JP2021039580A - Information processing apparatus, information processing method, and program - Google Patents

Abstract

To put label propagation into practical use in semi-supervised learning using multidimensional Delaunay division.SOLUTION: A data acquisition unit 30 acquires a labeled data group in which data is with a label indicating a class that data belongs and an unlabeled data group for which the class that the data belongs is unknown. A matrix calculation unit 31 calculates a metering matrix formed by arranging metering vectors that have metering elements indicating similarity between the data. A matrix compression unit 32 generates a compression metering matrix formed by arranging compression metering vectors that are obtained by compressing the dimensions of each metering vector forming the metering matrix. A division unit 33 performs multidimensional Delaunay division for points that each of the compression metering vectors is mapped in multidimensional space. A adjacency matrix acquisition unit 34 acquires connection relationship of each point after the Delaunay division as an adjacency matrix. A label propagation unit 35 propagates the label to each data forming the unlabeled data group based on the adjacency matrix and the labels of the labeled data group.SELECTED DRAWING: Figure 1

Description

The present invention relates to an information processing apparatus, an information processing method, and a program, and more particularly to a technique in a machine learning field called semi-supervised learning.

For example, Non-Patent Document 1 discloses a method of performing label propagation from labeled data to unlabeled data after obtaining a metric of a data manifold by expressing the similarity between data as a Gaussian kernel. ..

Further, in Non-Patent Document 2, in a semi-supervised learning method in which unlabeled data is used for learning based on the adjacency of data, Delaunay triangulation is multidimensionalized for the purpose of appropriately expressing the adjacency of data. A technique is disclosed that extends to and incorporates wide-area properties by extracting data adjacencies.

Zhou, D., Bousquet, O., Lal, N.T., Weston, J., Scholkopf, B. Learning with local and global consistency, Proceeding of Advances in neural information processing systems 2004. Kazunori Matsumoto, Keiichiro Hoashi, Kazushi Ikeda, Study of label-propagated semi-supervised learning using Delaunay division, Shingaku Giho 116 (209), 211-214, 2016-09-05.

In the technique disclosed in Non-Patent Document 2, a graph structure considering a wide range of data is obtained by the multidimensional version of Delaunay division. However, when a metric such as the technique disclosed in Non-Patent Document 1 is used as the similarity between data, the number of dimensions of the metric is equal to the total number of labeled and unlabeled data, and the number of dimensions is very large. growing. As a result, the amount of calculation for the Delaunay division of the multidimensional version becomes enormous, and there is a problem that the calculation in a realistic time becomes difficult.

The present invention has been made in view of these points, and an object of the present invention is to provide a technique for putting label propagation into practical use in semi-supervised learning using multidimensional Delaunay division.

The first aspect of the present invention is an information processing device. This device includes a data acquisition unit that acquires a labeled data group with a label indicating a class to which it belongs, an unlabeled data group whose class belongs to unknown, and the labeled data group and the unlabeled data group. Calculate a metric matrix composed of metric vectors whose elements are metric showing the similarity between one data in the data constituting each of the above and the other data including the one data, arranged for each data. A matrix calculation unit, a matrix compression unit that generates a compression metric matrix formed by arranging compression metric vectors that compress the dimensions of each metric vector that constitutes the metric matrix, and a plurality of that have elements of each of the compression metric vectors as coordinates. Is mapped to a multidimensional space having the same dimension as the number of dimensions of the compression measurement vector, and the connection relationship between the division part that performs multidimensional drone division for the plurality of points and each point after the drone division is adjacent It includes an adjacent matrix acquisition unit that acquires as a matrix, and a label propagation unit that propagates a label to each data constituting the unlabeled data group based on the labels of the adjacent matrix and the labeled data group.

The matrix calculation unit may calculate the metric using a function having definite matrix.

The matrix calculation unit may calculate the metric using a Gaussian kernel.

The matrix compression unit may generate the compression metric matrix by using matrix factorization based on a sparse matrix after substituting 0 for elements of the metric matrix that are less than a predetermined threshold.

A vector selection unit that sequentially selects the metric vectors constituting the metric matrix may be further provided, and the matrix compression unit extracts elements of the metric vector selected by the vector selection unit that are equal to or greater than a predetermined threshold. At the same time, other metric vectors constituting the metric matrix may also extract elements corresponding to the elements constituting the metric vector, and a matrix composed of the extracted elements may be generated as the compressed metric matrix. The matrix acquisition unit corresponds to the metric vector selected by the vector selection unit by specifying the connection relationship between the point corresponding to the metric vector selected by the vector selection unit and another point based on the compression metric matrix. The elements of the adjacent matrix may be determined.

