JP5262582B2 - Surface defect distribution form analysis apparatus, method, and program - Google Patents

Description

  The present invention relates to a distribution analysis device, method, and program for surface defects of thin plates, for example, surface defects such as wrinkles and dirt that occur in thin plate products that require a good appearance, such as the outer plate of automobiles and home appliances, etc. It belongs to a suitable technique used for analyzing the generation factor of the surface defect from the number and the generation position of the generation and the distribution form.

  In order to analyze the cause of surface defects such as wrinkles and dirt generated in steel products such as thin coil, the surface defects of coils passing through the process line are detected using, for example, an optical automatic wrinkle inspection device. Storing information about detected surface defects.

  In Patent Document 1, information on the distribution form of wrinkles is automatically extracted as a quantitative index from wrinkle data including at least the generation position generated and accumulated by an automatic wrinkle inspection device or the like generated in a thin plate coil, A method for analyzing the distribution pattern of surface defects of a thin plate is disclosed.

  In the thin-film surface defect distribution form analysis method disclosed in Patent Document 1, wrinkles are automatically grouped based on wrinkle data collected by an automatic wrinkle detection device. In that case, it would be useful if the situation where a linear distribution and an elliptical distribution were mixed could be handled with a unified index. The distribution form is expressed by a two-dimensional Gaussian function.

  The clustering method disclosed in Non-Patent Document 1 is a method for generating a cluster in which a portion considered to be noise is separated.

JP 2005-257660 A C. Bohm, C. Faloutsos, J. Pan, and C. Plant. Robust Information-theoretic Clustering. In KDD Conference, pages 65-75, 2006. D. Chakrabarti, S. Papafimitriou, D. S. Modha, and C. Faloutsos. Fully automatic cross-associations. In KDD Conference, pages 79-88, 2004. D.A.Huffman, "A Method for the Construction of Minimum-Redundancy Codes", Proceedings of the I.R.E., sept 1952, pp 1098-1102

  By the way, in a thin coil, it is necessary to distinguish between a dense distribution form and a sporadic distribution form. If the clustering method that cannot handle the sporadic distribution form as described above is used as it is when grouping moths together, an erroneous analysis result will be obtained in the cause analysis. By applying the method of Non-Patent Document 1, it is possible to represent a dense distribution form and a sporadic distribution form that need to be handled separately in a thin coil, but if the number of initial clusters is small, an appropriate cluster cannot be generated. If there are more, there is a problem that the calculation time increases in the order of the cube of the number of clusters.

  The present invention distinguishes sporadic distribution forms, and when grouping the surface defects of a thin plate in a natural manner, it is possible to generate appropriate clusters even if the number of initial clusters is different. Objective.

The surface defect distribution form analysis apparatus of the present invention is a surface defect distribution form analysis apparatus that analyzes the distribution form of surface defects generated on a thin plate, and inputs at least coordinate data relating to the surface defect occurrence position of the thin plate to be analyzed. Based on the coordinate data of the surface defect in which the concentrated distribution and the sporadic distribution input by the input unit are mixed, a predetermined clustering method is used to represent the surface defect distribution form of the thin plate. An initial cluster generation means for generating an initial cluster, and a compression cost for calculating a compression cost, which is an index for evaluating the goodness of the generated cluster, as an information amount when the coordinate data is compressed according to the cluster distribution form A calculation unit and an initial cluster generated by the initial cluster generation unit are intensively distributed based on the compression cost. Separation means for generating clusters separated into a combination of coordinate data having a sporadic distribution, and clusters including coordinate data having a intensive distribution generated by the separation means, and using the compression cost as a joint criterion and means for combining with said incorporating coordinate data constituting the separated sporadic distribution from the cluster in the separating means, as the coordinate data forming the intensive distribution of new or another cluster, said separating means Is a variance-covariance matrix generated by adjusting the average of the coordinate data of all points in the cluster as a weighting matrix that shows the variation of the coordinate data in the cluster, centered on the coordinates obtained by the adjustment average of the coordinate data in the cluster characterized in that the defined distance from the center by using the inverse matrix, to select the coordinate data forming the intensive distribution distance in ascending order To.
The surface defect distribution pattern analysis method of the present invention is a surface defect distribution pattern analysis method for analyzing the distribution pattern of surface defects generated on a thin plate, and inputs at least coordinate data relating to the generation position of the surface defect of the thin plate to be analyzed. Based on the input procedure and the coordinate data of the surface defect in which the concentrated distribution and the sporadic distribution input by the input procedure are mixed, a predetermined clustering method is used to represent the surface defect distribution form of the thin plate. An initial cluster generation procedure for generating an initial cluster, and a compression cost for calculating the compression cost, which is an index for evaluating the goodness of the generated cluster, as the information amount when the coordinate data is compressed according to the cluster distribution form A calculation procedure and an initial cluster generated by the initial cluster generation procedure are intensively distributed based on the compression cost. A separation procedure for generating a cluster separated into a combination of coordinate data having a sporadic distribution, and clusters including coordinate data having a concentrated distribution generated by the separation procedure, and using the compression cost as a joint criterion and a coupling procedure for coupling with, incorporated coordinate data forming the sporadic distribution separated from the cluster in the separation procedure, the coordinate data forming the intensive distribution of new or another cluster, the separation In the procedure, the variance covariance generated by the adjustment average of the coordinate data of all the points in the cluster is used as a weighting matrix that shows the variation of the coordinate data in the cluster centered on the coordinates obtained by the adjustment average of the coordinate data in the cluster It determines the distance from the center by using the inverse matrix of the matrix, especially the selection of coordinate data constituting the intensive distribution short distance forward To.
The program of the present invention is a program for causing a computer to execute a process of analyzing a distribution form of surface defects generated on a thin plate, and an input process for inputting at least coordinate data relating to the generation position of the surface defect of the thin plate to be analyzed; Based on the coordinate data of the surface defect mixed with the concentrated distribution and the sporadic distribution input by the input process, the initial cluster representing the distribution form of the surface defect of the thin plate is generated by using a predetermined clustering method. An initial cluster generation process, and a compression cost calculation process for calculating a compression cost, which is an index for evaluating the goodness of the generated cluster, as an information amount when the information compression of the coordinate data is performed according to the distribution form of the cluster, Based on the compression cost, the initial cluster generated by the initial cluster generation process is concentrated. Separation processing for generating clusters separated into a combination of cloth and sporadic coordinate data, and clusters including coordinate data having a concentrated distribution generated by the separation processing are combined to determine the compression cost. Coordinate processing using the reference and combining processing is performed by the computer, and the coordinate data forming the sporadic distribution separated from the clusters in the separation processing is used as coordinate data forming a concentrated distribution of new or different clusters. In the incorporation and separation process, a coordinate matrix obtained by adjusting the average of the coordinate data in the cluster is used as a weight matrix indicating the variation of the coordinate data in the cluster, and the coordinate data of all the points in the cluster is generated. The distance from the center is determined using the inverse matrix of the variance-covariance matrix, and the coordinate data with a concentrated distribution has a short distance. And selects sequentially.

