loss function by CosFace according to Equation (13). The loss calculator 45 applies cross entropy as a loss function to the logit logit calculated by the logit calculator 43 to calculate a cross entropy error as a loss function value Loss _cos . In calculating the cross-entropy error, the correct label 12a in the learning data 12 is used.

That is, the loss function by CosFace shown in Equation (13) functions basically in the same way as ArcFace by adding a margin _mc . In other words, the loss function by CosFace underestimates the cos distance between the weight vector _Wyi of the correct class j and the feature vector _x'i , and the cos distance between the weight vector W of the incorrect class j and the feature vector x'. It is equivalent to making a larger estimate. That is, since the loss function value Loss _cos is given so as to be closer to the weight vector _Wyi of the correct class j than the weight vector W of other classes, the weight vector of the correct class and the weight vector of the incorrect class are divided into It has a pulling effect.

When the angle θ between the normalized feature vector x″ and the normalized weight vector W′ of the correct class j is equal to or greater than a predetermined value _θTh , the learning processing unit 26 calculates the loss calculation unit 35 of the ArcFace application unit 30. The machine learning model 11 is trained by the gradient method using the loss function value Loss _arc (shown in Equation (12)) calculated by .

Further, when the angle θ between the normalized feature vector x″ and the normalized weight vector W′ of the correct class j is smaller than a predetermined value θ _Th , the learning processing unit 26 calculates the loss of the CosFace application unit 40. Using the loss function value Loss _cos (shown in equation (13)) calculated by the unit 45, the machine learning model 11 is learned by the gradient method.

(4. Values of cos distance and loss function when applying the first margin)
The relationship between the "cos distance between the normalized feature vector x" and the weight vector W' of the correct class and the "loss function value Loss" when the first margin is applied will be described with reference to FIG. Here, in FIG. 3, the solid line indicates this embodiment as a combined pattern of ArcFace and CosFace in the learning of the machine learning model 11, and the dashed line indicates a pattern in which only ArcFace is applied as a comparative example.

When only ArcFace as a comparative example is applied, the value of the loss function with respect to the cos distance has an extreme value (maximum value in this embodiment) at cos θ _E in the small cos distance region. When the cos distance is larger than cos θ _E in the initial stage of learning, learning by applying the gradient method causes the cos distance to move to a larger value. Therefore, learning progresses in the direction of increasing the cos distance, and the ideal state is approached. On the other hand, when the cos distance is smaller than cos θ _E in the initial stage of learning, learning by applying the gradient method moves the cos distance to a smaller value. Therefore, learning does not progress in the direction of increasing the cos distance.

The margin adding process by ArcFace is a process of adding an angle margin _ma to the formed angle θ as shown in equation (7). Therefore, when the formed angle θ is large (in the vicinity of 180°), and when the angle θ+ _ma exceeds 180°, the change in the value of the cos distance after conversion may be reversed in magnitude. For this reason, margin addition processing by ArcFace has the above relationship.

When this embodiment is applied, as shown in FIG. 3, there are areas to which CosFace is applied and areas to which ArcFace is applied. Here, the margin adding process by CosFace is the process of subtracting the margin _mc from cos θ as shown in equation (8). Therefore, the change in the value of the cos distance after conversion is the same as the change in cos θ, and unlike the case of ArcFace, the magnitude is not reversed.

Then, the angle θ formed by the boundary between the area to which ArcFace is applied and the area to which CosFace is applied becomes the cos distance value cos _θTh corresponding to the predetermined value _θTh . The margin addition processing by ArcFace and the margin addition processing by CosFace are set so that the value Loss of the loss function monotonically decreases or increases with respect to the cos distance when the formed angle θ reaches a predetermined value _θTh . ing. In this embodiment, the loss function value Loss is set to monotonically decrease as the cos distance increases.

In particular, the cos distance value cos θ _Th corresponding to the predetermined value θ _Th is greater than the cos distance value cos θ _E when the loss function value Loss _arc with respect to the cos distance becomes the extreme value in the margin addition processing by ArcFace. The predetermined value θ _Th is set so that

In other words, in this embodiment, there is no extreme value unlike when only ArcFace is applied. Therefore, no matter where the cos distance is located at the initial stage of learning, learning by applying the gradient method moves to the direction where the cos distance is larger. Therefore, learning progresses in the direction of increasing the cos distance, and the ideal state is approached.

Furthermore, margin addition processing by ArcFace and margin addition processing by CosFace are set so that the value Loss of the loss function has a continuous relationship with the cos distance when the formed angle θ is a predetermined value _θTh . In this case, learning progresses continuously. Therefore, learning is stabilized. In particular, it is preferable that the angle .theta. is set to a predetermined value _.theta.Th so that the value Loss of the loss function has a smooth continuous relationship with the cos distance. That is, when the formed angle θ is a predetermined value θ _Th , the values obtained by partially differentiating the value Loss of the loss function with respect to the cos distance match.

In order to set the margin addition processing by ArcFace and the margin addition processing by CosFace as described above, for example, the setting of the predetermined value _θTh and the setting of the margin _mc by CosFace can be done.