A second aspect of the present invention is an information processing method. In this method, the processor obtains a labeled data group with a label indicating the class to which it belongs, a step of acquiring an unlabeled data group to which the class to which it belongs is unknown, and the labeled data group and the label. None A metric composed of metric vectors whose elements are metric showing the degree of similarity between one data in the data constituting each of the data groups and the other data including the one data, arranged side by side for each data. A step of calculating a matrix, a step of generating a compression metric matrix composed by arranging compression metric vectors obtained by arranging the dimensions of each metric vector constituting the metric matrix, and a plurality of coordinates having each element of the compression metric vector as coordinates. Is mapped to a multidimensional space having the same dimension as the number of dimensions of the compression metric vector, and the step of performing multidimensional drone division for the plurality of points and the connection relationship of each point after the drone division are shown in an adjacent matrix. And the step of propagating the label to each data constituting the unlabeled data group based on the label of the adjacent matrix and the labeled data group is executed.

A third aspect of the present invention is a program. This program has a function of acquiring a labeled data group with a label indicating a class to which the computer belongs, a function of acquiring an unlabeled data group of which the class to which the computer belongs is unknown, and the labeled data group and the label. None A metric composed of metric vectors whose elements are metric showing the degree of similarity between one data in the data constituting each of the data groups and the other data including the one data, arranged side by side for each data. A function to calculate a matrix, a function to generate a compressed metric matrix composed by arranging compressed metric vectors obtained by compressing the dimensions of each metric vector constituting the metric matrix, and a plurality of coordinates having each element of the compressed metric vector as coordinates. Is mapped to a multidimensional space having the same dimension as the number of dimensions of the compression metric vector, and the function of performing multidimensional drone division for the plurality of points and the connection relationship of each point after the drone division are shown in an adjacent matrix. And a function of propagating the label to each data constituting the unlabeled data group based on the labels of the adjacent matrix and the labeled data group are realized.

In order to provide this program or to update a part of the program, a computer-readable recording medium on which the program is recorded may be provided, or the program may be transmitted over a communication line.

It should be noted that any combination of the above components and the conversion of the expression of the present invention between methods, devices, systems, computer programs, data structures, recording media and the like are also effective as aspects of the present invention.

According to the present invention, label propagation in semi-supervised learning using multidimensional Delaunay division can be put into practical use.

It is a figure which shows typically the functional structure of the information processing apparatus which concerns on embodiment. It is a figure for demonstrating the Delaunay division performed by the division part which concerns on embodiment. It is a figure which shows typically an example of the adjacency matrix acquired by the adjacency matrix acquisition part which concerns on embodiment. It is a figure which shows typically an example of the metric matrix calculated by the matrix calculation part which concerns on embodiment. It is a figure for demonstrating the matrix compression performed by the matrix compression part which concerns on embodiment. It is a flowchart for demonstrating the flow of information processing executed by the information processing apparatus which concerns on embodiment.

<Outline of the embodiment>
The information processing method according to the embodiment is attached to the labeled learning data based on the adjacency relationship between the labeled learning data with a label indicating the class to which it belongs and the unlabeled learning data to which the class to which it belongs is unknown. The present invention relates to a method for propagating the labeled label to each data constituting the unlabeled learning data.

The information processing apparatus according to the embodiment first generates a metric matrix showing a similarity relationship between the data constituting each of the labeled learning data and the unlabeled learning data. Subsequently, the information processing apparatus according to the embodiment compresses the generated metric matrix to generate a small-sized compressed metric matrix. Next, the information processing apparatus according to the embodiment is on an N-dimensional space having the same dimension as the number N of the data of each of the labeled learning data and the unlabeled learning data based on the elements constituting the compression metric matrix. The points corresponding to each training data are mapped to, and N-dimensional Delaunay triangulation is executed for the mapped point cloud. Finally, the information processing apparatus according to the embodiment propagates the label attached to the labeled learning data to each data constituting the unlabeled learning data based on the connection relationship of each point after the Delaunay triangle division.

[Delaunay triangle division]
Here, "Delaunay triangle division" is a kind of method of dividing a two-dimensional plane without omission and overlap by a triangle whose vertices are points distributed discretely on the two-dimensional plane. The triangle divided by the Delaunay triangulation has the properties described below. That is, the property is that the points constituting other triangles are not included in the circumscribed circle of any triangle divided by the Delaunay triangulation.