  According to the present invention, the surface defects of the thin plates can be grouped in a natural form according to the density of the distribution. Even if the number of initial clusters is different, an appropriate cluster can be generated. As a result, the analysis accuracy of the distribution pattern of surface defects on the thin plate is enhanced, and feature extraction related to the distribution of surface defects such as the center of gravity position of the surface defect group, space size, and number density of surface defects can be extracted at high speed and in large quantities. It becomes possible to do.

Preferred embodiments of the present invention will be described below with reference to the accompanying drawings.
FIG. 1 is a diagram showing an example of the configuration of a thin plate surface defect distribution pattern analyzer according to the present embodiment. Hereinafter, defects will be referred to as 疵. 101 is a saddle data input unit, and the saddle data including at least the generated position information (coordinate data) measured by the automatic saddle inspection apparatus installed in the process line and inspection line of the thin coil that is a steel product, It functions as an input means for inputting to the apparatus via a computer-readable recording medium. The wrinkle data includes coordinate data relating to a wrinkle generation position with a certain reference position in the two-dimensional plane of the thin coil as the origin. When the coordinate in the rolling direction of the thin coil is x and the coordinate in the width direction is y, and N defects are generated in the thin coil, the coordinate data can be expressed by a matrix of N rows and 2 columns. In addition, the wrinkle data includes information for identifying whether each wrinkle is generated on the front surface or the back surface of the thin coil, the length and width in the rolling direction of the thin coil, etc. Contains information. Furthermore, information such as the dimension value in the rolling direction and the dimension value in the width direction of the ridge, the type of ridge, and the degree of hazard of the ridge may be included.

  102 is a bag data storage unit that stores and stores bag data input by the bag data input unit 101. And when analyzing, it has a function which takes out wrinkle data per coil according to the wrinkle distribution output instruction | indication input from the outside. In addition, if you want to analyze the wrinkle data separately for the front and back surfaces of the thin coil, separate the wrinkle data using the information on the generation surface of each wrinkle (information on whether the wrinkle is on the front or back surface) By doing so, only the information of the surface to be analyzed is extracted.

  103 is an arithmetic unit, which performs clustering based on the cocoon data input by the cocoon data input unit 101 and accumulated in the cocoon data storage unit 102, and performs arithmetic processing for converting the obtained clusters into feature quantities. Run. The calculation unit 103 includes an initial cluster generation unit 103a, a compression cost calculation unit 103b, a separation unit 103c, and a combination unit 103d. These units 103a to 103d group cocoons (clustering), and further It also functions as a feature amount calculation means for obtaining a feature amount related to the distribution of wrinkles such as the center of gravity position, space size, and number density of the wrinkle group (cluster). As to how to obtain the center of gravity position, space size, and number density of the cocoon group, for example, as disclosed in Patent Document 1, the center of gravity is obtained by averaging the coordinate data, and the center of gravity that covers the data that distributes the space size is covered. The existing technology is used so that two standard deviations, which are parameters of a two-dimensional Gaussian function centered on the position, are used, and the number density is the value obtained by dividing the number of cells in the group by the respective standard deviations indicating the space size. That's fine.

  The initial cluster generation unit 103a uses the clustering technique such as the K-means method based on the cocoon data input by the cocoon data input unit 101 and stored in the cocoon data storage unit 102, and sets the expected number of clusters as the lower limit. , Functions as an initial cluster generating means for generating an initial cluster representing the distribution form of ridges. Although the detailed description of the K-means method is omitted, the K-means method determines the center point of each cluster, obtains the distance between each saddle data in the cluster and the center point, and calculates the sum of the squares of the distances. This is a method of repeatedly reassigning the saddle data to each cluster and correcting the center point of the cluster by reassignment so as to minimize.

  Although described in detail later, the compression cost calculation unit 103b calculates a compression cost, which is an index for evaluating the goodness of the generated cluster, as an information amount when the coordinate data is compressed according to the cluster distribution form. It functions as a compression cost calculation means.

  As will be described in detail later, the separation unit 103c separates clusters obtained by separating the initial cluster generated by the initial cluster generation unit 103a into a set of coordinate data having a concentrated distribution and a sporadic distribution based on the compression cost. It functions as a separating means for generating.

  Although the details will be described later, the combining unit 103d functions as a combining unit that combines clusters including coordinate data having a concentrated distribution generated by the separating unit 103c using the compression cost as a combination determination criterion.

  Reference numeral 104 denotes an analysis result display unit that functions as an analysis result display unit that displays feature quantities related to the clustered wrinkle distribution based on the calculation result of the calculation unit 103 regarding the specified thin plate coil.

  Here, an overview of the clustering technique introduced in the present invention will be described.

  When a certain data set is considered, FIG. 2 (a) shows an example of clustering that seems to be good for many human senses. One cluster of Gaussian distribution, one cluster of linear distribution, and sporadically The point which has generate | occur | produced (henceforth an outlier point) is included. On the other hand, FIG. 2B shows an example of clustering by a general clustering method (for example, K-means method), and five clusters having Gaussian distributions including sporadic outliers are generated. Has been.

  The clustering method introduced in the present invention is an unsupervised cluster division method, and a new index of compression cost is introduced in order to realize clustering as shown in FIG. The compression cost is used as an index indicating whether it is appropriate to belong to one of the two clusters. For example, after grouping by the K-means method (specifying the number of clusters k), algorithms such as outlier separation and cluster combination are executed based on the compression cost.

In other words, using an index of compression cost indicating the goodness of the cluster,
(M1) Robust evaluation of cluster shape in the presence of outliers (M2) Identification of outliers based on compression cost, separation (M3) Algorithm of cluster construction by combination according to compression cost is executed.

<Compression cost>
The compression cost is the minimum average code length (in bits) when compression is performed using the appearance probability of the code before compression using one Huffman coding (see Non-Patent Document 3) of the information amount compression method. This is an application of the features.