(5. Values of cos distance and loss function when applying the second margin)
The relationship between the cos distance between the normalized feature vector x″ and the weight vector W′ of the correct class and the loss function value Loss when the second margin is applied will be described with reference to FIG. 4, similar to FIG. 3, this embodiment as a pattern of combined use of ArcFace and CosFace in the learning of the machine learning model 11 is indicated by a solid line, and a pattern applying only ArcFace as a comparative example is indicated by a broken line. there is

When the second margin shown in FIG. 4 is applied, _compared with FIG. It is set to have a discontinuous relationship with respect to However, the angle θ formed by the boundary between the area to which ArcFace is applied and the area to which CosFace is applied is the cos distance value cos _θTh corresponding to the predetermined value _θTh . The margin addition processing by ArcFace and the margin addition processing by CosFace are set so that the value Loss of the loss function monotonically decreases or increases with respect to the cos distance when the formed angle θ reaches a predetermined value _θTh . ing.

Again, in this embodiment, there are no extrema as in the case of applying only ArcFace. Therefore, no matter where the cos distance is located at the initial stage of learning, learning by applying the gradient method moves to the direction where the cos distance is larger. Therefore, learning progresses in the direction of increasing the cos distance, and the ideal state is approached.

In order to set the margin addition processing by ArcFace and the margin addition processing by CosFace as described above, for example, the setting of the predetermined value _θTh and the setting of the margin _mc by CosFace can correspond.

(6. Effect)
As described above, the learning of the machine learning model 11 uses both ArcFace and CosFace as distance learning using angles. Specifically, when the angle θ between the feature vector x′ and the weight vector W is smaller than a predetermined value θ _Th , the loss function calculator 25 calculates , Apply margin addition processing by ArcFace. On the other hand, when the formed angle θ is equal to or greater than the predetermined value _θTh , the loss function calculator 25 applies margin addition processing by CosFace as shown in Equations (8) and (13).

Therefore, margin addition processing by CosFace is applied to areas where there is a possibility that learning will not progress if only margin addition processing by ArcFace is performed. Therefore, as a whole, there is no region where learning is not progressed with ArcFace, and a state can be established in which learning is reliably progressed with CosFace.

Furthermore, as the learning progresses, the angle θ between the feature vector x' and the weight vector W of the correct class becomes smaller. In the initial stage of learning, when the angle θ formed by the feature vector x′ and the weight vector W of the correct class is greater than a predetermined value _θTh (when the cos distance is smaller than _cosθTh ), margin addition processing by CosFace is applied. . After that, as the learning progresses, the formed angle θ becomes smaller. Then, the formed angle θ reaches a predetermined value _θTh , and the region of CosFace shifts to the region of ArcFace. After that, as learning by ArcFace progresses, a machine learning model 11 capable of highly accurate prediction is generated.

REFERENCE SIGNS LIST 1 data analysis system 2 storage device 3 arithmetic processing unit 21 machine learning model execution unit 23 weight vector acquisition unit 25 loss function calculation unit 26 learning processing unit

Claims (8)

A data analysis system configured by a computer device comprising an arithmetic processing device and a storage device,
The storage device is composed of a neural network, and outputs a feature vector using the weight vector of the fully connected layer at the final stage. store a machine learning model for classifying,
The arithmetic processing unit is
a machine learning model execution unit that outputs the feature vector by executing the machine learning model when learning data is input;
a weight vector acquisition unit that acquires the weight vector when the machine learning model execution unit outputs the feature vector;
when the angle θ between the feature vector and the weight vector of the correct class is smaller than a predetermined value, applying margin addition processing by ArcFace using the feature vector and the weight vector to calculate the value of the loss function; a loss function calculation unit that calculates a loss function value by applying margin addition processing by CosFace using the feature vector and the weight vector when the formed angle θ is equal to or greater than the predetermined value;
a learning processing unit that learns the machine learning model by a gradient method based on the value of the loss function;
A data analysis system comprising: In the margin addition processing by ArcFace and the margin addition processing by CosFace, when the formed angle θ is before and after the predetermined value, the value of the loss function is 2. The data analysis system according to claim 1, which is set to have a monotonically decreasing or monotonically increasing relationship with . In the margin addition processing by ArcFace and the margin addition processing by CosFace, when the formed angle θ is the predetermined value, the value of the loss function is continuous with respect to the cos distance between the feature vector and the weight vector of the correct class. 3. The data analysis system of claim 2, wherein the data analysis system is set to have a relationship of In the margin addition processing by ArcFace and the margin addition processing by CosFace, when the formed angle θ is the predetermined value, the value of the loss function is inconsistent with the cos distance between the feature vector and the weight vector of the correct class. 3. The data analysis system of claim 2, configured to have a sequential relationship. The value of the cos distance corresponding to the predetermined value is the cos distance when the value of the loss function with respect to the cos distance between the feature vector and the weight vector of the correct answer class in the margin addition processing by ArcFace becomes an extreme value. 5. The data analysis system according to any one of claims 1 to 4, wherein said predetermined value is set such that the value of . 6. The machine learning model according to any one of claims 1 to 5, wherein the machine learning model is a model for performing class classification based on a cos distance between the feature vector relating to the target image data and the feature vector relating to the class representative image data. Data analysis system as described. The machine learning model is a model used for appearance inspection of an industrial product, and determines whether the industrial product is a non-defective product or a defective product based on the input image data of the appearance of the industrial product. 7. The data analysis system of claim 6, which is a model for. The machine learning model calculates the cos distance between the feature vector related to the input image data and the feature vector related to the representative image data of the non-defective product, and the feature vector related to the input image data and the representative image of the defective product. 8. The data analysis system according to claim 7, wherein determination is made as to whether said industrial product is said non-defective product or said defective product based on the cos distance with said feature vector regarding data.

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