It is known that Delaunay triangulation can be extended to a space division method for a point cloud in a multidimensional space of three or more dimensions. In the extended Delaunay triangulation, the multidimensional space is divided by a simplex (simplex) whose vertices are points distributed discretely in the multidimensional space.

For example, since the simplex in the three-dimensional space is a tetrahedron, the Dronay triangle division in the three-dimensional space divides the three-dimensional space by a tetrahedron whose apex is a point distributed discretely in the three-dimensional space. .. When the Delaunay triangulation is performed in three-dimensional space, the circumscribed sphere of any tetrahedron does not contain the points that make up the other tetrahedron.

Similarly, since the simplex in the four-dimensional space is a five-cell body, the Delaunay triangulation in the four-dimensional space divides the four-dimensional space by the five-cell bodies whose vertices are points distributed discretely in the four-dimensional space. .. When the Delaunay triangulation in four-dimensional space is performed, the circumscribed sphere of any 5-cell does not contain the points that make up the other 5-cell.

The "hyperplane" in the tetrahedron is a triangle, and the hyperplane in the pentatope is a tetrahedron. In general, the hyperplane that constitutes an N-dimensional simplex is an N-1 dimensional simplex.

As described above, the Delaunay triangulation for a point cloud in a multidimensional space of three or more dimensions is, to be exact, a "simplex division". In the present specification, a division targeting a multidimensional space of two or more dimensions is simply referred to as "Delaunay division" for convenience, and a two-dimensional or higher dimensional simplex obtained by Delaunay division is simply referred to as "simplex". It is described as. Any simplex obtained by performing a Delaunay split does not include the points that make up the other simplex inside the circumscribed hypersphere of that simplex. This property is a wide-area property that holds throughout the space where known data is distributed.

Generally, the computational complexity of Delaunay division in N-dimensional space is on the order of N cubed. Since the number of data used for machine learning (that is, the number of dimensions N in the N-dimensional space) can be on the order of tens of thousands to millions, in such a case, processing in a realistic time becomes difficult. Therefore, the information processing apparatus according to the embodiment compresses a metric matrix showing a similarity relationship between the data constituting each learning data of the labeled learning data and the unlabeled learning data to reduce the amount of calculation. As an example, the information processing apparatus according to the embodiment compresses the size of the measurement matrix by a factor of 100. As a result, the Delaunay division in the multidimensional space can be executed in a realistic time.

<Functional configuration of the information processing device 1 according to the embodiment>
FIG. 1 is a diagram schematically showing a functional configuration of the information processing device 1 according to the embodiment. The information processing device 1 includes a storage unit 2 and a control unit 3. In FIG. 1, the arrows indicate the main data flows, and there may be data flows not shown in FIG. In FIG. 1, each functional block shows not a hardware (device) unit configuration but a functional unit configuration. Therefore, the functional block shown in FIG. 1 may be mounted in a single device, or may be mounted separately in a plurality of devices. Data can be exchanged between functional blocks via any means such as a data bus, a network, or a portable storage medium.

The storage unit 2 includes a ROM (Read Only Memory) for storing the BIOS (Basic Input Output System) of the computer that realizes the information processing device 1, a RAM (Random Access Memory) that serves as a work area for the information processing device 1, and an OS (OS). It is a large-capacity storage device such as an HDD (Hard Disk Drive) or an SSD (Solid State Drive) that stores an Operating System), an application program, and various information referred to when the application program is executed.

The control unit 3 is a processor such as a CPU (Central Processing Unit) or GPU (Graphics Processing Unit) of the information processing device 1, and a data acquisition unit 30 and a matrix calculation unit are executed by executing a program stored in the storage unit 2. It functions as 31, a matrix compression unit 32, a division unit 33, an adjacent matrix acquisition unit 34, a label propagation unit 35, and a vector selection unit 36.

Note that FIG. 1 shows an example in which the information processing device 1 is composed of a single device. However, the information processing device 1 may be realized by computing resources such as a plurality of processors and memories, such as a cloud computing system. In this case, each unit constituting the control unit 3 is realized by executing a program by at least one of a plurality of different processors.