When encoding is performed using a plurality of probability distributions prepared in advance (for example, arbitrary distributions such as Gaussian distribution, Laplace distribution, uniform distribution, etc.) instead of the occurrence probability of the occurrence position in the cluster, the code length is minimum. This probability distribution is the distribution that best represents the shape (feature) of the cluster.

  Furthermore, in addition to the compression cost due to the probability distribution of individual clusters, multiple clusters are identified such as the cluster center position, information indicating the form of the probability distribution, parameters indicating the probability distribution such as mean and variance, the number of data in the cluster, etc. The information for encoding is also encoded and compressed, and added to the compression cost. This can prevent excessive separation into a plurality of clusters.

  In the present invention, the information amount is compressed by using a probability distribution indicating the shape of the cluster, and the code length corresponding to the cluster number and the coordinate of the data point at that time and the other information amount necessary for encoding are used. Are defined as compression costs, and a method for generating a desired cluster by minimizing the compression costs is presented.

  The compression cost corresponding to the amount of other information necessary for encoding includes a code length indicating the number of clusters k, and a parameter indicating the shape of each cluster (for example, average and variance when the cluster is a Gaussian cluster). The code length shown is included. Details will be mentioned below.

  Since all the coordinate data handled here handle only finite precision, encoding is performed assuming that it is an integer. That is, the data point is assumed to exist on a d-dimensional grid. The resolution of the grid can be selected arbitrarily. For example, if the significant digits of the coordinate data are up to the first digit of the decimal point, the resolution of the grid represented by the grid constant may be set to 0.1 which is the minimum value of the first digit of the decimal point.

  The following method of the present application includes (a) an integer encoding method and (b) a point encoding method that once belongs to a cluster.

Assume that the user has the data set shown in FIG. Here, it is assumed that two distributions such as a Gaussian distribution and a uniform distribution (a uniform distribution with a minimum circumscribed rectangle as a range) can be used. Once a point is assigned to a cluster, it can be efficiently recorded with a small amount of data by applying Huffman coding (see Non-Patent Document 3) to the deviation from the cluster center.

(Integer encoding)
In order to encode a smaller integer with a smaller number of bits and a larger integer with a larger number of bits, the integer is encoded in a decimal notation. The basic notation method in the decimal notation is that zeros are arranged according to the size of a natural number. In the present application, an erasure code that is a decimal notation using 0 and 1 or a unicode encoding called a self-delimiting method (see Non-Patent Document 2) is used. In these encoding methods, since the positive integer i is expressed using the number of bits of O (log (i)), even if the integer value changes by a certain amount, the change in the number of bits after encoding changes. The smaller the previous integer value, the greater the change. It can be encoded as shown in Table 1 below. In the decimal notation, it consists of a part indicating the encoded length (code length) of the integer i and a part indicating the encoded value (code value). It should be noted that the first bit of the code value is always indicated by “1”. Since the code length indicating the encoded length of the integer i is indicated by the number of consecutive zero bits, the part indicating the code value has the same number of bits as the code length zero from the part where the bit is first “1”. Range. To handle zero that is not a positive integer, it can be handled by adding 1 to the value and encoding. In order to handle negative numbers, it can be expanded by adding a bit indicating the positive or negative value.

(Point coding)
For each cluster C, a flag R indicating the necessity of cluster decorrelation, a matrix Σ _* for performing decorrelation, and a flag T indicating the shape of cluster data distribution (arbitrary probability distribution is prepared in advance) For example, a Gaussian distribution, a Laplace distribution, and a uniform distribution) and their center coordinates and data distribution parameters are related. Once it is determined that the point P belongs to the cluster C, the coordinates of the point can be encoded using the fact that the point P follows the distribution of the cluster C. When the value of the probability of the i-th coordinate Pi of the point P is p, O (log (1 / p)) bits are required due to the encoding of the coordinates.

The number of bits at the time of encoding with a uniform distribution with a constant probability is defined as the range of the minimum circumscribed rectangle (the i-th dimension is represented by the lower limit lb _i and the upper limit ub _i ), and the minimum circumscribed rectangle It is determined by the number of bits of O (log (1 / (ub _i −lb _i ))) proportional to the range of.

  The purpose of the point coding is that the point x → of the cluster C that minimizes the compression cost when the point follows the cluster subspace and the cluster-specific probability distribution (in this specification, the notation a → → is assumed to mean that it is a vector). As will be described later, a probability density function that minimizes the compression cost is obtained by a correct selection.

  Here, it is assumed that the coordinates of the points of the cluster are decorrelated by coordinate transformation by principal component analysis (PCA), and a probability distribution is already selected from each coordinate together with a corresponding parameter. In the example of FIG. 3, the abscissa is a Laplace distribution and the ordinate is a Gaussian distribution. Both distributions assume a mean μ = 3.5 and a standard deviation σ = 1. It is necessary to encode the coordinate values and assign the necessary number of bits. That is, a short bit number (sign) is assigned to a coordinate value corresponding to a high probability (eg, 3 <x <4), and a long bit number (y = 12 as an extreme example) is assigned to a coordinate value corresponding to a low probability (y = 12 as an extreme example). (Sign).

If the probability distribution indicated by the flag T indicating the shape of the data distribution of the cluster matches the data distribution, the number of bits (code length = compression cost) by Huffman coding is minimized. Huffman coding assigns a number of bits P when (x _i) is the value of the probability density function for each coordinate value, the length log ₂ to each of the coordinates _{x i (1 / P (x} i)).

(Calculation method of compression cost)
Here, the compression cost of the cluster C is defined according to the following four definitions.
Definition 1 (compression cost E of point x →)
Suppose x → ∈R ^d belongs to cluster C, and pdf → (x →) is a d-dimensional vector of the probability density function of cluster C. The probability density function pdf _i (x _i ) of each coordinate is represented by a corresponding parameter (ie, PDF = {pdf _Gauss ( _ui, σ _i) , pdf uniform _{(lbi, ubi)} , pdf rough _{(ai, bi) ,.} ..}, A set of predetermined probability density with mean u _i , lower limit lb _i , upper limit ub _i , one-sided mean a _i ∈R, standard deviation σ _i , standard deviation b _i ∈R ^{+ of} √2) Selected from functions. γ is a grid constant (grid resolution, that is, a distance between grids), the compression cost E _i of the point x → on the coordinate axis _i is expressed by the following equation (1), and the compression cost of the point x → is expressed by the following equation ( 2).

In the hatched exemplary position of FIG. 3, the probability of the x coordinate (between 2 and 3) is 19%, and Huffman coding requires log ₂ (1 / 0.19) = 2.3 bits. The y coordinate is at a lower probability (5%) and requires a larger number of bits (4.3 bits). The compression cost of the point x → is log ₂ (n / |) indicating the cluster number to which the cluster belongs in addition to 6.6 bits which is the total number of bits of the x coordinate and the y coordinate. C |) bit is added.