The data acquisition unit 30 acquires a labeled data group, which is a data group with a label indicating the class to which the data belongs. The labeled data group is stored in, for example, the storage unit 2. In this case, the data acquisition unit 30 reads the labeled data group from the storage unit 2 and acquires it. Each data constituting the labeled data group is represented by a vector. This vector may be a vector having a plurality of feature quantities that characterize the data as elements.

The data acquisition unit 30 also acquires an unlabeled data group, which is a data group to which the class to which the data belongs is unknown. Like the labeled data group, the unlabeled data group is also stored in, for example, the storage unit 2. Each data constituting the unlabeled data group is represented by a vector having the same dimension as each data constituting the labeled data group.

The matrix calculation unit 31 uses a metric indicating the degree of similarity between one data in the data constituting each of the labeled data group and the unlabeled data group and the other data including the one data as an element. A metric matrix composed of arranging the metric vectors to be performed for each data is calculated.

Specifically, the total number of data constituting each of the labeled data group and the unlabeled data group is N (N is a natural number of 2 or more), and each of them is x ₁ , x ₂ , ..., X. It is represented by _N. Matrix calculating unit 31 selects the data in order to reach the first time x _N from x _{1. Now, let xi} be the data selected by the matrix calculation unit 31. Matrix calculating unit 31 calculates a metric that indicates the degree of similarity with other data including x _i and x _i. other data, including the x _i and _{x j,} a metric indicating the degree of similarity between _{x i} and _{x j} and _{g ij.}

g _ij = F (x _i , x _j ) (1)
In equation (1), F is a function for calculating the metric _{of x i} and x _j. The details of the function F will be described later.

Matrix calculating unit 31, for each _{x i,} and generates a metric vector _{g i} for the metering _{g ij} as elements. That is, the metric vector _{g i} is expressed by the following equation (2).

Matrix calculating unit 31 generates a matrix obtained by arranging metric vector g _i, the metric matrix G. That is, the metric matrix G is represented by the following equation (3).

As is clear from equation (3), the metric matrix G is an Nth-order square matrix. Both the labeled data group and the unlabeled data group acquired by the data acquisition unit 30 are data used for so-called supervised learning such as DNN (Deep Neural Network) and SVM (Support Vector Machine). Therefore, the total N of the data constituting each of the labeled data group and the unlabeled data group is often on the order of 100 even if it is small, and on the order of 1 million if it is large.

Therefore, the matrix compression unit 32 generates a composed compressed metric matrix by arranging a compression metric vector obtained by compressing the dimension N of the metric vector g _i constituting the metric matrix G. Although matrix compression unit 32 is more compression processing to be executed will be described later, the matrix compression unit 32 to compress each metric vector g _i, to generate compressed metric vector c _i m-dimensional (m << N) .. As an example, m is about one-hundredth of N. Matrix compression unit 32 generates a compression metric matrix C composed by arranging a compression metric vector c _i. The compression metric matrix C is represented by the following equation (4).

なお、ｍ＜Ｎであるため、圧縮計量行列Ｃは正方行列ではない。

Since m <N, the compression metric matrix C is not a square matrix.

Dividing unit 33 maps the plurality of points the compression metric vector c _i each element and coordinates dimensionality and the same dimension of the multidimensional space of the compression metric vector c _i, multidimensional Delaunay for a plurality of points Divide.

2 (a)-(b) are diagrams for explaining Delaunay division executed by the division unit 33 according to the embodiment. Specifically, FIG. 2 (a) is a diagram illustrating a mapping result of the compression metric vector c _i by dividing unit 33. Further, FIG. 2B is a diagram showing the result of Delaunay division by the division unit 33. By setting the first element f1 of the compressed metric vector c _i as the first axis and the second element f2 as the second axis, the dividing unit 33 sets the compressed metric vector c _i as one point on the two-dimensional space. Can be mapped to.

Generally, the dimension of the compression metric vector c _i is larger than 2, but for convenience of illustration, FIGS. 2 (a)-(b) show an example in which the dimension _{of the compression metric vector c i is 2.} When the compression metric vector c _i is two-dimensional, the compression metric vector c _i is composed of two elements f1 and f2. As shown in FIG. 2A _{, each compression metric vector c i} is compressed _{by having one element f1 of the compression metric vector c i} as the first axis and the second element f2 as the second axis. It is mapped to one point in the space of the same dimension as the dimension of the metric vector c _{i (two dimensions in FIG. 2).}

Dividing unit 33 performs Delaunay division for each compression metric vector c _i which is mapped to the multidimensional space. As a result, as shown in FIG. 2 (b), a plurality of simplex whose vertices each compression metric vector c _i mapped in multi-dimensional space (triangles in FIG. 2 (b)) is generated. That is, each compression metric vector c _i mapped in the multidimensional space is connected to a plurality of other compression metric vectors c _{i by edges.}

The adjacency matrix acquisition unit 34 acquires the connection relationship of each point after the Delaunay division as an adjacency matrix. Specifically, the adjacency matrix acquisition part 34, Delaunay division result "Yes connection relationship" compression metric vector c _i with each other that corresponds to the point tied directly at the sides to each other, a point that is not connected directly with the sides to each other Generate and acquire a connection matrix that makes each other "no connection relationship".

FIG. 3 is a diagram schematically showing an example of an adjacency matrix acquired by the adjacency matrix acquisition unit 34 according to the embodiment. In FIG. 3, the area indicated by the broken line rectangle indicates the adjacency matrix.

Since the adjacency matrix is a known concept, detailed explanation is omitted, but it shows the relationship between whether or not a pair of points (vertices) mapped in a multidimensional space are connected by an edge (that is, an edge). It is a matrix. Specifically, the elements of the vector that make up each row of the adjacency matrix indicate the connection relationship between the vertices corresponding to the vector and other vertices. Therefore, the adjacency matrix is a symmetric matrix with the same dimensions as the number of vertices.

_{In the example shown in FIG. 3, N data x 1} , x ₂ , ..., X _N constituting each of the labeled data group and the unlabeled data group have a connection relationship with other vectors. In the case, it is expressed as 1, and if there is no connection relationship, it is expressed as 0. Specifically, each row of the adjacency matrix shows the connection relationship with other vectors related to the _{data x 1} , x ₂ , ..., X _{N, respectively.} For example, since the data x ₁ has no connection relationship with itself, the first column of the vector forming the first row corresponding to the _{data x 1 is 0.} Further, since the data x ₁ is connected to the data x _N , the element of 1 row N column of the adjacency matrix shown in FIG. 3 is 1.

The label propagation unit 35 propagates the label to each data constituting the unlabeled data group based on the labels of the adjacency matrix and the labeled data group. Since the method of label propagation when the adjacency matrix is known is known, an example of the propagation algorithm will be briefly described below in the case where the label has two classes of +1 and -1.

Now, the adjacency matrix is represented by W. _{Further, the labels of the N data x 1} , x ₂ , ..., X _N constituting each of the labeled data group and the unlabeled data group are represented by y. Specifically, the label y of each data constituting the labeled data group is either +1 or -1. The label y of each vector constituting the unlabeled data group is set to 0.

Let f be the predicted value of the label y of each data constituting the unlabeled data group. f can take a real number between -1 and +1. At this time, the objective function J (f) that maximizes the prediction performance is represented by the following equation (5).

ここで、Ｌ＝Ｄ−Ｗであり、ＤはＷの各行の和を対角成分に持つ行列、λは右辺第１項と第２項とのバランスを取る定数である。

Here, L = D-W, D is a matrix having the sum of each row of W as a diagonal component, and λ is a constant that balances the first term and the second term on the right side.

In the equation (5), when the value of the objective function J (f) is minimized, the following equation (6) holds.
(1 + λL) f = y (6)

By using the equations (5) and (6), the label propagation unit 35 can propagate the label to each data constituting the unlabeled data group based on the labels of the adjacency matrix and the labeled data group. ..

The information processing apparatus 1 according to the embodiment, for mapping the multi-dimensional space after compressing each metric vector g _i, can be terminated by the operation time of the practical range of Delaunay division. As described above, the information processing apparatus 1 according to the embodiment can put label propagation in semi-supervised learning using multidimensional Delaunay division into practical use.

[Calculation of measurement]
The function F used by the matrix calculation unit 31 to calculate the metric matrix G will be described.
The matrix calculation unit 31 according to the embodiment calculates the metric between each data by using the function F having semi-fixed value. An example of the function F having definite matrix is a kernel function in SVM. Specific examples include a polynomial kernel, a Gaussian kernel, and a hyperbolic tangent kernel. In the following, it is assumed that the matrix calculation unit 31 calculates the metric between each data using the Gaussian kernel.

As described above, each data constituting the labeled data group and the unlabeled data group is represented by a vector. Let them be vectors x ₁ , x ₂ , ..., X _N. At this time, the function F when using the Gaussian kernel is expressed by the following equation (7).