(Determining the probability density function that fits the cluster)
Next, which probability density function is assigned to cluster C is shown. The ultimate goal is to minimize the compression cost (number of bits). Therefore, it is necessary to select a probability density function pdf (and corresponding parameters) that minimizes the cluster compression cost for each coordinate axis. As for the probability density function pdf such as Gaussian distribution, it is known that the optimum parameters correspond to the statistics of the data set (for example, average, variance σ _i ² , upper and lower limit values).

Therefore, when a Gaussian distribution is selected as the probability density function pdf of the coordinate axis i, the mean u _i and the variance σ _i ² of the point coordinate axis i are used as parameters of the probability density function. Similarly, for the Laplace distribution, the mean u _i and the variance 2σ _i ² are applied. For the uniform distribution, the upper limit ub _i and the lower limit lb _i of the coordinate value range are applied. A probability density function that minimizes the cluster compression cost is selected from these probability density functions PDF such as a Gaussian distribution, a Laplace distribution, and a uniform distribution prepared in advance.

Definition 2 (pdf of cluster C → (x →))
Let C be a cluster of points x → ∈C. Let Stat = (u _i , σ _i , lb _i , ub _i ...) Be a statistic required by a probability density function PDF prepared in advance. At this time, the probability density function that minimizes the compression cost is selected from pdf _i ∈ PDF, as shown in the following equation (3).

For the x coordinate in FIG. 3, the average (3.5), variance (1.0), and upper and lower limits (1.4, 6.2) are calculated as statistics. Thereafter, compression costs E _x is previously prepared probability density function to the appropriate statistics the applied pdf uniform in the x-coordinate _(1.4,6.2), pdf mosquito Bu mouse _(3.5,1.0), in the pdf Rough ° lath _(3.5,0.7) selecting the minimum probability density function to be compressed cost E _x from. The probability density function is selected in the same procedure for the compression cost E _y for the y coordinate. Here, three distributions such as a Gaussian distribution, a Laplace distribution, and a uniform distribution are taken up, but other probability density functions can also be used.

(Encoding using decorrelation matrix)
If the clusters are correlated with each other on different coordinate axes, that is, if a coordinate value of a point of the cluster depends on at least one other coordinate value, compression is performed by converting to a new coordinate axis using a decorrelation matrix In some cases, the cost can be reduced. The decorrelation matrix can be calculated as, for example, a matrix composed of principal components calculated by principal component analysis (PCA) of the cluster covariance matrix Σ or an eigen matrix V of the cluster covariance matrix Σ. A method for evaluating the variance-covariance matrix in a robust manner that is less susceptible to outliers (outliers when focusing on one coordinate axis) will be described later.

  Decorrelating the data is necessary to reduce the compression cost of the cluster. Instead of having two coordinates with large variance and high correlation, if two new coordinates that are not correlated with each other are generated, for example, if one new coordinate can be converted to a coordinate value with variance close to 0, the probability of one grid Therefore, the average code length is expected to be a compression cost of almost 0 bits. Therefore, when considering improvement in compression cost, a decorrelation matrix is used.

Definition 3 (cluster decorrelation)
The decorrelation matrix is calculated by principal component analysis (PCA) of cluster C, where C is a cluster of points x (original coordinates that have not been decorrelated) and the covariance matrix Σ of cluster C. It is assumed that the matrix VΛ ^−1/2 is composed of principal components (Σ = VΛV ^T ). Alternatively, suppose that a matrix obtained by diagonalization (Σ = VΛV ^T ) with eigenvalues and eigenvalues of the variance-covariance matrix Σ of the cluster C is defined as a decorrelation matrix V. Let Y be represented as a set of uncorrelated points y, ie y → ∈Y: y → = V ^T · x →. Let pdf → (x →) be a probability density function (probability distribution) characterizing the uncorrelated set Y in the original coordinate system, and pdf → (y →). The decorrelation matrix finally used is determined based on the compression cost. The decorrelation matrix dec (C) of cluster C is expressed by the following equation (4), and the corresponding compression cost is expressed by the following equation (5). It is.

When encoding a decorrelation matrix V of d rows × d columns, if a small number is expressed by a code length f bits, each element is encoded by a total of d ² f bits. Therefore, decorrelation is performed when the reduction in compression cost due to decorrelation exceeds this. When decorrelation is unnecessary, a unit matrix is used instead of the decorrelation matrix, and only one bit corresponding to a flag indicating the presence or absence of decorrelation is added to the compression cost.

Definition 4 (cluster compression cost)
Definition 4 summarizes the above items. When the cluster C is encoded, it is performed using a decorrelation matrix dec (C) and a probability density function pdf → (y →) representing each decorrelated coordinate y →. The compression cost of cluster C is expressed by the following equation (6).

  As described above, the compression cost calculation unit 103b calculates the compression cost represented by the above equation (6) based on the bag data input by the bag data input unit 101 and stored in the bag data storage unit 102. To do.

<Separation of outliers>
In the present application, a cluster obtained by a conventional method is regarded as consisting of two subsets. One is a set of data (core points) indicating the core of a concentrated distribution, and the other is a set of data (outliers) having a sporadic distribution.

  In a general clustering method such as the K-means method or the K-medoids method, a cluster in which core points and outliers are mixed may be generated, and the cluster may be difficult to capture features.

  Therefore, the outliers are separated from the once generated cluster (initial cluster).

The most reliable method is that when there are N points of coordinate data, there are 2 ^N combinations for classifying the core points and outliers. The compression cost is calculated for each combination, and the combination of the core point and the outlier point that minimizes the compression cost is adopted. However, since the amount of calculation increases exponentially with respect to the number of coordinate data, if it exceeds a certain number, it is difficult to finish the calculation in a realistic time.

  Thereafter, the coordinate data is ranked so that the calculation is completed in a realistic time even if the number exceeds a certain number, and the calculation amount required to separate the core point from the outlier point is proportional to N. Provide a method.

  As a ranking method, the calculation is based on the distance from the center of the core point. In the following, core points and outliers are selected by boundaries defined by distances instead of ranks. The definition of the distance uses a plurality of definitions to determine the outline of the core point.