式（７）において、ｘ_ｉｋは、ベクトルｘ_ｉのｋ番目の要素を示す。ｘ_ｊｋも同様である。

In equation (7), x _ik represents the kth element of the vector x _i. The same applies to _{x jk.}

FIG. 4 is a diagram schematically showing an example of a measurement matrix calculated by the matrix calculation unit 31 according to the embodiment. In FIG. 4, the area indicated by the broken line rectangle indicates the metric matrix. As is clear from the definition of the function F shown in the equation (7), the metric _gij takes a value of 0 or more and 1 or less, and when the vector x _i and the vector x _j have the same value (that is, when they are most similar). ) 1, and the _{farther the vector x i} and the vector x _j are, the closer the value becomes to 0. In the example shown in FIG. 4, the vector x ₁ is shown to be more similar to the vector x ₂ than the vector x _N.

[Compression of metric matrix G]
Subsequently, the compression of the metric matrix G by the matrix compression unit 32 will be described. The matrix compression unit 32 compresses the metric matrix G by using two methods independent of each other.

(First method)
As is clear from the definition of the function F shown in the equation (7), the metric g _ij rapidly approaches 0 as the vector x _i and the vector x _j are separated from each other. Therefore, assuming that there is no bias between the labeled data group and the unlabeled data group, it is considered that many of the elements of the metric matrix G are close to zero.

Therefore, the matrix compression unit 32 replaces the elements of the metric matrix G that are less than a predetermined threshold value with 0 to generate the matrix D. The “predetermined threshold value” is a “reference threshold value at the time of determining the connection relationship” that the matrix compression unit 32 refers to in order to consider that there is no connection relationship between the data. The specific value of the reference threshold value at the time of determining the connection relationship may be determined experimentally in consideration of the balance between the compression efficiency (that is, the calculation efficiency) and the accuracy, the value of γ in the equation (7), and the like. It is 0.5. As a result, the matrix compression unit 32 converts the metric matrix G calculated by the matrix calculation unit 31 into a sparse matrix D. Subsequently, the matrix compression unit 32 generates a compression metric matrix C by using the matrix factorization based on the sparse matrix of the matrix D.

5 (a)-(b) are diagrams for explaining the matrix compression executed by the matrix compression unit 32 according to the embodiment. Specifically, FIG. 5A is a diagram for explaining general singular value decomposition, and FIG. 5B is a diagram for explaining vector compression using singular value decomposition. is there.

As shown in FIG. 5A, the matrix compression unit 32 performs singular value decomposition on the matrix D, so that the matrix D is diagonally opposite to the matrix S formed by arranging the left singular vectors. a matrix Σ with the components, the matrix V ^T constructed by arranging the right singular vectors ^(T is the transpose of the matrix) is decomposed into. Since FIG. 5A is a diagram for explaining a general singular value decomposition, the matrix D is shown so that the row length and the column length are different, but the metric matrix G is a square matrix. Therefore, the row length and the column length are equal.

The diagonal components of the matrix Σ are configured by arranging the singular values in descending order. The matrix compression unit 32 generates a new matrix Σ'by truncating a singular value that is equal to or less than a predetermined value. The matrix Σ'has a shorter row length than the matrix Σ.

The matrix compression unit 32 calculates a new matrix D'by multiplying the matrix S formed by arranging the left singular vectors by the matrix Σ'. The row length of the matrix D'is shorter than that of the matrix D. The length of the matrix D'is the same as that of the matrix D, and is equal to the number of data constituting the labeled data group and the unlabeled data group. Matrix compression unit 32, the i-th row vector constituting the matrix D ', the compression metric vector c _i. As a result, the matrix compression unit 32 can compress the size of the weighing matrix G in the row direction.

(Second method)
Subsequently, a second method of compressing the metric matrix G by the matrix compression unit 32 will be described.

Summary of the second approach of the compression of the metric matrix G is weighed in determining the connection relationship of the vector g _i selects only metric vector g _j present in the vicinity of the metric vector g _i in a multidimensional space It is to decide.

To achieve this, the vector selection unit 36 selects a metric vector g _i first configure the metric matrix G in this order. Each element of the metric vector g _i represents the degree of similarity with _{other metric vectors g j.} Therefore, the matrix compression unit 32 extracts a predetermined threshold value or more elements among the elements of the metric vector g _i the vector selection unit 36 has selected. Here, the predetermined threshold value is a "neighborhood" referred to by the matrix compression unit 32 for determining whether or not the pairs of the metric vectors g are close to each other, in other words, whether or not the pairs of the metric vector g are similar. Judgment threshold ". The specific value of the threshold value for neighborhood determination may be determined experimentally in consideration of the balance between compression efficiency (that is, calculation efficiency) and accuracy, the range of the function F used for calculating the metric, and the like.

The matrix compression unit 32 extracts elements corresponding to the elements constituting the metric vector g _{i as well as other metric vectors g j} constituting the metric matrix G, and compresses the matrix composed of the extracted elements with respect to the metric vector g _j. generating a metric matrix _{C i.}

For example, suppose that the vector selection unit 36 selects the metric vector g _{1 corresponding to the vector x 1} . As a result of the matrix compression unit 32 extracting the elements above the neighborhood determination threshold value from the elements (g ₁₁ , g ₁₂ , ..., G _{1N ) constituting the metric vector g 1, the first, fifth, and} It is assumed that the Nth elements g ₁₁ , g ₁₅ , and g _{1N are extracted.} In this case, the compression metric vector c ₁ becomes c ₁ (g ₁₁ , g ₁₅ , g _N ). The matrix compression unit 32 also extracts the first, fifth, and Nth elements of the remaining metric vector c _j (metric vector g ₂ to metric vector g _N ) to generate a _{compressed metric vector c j.} As a result, the matrix compression unit 32 generates a compression metric matrix C _{1 with respect to the metric vector g 1.}

Each time a vector selection unit 36 selects a metric vector g _i, the matrix compression unit 32 generates a compression metric matrix C _i corresponding to the selected metric vector g _i. Adjacency matrix acquisition unit 34, by specifying, based connection between points in the other point corresponding to the metric vector g _i the vector selection unit 36 selects the compression metric matrix C _i, selected vector selection unit 36 determining the elements of the adjacency matrix corresponding to the metric vector g _i.

As a result, the information processing apparatus 1 can determine an adjacency matrix for each metric vector g by using only the metric vector g in the vicinity of the metric vector g. Therefore, the information processing apparatus 1 can shorten the calculation time required for calculating the adjacency matrix as compared with the case of specifying the connection relationship of all the metric vectors g.

(Relationship between the first method and the second method)
The first method and the second method regarding the compression of the metric matrix G described above are independent of each other. Therefore, the matrix compression unit 32 can use both the first method and the second method together. Specifically, the matrix compression unit 32 can further compress the matrix calculated by using the first method by using the second method.

<Processing flow of information processing method executed by information processing device 1>
FIG. 6 is a flowchart for explaining the flow of information processing executed by the information processing apparatus 1 according to the embodiment. The process in this flowchart starts, for example, when the information processing device 1 is activated.

The data acquisition unit 30 acquires labeled data with a label indicating the class to which it belongs (S2). Further, the data acquisition unit 30 acquires an unlabeled data group to which the class to which the data belongs is unknown (S4).

The matrix calculation unit 31 uses a metric indicating the degree of similarity between one data in the data constituting each of the labeled data group and the unlabeled data group and the other data including the one data as an element. A metric matrix G is calculated by arranging the metric vectors g to be performed for each data (S6).

The matrix compression unit 32 generates a compression metric matrix C formed by arranging compression metric vectors c obtained by compressing the dimensions of each metric vector g constituting the metric matrix G (S8). The division unit 33 maps a plurality of points whose coordinates are each element of the compression measurement vector c to a multidimensional space having the same dimension as the number of dimensions of the compression measurement vector c, and performs multidimensional drone division for the plurality of points. Execute (S10).

The adjacency matrix acquisition unit 34 acquires the connection relationship of each point after the Delaunay division by the division unit 33 as an adjacency matrix (S12). The label propagation unit 35 propagates the label to each data constituting the unlabeled data group based on the labels of the adjacency matrix and the labeled data group (S14).

When the label propagation unit 35 propagates the label to each data constituting the unlabeled data group, the process in this flowchart ends.

<Effects of the information processing device 1 according to the embodiment>
As described above, according to the information processing apparatus 1 according to the embodiment, label propagation in semi-supervised learning using multidimensional Delaunay division can be put into practical use.

Although the present invention has been described above using the embodiments, the technical scope of the present invention is not limited to the scope described in the above embodiments, and various modifications and changes can be made within the scope of the gist thereof. is there. For example, all or a part of the device can be functionally or physically distributed / integrated in any unit. Also included in the embodiments of the present invention are new embodiments resulting from any combination of the plurality of embodiments. The effect of the new embodiment produced by the combination also has the effect of the original embodiment.