The method of separating the core point and the outlier by the distance by the weight matrix indicating the distribution of the distribution of coordinate data in the cluster is a cluster group C = {C ₁ , calculated by an arbitrary clustering method (for example, K-means method). ..., and calculates the orthonormal matrix V (referred to as "decorrelation matrix V ') defining a subspace for a cluster C _i of C _k}. A weight matrix using the decorrelation matrix V is calculated, and a distance for determining a boundary separating the core point and the outlier point is determined. A boundary (ellipse) that is equidistant from the center of the cluster where the sum of the compression costs of the core points and outliers in the cluster C _i is the minimum value is selected, and as a result, a new cluster that separates outliers from the cluster is selected. Generate. At this time, the center of the cluster uses coordinates obtained by average of coordinate data or adjustment average.

Hereinafter, the weight matrix for determining the distance will be described in detail. First, one of the weight matrix evaluation methods will be described. Weight matrix of the cluster C _i uses the inverse matrix of the variance-covariance matrix ^{(Σ -1 = V∧ -1 V T} ) as defining a space containing the points belonging to the cluster C _i. When the inverse matrix cannot be directly calculated, a matrix that changes to this is calculated by using a principal component by principal component analysis (PCA). Also, when expressed using the diagonal matrix cluster C _i covariance matrix of points belonging to Σ Alternatively by eigenvalues orthonormal matrix V is obtained consisting of eigenvectors. This matrix V is the decorrelation matrix described above. The decorrelation matrix V defines the space (new coordinate axis) in which the points of the cluster C _i are included, and the eigenvalue determines the shape of the boundary ellipse (elliptical sphere) composed of equal distances, which will be described later. Since all eigenvalues of the diagonal matrix ∧ are positive, the variance-covariance matrix Σ and its inverse matrix Σ ⁻¹ are semi-positive definite matrices. That is, when a vector connecting two points is x, it is always positive when expressed in a quadratic form like x ^t Σ ⁻¹ x, and even in a multidimensional space, it is as if the distance between two points A value (pseudorange) can be defined. For example, considering the cluster structure (covariance), the distance between the two points x → and y → can be defined as the Mahalanobis distance as shown in the following equation (7).

If the center of the cluster C is given as μ →, the variance-covariance matrix Σ can be evaluated by calculating the matrix Σ _C by the following equation (8). Note that | C | is the number of data points of cluster C. (X → −μ →) · (x → −μ →) ^T is an outer product of vectors, and is a matrix of d × d. Since all of x → (εC) are calculated and averaged with the number of data points | C | of the cluster C, Σ _C is an i-th row and j-th column element (Σ _C ) _ij is the i-th coordinate and j-th (X _i −u _i ) · (x _j −u _j ).

  Here, since the outlier is included in the above calculation method, there arises a problem that the core point and the outlier can not be separated as desired. In order to perform the desired division, it is necessary to accurately estimate the center of the core point and the variance-covariance matrix, as will be described in detail later. However, the center of the cluster C calculated by a simple average may deviate from the center of the core point due to the presence of an outlier. If the center different from the center of the core point is followed, the space generated by the decorrelation matrix V based on the variance-covariance matrix, that is, the “spread of the core point” that is a candidate for the boundary between the core point and the outlier point is evaluated. Outliers can also affect the direction of the ellipse. Even when the number of outliers is one, the center of the core point to be estimated and the decorrelation matrix may be greatly affected. FIG. 4 shows a state in which the center is erroneously estimated by the conventional evaluation and the ellipse representing the covariance of the data is shifted from the core point.

(Method for estimating the robust center μ _R → of the core point)
When determining the center, an α adjustment average of each coordinate is independently determined for a robust center in the sense that it is not easily affected by an outlier. Here, the α-adjusted average is a method of performing averaging using a portion obtained by excluding data corresponding to upper α / 2% and lower α / 2% of the number of data from target data. That is, the median corresponds to the case where α is brought close to 100 and only the last one point remains. The value of α may be set to the ratio of the core points in the assumed initial cluster. As a result, the origin (μ _R →) of the data by the median is closer to the center of the central point of the cluster than the center (μ →) of all the points.

(Robust weighting matrix core point (variance-covariance matrix) sigma _R estimation method)
Similarly, robust preparative variance-covariance matrix (Σ _{R) ij} is as produced by α adjusted mean of all points in the cluster x → for the _{(x i -μ Ri) · (} x j -μ Rj) Yes. The adjusted average is an average obtained by arranging numerical values to be averaged in order of magnitude and using data near the median value except for data of a fixed ratio α from the head or tail. The value of α may be set to the square of the assumed ratio of the core points in the initial cluster. It can be expected that the matrix Σ _R reflects the covariance of the core point compared to the covariance matrix by arithmetic mean.

The covariance matrix Σ _C by arithmetic mean is diagonally dominant (= positive definite matrix). That is, each diagonal component Σ _{i, i} is larger than the sum of the other elements Σ *, i. In addition, all eigenvalues of the corresponding diagonal matrix Λ are positive.

On the other hand, if the robust covariance matrix sigma _R is not a diagonal dominant matrix, if a value expressed in a quadratic form becomes negative occurs, you can not define distance. Therefore, by adding a unit matrix φ · I multiplied by φ, calculation is possible without affecting the decorrelation matrix V. φ is given by the following equation (9). The value of φ is represented by the maximum difference between the sum of the columns and the diagonal component (a value of about 10% may be added).

By adding the matrix φ · I, the eigenvalue is affected, but the eigenvector is not affected. When Σ = VΛV ^T , Σ + φ · I = VΛV ^T + φ · I. Since V is orthonormal, φ · I can also be described as VφIV ^T, and according to the distribution rule, Σ + φ · I = V (Λ + φ · I) V ^T , that is, even if each eigenvalue increases. The decorrelation matrix V is not affected.

(Conversion that reflects the features of the core points in the weight matrix)
In the above description, since the distance is determined based on the variance-covariance matrix and the core points are selected in order of increasing distance, the boundary that forms the outer shape of the cluster (core point) is an ellipse (elliptical sphere). For this reason, when separating clusters (core points) that are difficult to represent with ellipses such as straight lines, there are cases in which some of the outliers cannot be separated. The present application provides a weight matrix conversion method according to a probability distribution used for calculating a compression cost of a cluster (core point).

  A method of extracting a cluster having a shape other than an ellipse by modifying a weight matrix will be described. The eigenvalue of the weight matrix is a value proportional to the lengths of the major axis and the minor axis of the ellipse indicating the outer shape of the cluster. Therefore, by changing the eigenvalue and changing the ratio of the length of the major axis to the minor axis, by changing the shape of the boundary, to the core point of the point you want to be the outlier, or Reduce contamination at outliers.

  The weight matrix is decomposed by diagonalization, and distances are determined using a matrix obtained by reconstructing the weight matrix using diagonal elements converted by a function corresponding to the distribution form of the cluster, and a candidate for the core point is selected. Specifically, the weight matrix is decomposed into an eigen matrix and a matrix having eigen values as diagonal elements, and the eigen values are converted by a function corresponding to the cluster distribution form used when calculating the compression cost. Using the converted values as elements of a new diagonal matrix, the weight matrix is reconstructed and used for distance calculation.

When the weighting matrix Σ is diagonalized, the following equation (10) is shown using a matrix と す る having eigenvalues as diagonal elements and the eigenmatrix V:
Σ = V∧V ^T (10)

At this time, if the weight matrix Σ is not diagonally dominant, the unit matrix φ · I multiplied by φ is added to the matrix と す る having eigenvalues as diagonal elements. The value φ is set such that the ratio between the eigenvalues does not change so much by this operation.

  When calculating the compression cost, a probability distribution is determined for each eigenvector corresponding to the eigenvalue. When changing the ratio of the eigenvalues, the eigenvalues are changed according to the probability distribution used when calculating the compression cost. At this time, since the inverse matrix of the weight matrix is used when calculating the distance for determining the order of selecting the core points, the larger the eigenvalue of the weight matrix, the smaller the reciprocal of the eigenvalue becomes, and the change of the distance in the corresponding direction changes. Get smaller.

  When changing the ratio based on the normal distribution, if the distribution is uniform, even if the deviation from the average is large, the probability does not change, i.e. we want to eliminate the difference in distance. By increasing the apparent variance with a monotonically increasing function (for example, multiplying by a constant with a linear function) or not using it to calculate the distance so as not to affect it, the distance is estimated short at both ends of the uniform distribution. be able to. If it is Laplace distribution, the probability will change greatly if it is slightly off the average, that is, change the apparent variance by a monotonically decreasing function (for example, by gradually subtracting with a constant). Thus, the distance can be changed greatly even when slightly deviating from the average. Here, the constant is a positive real number exceeding 1, and is set according to the shape of the core point to be extracted. In some cases, a constant may be determined for each probability distribution.

As another method for converting the eigenvalue, there is a method of preparing and applying a common function regardless of the cluster distribution form used when calculating the compression cost. When the compression cost is minimized, the probability distribution to be applied tends to be determined by the size of the variance (or eigenvalue). Therefore, a function whose ratio changes so that a large eigenvalue is further increased and a small eigenvalue is further decreased may be prepared. For example, the power function f (x) = x ^r may be used. The power coefficient r is determined to be a positive real number larger than 1.

  As described above, it is possible to perform conversion that reflects the feature of the core point in the weight matrix.

  FIG. 7 shows in two dimensions three-dimensional coordinate data in which straight clusters (400 points) and other outliers (100 points) are distributed. First, the core points and outliers are separated by the above method, and the probability distribution to be applied to the core points when calculating the compression cost is determined.

With the above robust evaluation method, as shown in FIG. 4, the center can be accurately determined, and the ellipse represented by the variance-covariance matrix can be set as the distribution of the core points. As shown in FIG. 5, the proper decorrelation matrix V is composed of eigenvectors indicating the dispersion direction of the core points of the cluster. Coordinate conversion can be performed by multiplication of V ^T to remove the correlation between the coordinates.

(Separation of core points and outliers)
Next, separation of the core points and outliers will be described. The distance is determined using the above-described various covariance matrices as a weight matrix. Next, the distance from the center (boundary) to the predetermined distance (boundary) is temporarily determined as the core point, and the rest is deviated, and the compression cost is repeatedly calculated when the boundary is changed. Among them, the boundary with the lowest compression cost is used to separate the core point and the outlier point.

Details are described below. First, an appropriate decorrelation matrix that determines the boundary is obtained. That is, from the candidate variance-covariance matrix, one with the optimum compression cost is selected. The candidate variance-covariance matrix includes the normal variance-covariance matrix, the matrix Σ _R by the robust method described above, the matrix Σ _C by the conventional method, and a weight matrix obtained by transforming each according to the probability distribution. Is included.

Furthermore, using the Mahalanobis distance defined by the robust center μ _R → and the robust variance-covariance matrix Σ _R , a point close to the center of the cluster is selected, and the source of the decorrelation matrix calculation Is calculated as a covariance matrix and added to the candidates. A number corresponding to a certain ratio (for example, 50%) in the cluster is selected from points close to the center μ _R → from the target cluster, and the matrix Σ _{C, 50} that is a candidate by conventional covariance based on the selected point Compute a matrix Σ _{R, 50} that is a candidate with a robust α-adjusted average. Further, there is a unit matrix I as a candidate for a decorrelation matrix when decorrelation is not performed. Among these matrices {Σ _C , Σ _R , Σ _{C, 50} , Σ _{R, 50} , I}, the matrix Σ * that gives the optimal (minimum) compression cost is selected. In the example of FIG. 4, the minimum value of the compression cost is 1600 in the conventional evaluation, whereas the minimum value of the compression cost is 1480 in the robust evaluation.

Next, find outliers in the cluster. So far, the center μ _R → of the core point has been obtained, and the candidate covariance matrix Σ * (corresponding decorrelation matrix V *) has been selected. The ultimate goal is to divide the cluster into two new sets: a set of core points (cluster) C core points and a set of outlier points C. Based on the Mahalanobis distance determined by the variance-covariance matrix Σ *, the boundary between the two is determined and divided into two sets. First, with all points as outliers (outer C point = C, C core point = {}), based on the Mahalanobis distance, a point x → at a distance close to the center μ _R → of the core point is removed from the set C outlier point. Repeatedly remove and incorporate into set C core. At that time, the compression cost before and after the movement of the point x → is calculated.

  In each iteration, the point x → that has moved from the point outside the set C to the core point of the set C moves to the space defined by the selected decorrelation matrix V *. Then, the compression cost due to the new division of the set (C core point ∪ {x →}, outer C point− {x →}) is determined using a probability distribution that leads to the minimum compression cost. The compression cost for outliers is encoded using a uniform distribution.

  In selecting such a set, the boundary that separates the core point and the outlier point is defined as an ellipse having a constant Mahalanobis distance by a decorrelation matrix, and the two sets are determined by dividing the ellipse into the inside and outside. In FIG. 4, the minimum (1480) is a set of 24 core points and 6 outliers.