1 ... Information processing device 2 ... Storage unit 3 ... Control unit 30 ... Data acquisition unit 31 ... Matrix calculation unit 32 ... Matrix compression unit 33 ... Division unit 34 ... Adjacency matrix acquisition unit 35 ... Label propagation unit 36 ... Vector selection unit

Claims (7)

A data acquisition unit that acquires a labeled data group with a label indicating the class to which it belongs and an unlabeled data group to which the class to which it belongs is unknown.
A metric vector whose element is a metric indicating the degree of similarity between one data in the data constituting each of the labeled data group and the unlabeled data group and the other data including the one data. A matrix calculation unit that calculates a metric matrix that is arranged side by side for each data,
A matrix compression unit that generates a compressed metric matrix composed by arranging compressed metric vectors that compress the dimensions of each metric vector that constitutes the metric matrix.
A division unit that maps a plurality of points whose coordinates are each element of the compression metric vector into a multidimensional space having the same dimension as the number of dimensions of the compression metric vector, and performs multidimensional drone division for the plurality of points. ,
An adjacency matrix acquisition unit that acquires the connection relationship of each point after Delaunay division as an adjacency matrix,
A label propagation unit that propagates a label to each data constituting the unlabeled data group based on the labels of the adjacency matrix and the labeled data group.
Information processing device equipped with. The matrix calculation unit calculates the metric using a function having definite matrix.
The information processing device according to claim 1. The matrix calculation unit calculates the metric using a Gaussian kernel.
The information processing device according to claim 1 or 2. The matrix compression unit generates the compressed metric matrix by using matrix factorization based on a sparse matrix after substituting 0 for elements of the metric matrix that are less than a predetermined threshold.
The information processing device according to claim 3. A vector selection unit for sequentially selecting the metric vectors constituting the metric matrix is further provided.
The matrix compression unit extracts elements of the metric vector selected by the vector selection unit that are equal to or greater than a predetermined threshold, and other metric vectors that make up the metric matrix also correspond to the elements that make up the metric vector. The elements to be used are extracted, and a matrix composed of the extracted elements is generated as the compression metric matrix.
The adjacency matrix acquisition unit specifies the connection relationship between a point corresponding to the metric vector selected by the vector selection unit and another point based on the compression metric matrix, so that the metric vector selected by the vector selection unit To determine the elements of the adjacency matrix corresponding to
The information processing device according to claim 3 or 4. The processor,
A step to acquire a labeled data group with a label indicating the class to which it belongs, and
The step to get the unlabeled data group whose class belongs to unknown,
A metric vector whose element is a metric indicating the degree of similarity between one data in the data constituting each of the labeled data group and the unlabeled data group and the other data including the one data. Steps to calculate the metric matrix constructed side by side for each data,
A step of generating a compressed metric matrix composed by arranging compressed metric vectors obtained by compressing the dimensions of each metric vector constituting the metric matrix, and
A step of mapping a plurality of points whose coordinates are each element of the compression metric vector into a multidimensional space having the same dimension as the number of dimensions of the compression metric vector, and performing multidimensional drone division for the plurality of points.
The step of acquiring the connection relationship of each point after Delaunay division as an adjacency matrix,
A step of propagating a label to each data constituting the unlabeled data group based on the labels of the adjacency matrix and the labeled data group.
Information processing method to execute. On the computer
A function to acquire a labeled data group with a label indicating the class to which it belongs, and
A function to get unlabeled data group whose class belongs to unknown,
A metric vector whose element is a metric indicating the degree of similarity between one data in the data constituting each of the labeled data group and the unlabeled data group and the other data including the one data. A function to calculate a metric matrix composed of data arranged side by side, and
A function to generate a compressed metric matrix composed by arranging compressed metric vectors obtained by compressing the dimensions of each metric vector constituting the metric matrix, and
A function of mapping a plurality of points whose coordinates are each element of the compression metric vector into a multidimensional space having the same dimension as the number of dimensions of the compression metric vector, and performing multidimensional drone division for the plurality of points.
A function to acquire the connection relationship of each point after Delaunay division as an adjacency matrix,
A function of propagating a label to each data constituting the unlabeled data group based on the labels of the adjacency matrix and the labeled data group.
A program that realizes.

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