FIG. 4 shows transitions of two compression costs corresponding to the conventional decorrelation matrix V _c and the robust decorrelation matrix V _R. In the initial stage, all points are set as outliers, and the compression cost is about 1800. As the point moves from the point outside the set C to the core point of the set C, the compression cost decreases. In the compression cost corresponding to the robust decorrelation matrix V _R , when the number of core points is 24, the minimum value is 1480. Thereafter, the compression cost again increases to about 1800.

  As described above, the separation unit 103c separates the initial clusters generated by the initial cluster generation unit 103a based on the compression cost, and includes the set C core points including data (core points) having a concentrated distribution. And out-of-set C points including data (outliers) having a sporadic distribution.

<Cluster join>
The combination of clusters is to change the division position and the number of divisions by an arbitrary clustering algorithm (for example, K-means method). Due to the shortcomings of clusters resulting from the algorithm, clusters that contain points that are originally part of another cluster may be generated. Therefore, a method of correcting an incorrect division caused by the conventional clustering method by cluster connection will be described.

  For example, in the K-means method, a cluster that should originally be one may be erroneously separated into a plurality. The algorithm of the proposed method corrects erroneous separation by performing cluster connection.

Again, the compression cost is used when combining two clusters, and it is determined whether or not the compression cost is reduced by combining a pair of clusters. That is, for the pair of clusters (C _i , C _j ), a reduction cost reduction cost (C _i , C _j ) is defined as shown in the following equation (11).

Reduction amount of compression cost due to cluster coupling When reducecost (C _i , C _j )> 0, it is assumed that there is a possibility of coupling to a pair of clusters (C _i , C _j ).

This procedure follows the greedy method and is repeated as long as there is a reduction in compression cost. In each iteration, two clusters having the largest reduce cost (C _i , C _j ) are combined to search for a cluster having the smallest compression cost. In addition, in order to avoid a deadlock due to a local minimum, the calculation is not stopped immediately even if there is no decrease in reducecost (C _i , C _j ). That is, even if reducecost (C _i , C _j ) ≦ 0, the algorithm is not stopped. Instead, the algorithm continues in another iteration of t, and reducecost (C _i , C _j ) becomes negative, that is, even if compression costs by the binding of C _i and C _j is increased, continues to bind the clusters (C _i, C _j) at the maximum _{reducecost (C i, C j)} .

  As described above, the combining unit 103d combines the core points of the cluster C including the data having a concentrated distribution generated by the separation unit 103c based on the compression cost.

  In addition, as a unique algorithm for reducing the calculation time when the number of initial clusters is larger than the appropriate number of initial clusters, the candidate cluster to be combined is based on the Delaunay diagram at the previous stage of cluster combination by the above calculation. To determine a set of adjacent clusters. Since the surface defects of the thin plate handled in the present invention are distributed two-dimensionally, it is possible to use a Delaunay diagram. Specifically, using the center of the cluster as a generating point, first select 4 generating points and create two triangles. Each triangle is a Delaunay triangulation and the circumscribed circle contains the vertices of the other triangles. If not, change the triangle division method. Add one more point, pay attention to the triangle including the added point, and divide it into triangles to confirm that it is a Delaunay triangulation. If this is the case, change the method of dividing the triangle. Further, generating a Delaunay diagram is performed by adding successive generating points and repeating until there are no generating points to be added and a Delaunay triangulation is performed. Clusters corresponding to generating points connected by Delaunay edges shown in the Delaunay diagram are set as candidates for connection. Thus, by determining candidates using Delaunay diagrams, the amount of calculation can be greatly reduced.

  Further, when the number of initial clusters is smaller than the appropriate number of initial clusters, as a unique algorithm of the present invention, outliers separated from clusters at the stage of outlier separation or cluster combination are incorporated into another cluster. For this purpose, the separated points are collected and treated as a virtual new cluster, and whether there is a point that can be incorporated into the core point is reduced cost reduction amount of the cluster consisting of the virtual cluster and the core point reducecost If this becomes large, a part of the detachment point is taken in again as the core point of another cluster. If a cluster composed of core points can be generated from a virtual cluster, a new cluster can be obtained.

  As described above, based on the coordinate data relating to the generation position of the eyelid data collected by the automatic eyelid inspection apparatus, the eyelids can be automatically grouped, for example, the center of gravity position of the eyelid group, the space size, It is possible to extract features related to the distribution of wrinkles such as the number density of wrinkles at high speed and in large quantities. In this case, calculation processing is performed so as to be optimal based on the index, and therefore it is possible to extract an objective and quantitative feature amount with high reproducibility compared to human analysis processing. Therefore, for example, analysis using a large amount of soot distribution data, such as correlation analysis between soot generation positions and operating conditions, can be quickly performed.

  Moreover, as described above, by separating the sporadic data (outliers) from the initial cluster, generating clusters containing data with a concentrated distribution, and combining the clusters, It is possible to group cocoons together in a natural way. As a result, the analysis accuracy of the wrinkle distribution form can be improved, and the feature amount relating to the wrinkle distribution can be extracted at high speed, in large quantities, and accurately.

  FIG. 6 is a diagram showing an example of the distribution of wrinkles generated in the thin coil, where the horizontal axis indicates the longitudinal position of the thin coil and the vertical axis indicates the width direction position. FIG. 6A shows the result of the technique disclosed in Patent Document 1, and three elliptical distributions centered on □ are extracted. On the other hand, FIG. 6 (b) shows the result of the method according to the present invention, which is separated into a core point with a concentrated distribution and an outlier point with a sporadic distribution, and is generated in a straight line. The cocoon group to be able to be extracted accurately. Based on this, it was possible to prevent the production of a large number of defective products by taking measures in the process that causes the generation of defects.

(Other embodiments of the present invention)
In order to operate various devices to realize the functions of the above-described embodiments, program codes of software for realizing the functions of the above-described embodiments are provided to an apparatus or a computer in the system connected to the various devices. What is implemented by operating the various devices according to a program supplied and stored in a computer (CPU or MPU) of the system or apparatus is also included in the scope of the present invention.

  In this case, the program code of the software itself realizes the functions of the above-described embodiments, and the program code itself and means for supplying the program code to the computer, for example, the program code are stored. The recorded medium constitutes the present invention. As a recording medium for storing the program code, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.

  Further, by executing the program code supplied by the computer, not only the functions of the above-described embodiments are realized, but also the OS (operating system) or other application software in which the program code is running on the computer, etc. It goes without saying that the program code is also included in the embodiment of the present invention even when the functions of the above-described embodiment are realized in cooperation with the embodiment.

  This technique is mainly used to analyze the cause of defective products due to surface defects in the manufacture of steel sheet products.

It is a figure which shows an example of a structure of the distribution form analyzer of the surface defect of the thin plate of this Embodiment. It is a figure which shows the example of clustering. It is a figure for demonstrating the example of compression cost. It is a figure which shows the result which compared the conventional method and the robust method, (a) is a figure which shows the relationship between the ellipse showing data and its covariance, (b) is the number of core points, and compression cost It is a characteristic view which shows a relationship. It is a figure for demonstrating a decorrelation matrix. It is a figure which shows an example of distribution of the wrinkles which generate | occur | produced in the thin plate coil. It is a figure showing the three-dimensional coordinate data in which the cluster (400 points) of a straight line and the other outlier (100 points) are distributed.

Explanation of symbols

101 疵 data input unit 102 疵 data storage unit 103 calculation unit 103a initial cluster generation unit 103b compression cost calculation unit 103c separation unit 103d combination unit 104 analysis result display unit

Claims (8)

In the surface defect distribution form analyzer that analyzes the distribution form of surface defects generated in the thin plate,
An input means for inputting at least coordinate data relating to the occurrence position of the surface defect of the thin plate to be analyzed;
Based on the coordinate data of the surface defect mixed with the concentrated distribution and the sporadic distribution input by the input means, an initial cluster representing the distribution form of the surface defect of the thin plate is generated using a predetermined clustering method. Initial cluster generation means to
A compression cost calculating means for calculating a compression cost, which is an index for evaluating the goodness of the generated cluster, as an information amount when information compression of coordinate data is performed according to the distribution form of the cluster;
Separating means for generating clusters obtained by separating the initial clusters generated by the initial cluster generating means into a combination of coordinate data having a concentrated distribution and a sporadic distribution based on the compression cost;
A combination unit that combines clusters including coordinate data having a concentrated distribution generated by the separation unit using the compression cost as a combination determination criterion;
Incorporating sporadic coordinate data separated from clusters in the separating means as coordinate data forming a new or intensive distribution of another cluster ,
The separation means is a variance generated by adjusting the average of the coordinate data of all points in the cluster as a weighting matrix centering on the coordinates obtained by the adjustment average of the coordinate data in the cluster and indicating the variation of the coordinate data in the cluster. A surface defect distribution pattern analysis apparatus , wherein a distance from a center is determined using an inverse matrix of a covariance matrix, and coordinate data having a concentrated distribution is selected in ascending order of distance . Feature quantity calculation means for calculating at least one of the center of gravity position, the space size and the number density of the clusters generated by each means as a feature quantity;
The surface defect distribution form analysis apparatus according to claim 1, further comprising an analysis result display unit configured to display a calculation result obtained by the feature amount calculation unit.   The separation means, as a procedure for selecting coordinate data having a concentrated distribution, selects from a combination obtained by designating whether individual coordinate data belongs to a concentrated or sporadic distribution. Item 3. A surface defect distribution pattern analyzer according to Item 1 or 2. The said separating means uses the inverse matrix of the matrix which is an adjustment average of the value which calculated | required the product of the deviation from an average using the variable whose matrix element has two variables to the said weight matrix . The surface defect distribution form analyzer according to any one of the preceding claims. The separation unit decomposes the weight matrix into an eigen matrix and a matrix having eigen values as diagonal elements, and reconstructs the weight matrix by using values obtained by converting eigen values by a function according to a cluster distribution form used when calculating the compression cost. 5. The surface defect distribution form analysis apparatus according to claim 1 , wherein the matrix is used. It said coupling means, the distribution form analyzer of surface defects according to any one of claims 1 to 5, characterized in that determined on the basis of the Delaunay diagram showing a candidate clusters of adjacencies of the cluster to which it binds. In the surface defect distribution form analysis method for analyzing the distribution form of surface defects generated in a thin plate,
An input procedure for inputting at least coordinate data regarding the occurrence position of the surface defect of the thin plate to be analyzed;
Based on the coordinate data of the surface defect mixed with the intensive distribution and the sporadic distribution input by the input procedure, the initial cluster representing the distribution form of the surface defect of the thin plate is generated by using a predetermined clustering method. Initial cluster generation procedure to
A compression cost calculation procedure for calculating a compression cost, which is an index for evaluating the goodness of the generated cluster, as an information amount when information compression of coordinate data is performed according to the distribution form of the cluster;
A separation procedure for generating a cluster obtained by separating the initial cluster generated by the initial cluster generation procedure into a combination of coordinate data having a concentrated distribution and a sporadic distribution based on the compression cost;
A joining procedure for joining clusters including coordinate data having a concentrated distribution generated by the separating procedure using the compression cost as a joining criterion;
Incorporating sporadic coordinate data separated from the clusters in the separation procedure as coordinate data forming a new or intensive distribution of another cluster ,
In the separation procedure, the variance generated by the adjustment average of the coordinate data of all the points in the cluster as a weight matrix indicating the variation of the coordinate data in the cluster centered on the coordinates obtained by the adjustment average of the coordinate data in the cluster A surface defect distribution pattern analysis method, wherein a distance from a center is determined using an inverse matrix of a covariance matrix, and coordinate data having a concentrated distribution is selected in order of increasing distance . In a program for causing a computer to execute a process of analyzing a distribution form of surface defects generated in a thin plate,
Input processing for inputting at least coordinate data relating to the occurrence position of surface defects of the thin plate to be analyzed;
Based on the coordinate data of the surface defect mixed with the concentrated distribution and the sporadic distribution input by the input process, the initial cluster representing the distribution form of the surface defect of the thin plate is generated by using a predetermined clustering method. Initial cluster generation processing to
A compression cost calculation process for calculating a compression cost, which is an index for evaluating the goodness of the generated cluster, as an information amount when the coordinate data is compressed according to the distribution form of the cluster;
A separation process for generating a cluster obtained by separating the initial cluster generated by the initial cluster generation process into a combination of coordinate data having a concentrated distribution and a sporadic distribution based on the compression cost;
Causing a computer to execute a joining process for joining clusters including coordinate data having a concentrated distribution generated by the separation process using the compression cost as a joining criterion;
Incorporating sporadic coordinate data separated from clusters in the separation process as coordinate data forming a new or another cluster intensive distribution ,
In the separation process, the variance generated by the adjustment average of the coordinate data of all the points in the cluster as a weight matrix indicating the variation of the coordinate data in the cluster centered on the coordinates obtained by the adjustment average of the coordinate data in the cluster A program characterized by determining a distance from the center using an inverse matrix of a covariance matrix and selecting coordinate data having a concentrated distribution in order of increasing distance .

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