Visualization device, visualization method, and program

Abstract

To visualize the distribution of multi-dimensional data with four or more dimensions.SOLUTION: A visualization device comprises: an axis point acquisition unit for acquiring the N-dimensional coordinate of an axis point in an N-dimensional space (N=integer 4 or greater); a distance calculation unit for calculating a distance matrix indicating the distance for each axis point combination; a dimension reduction unit for converting the N-dimensional coordinate into a three-dimensional coordinate on the basis of the distance matrix; a model generation unit for generating a conversion model having been trained by learning a relationship between the N-dimensional coordinate of the axis point and the three-dimensional coordinate of the axis point; a data conversion unit for converting a plurality of N-dimensional data into three-dimensional data on the basis of the conversion model; and a visualization unit for arranging the N-dimensional data and the axis point in a three-dimensional space on the basis of the N-dimensional data, the three-dimensional data, and the N-dimensional coordinate of the axis point and three-dimensional coordinate of the axis point.SELECTED DRAWING: Figure 5

Description

[Technical field]

[0001] The present disclosure relates to a visualization device, a visualization method, and a program. [Background technology]

[0002] When analyzing multidimensional data such as compositional information obtained from experiments, techniques for visualizing and expressing data are sometimes used to support the analyst's intuitive understanding. For example, being able to contrast areas where data exists with areas where no data exists makes it easier for the analyst to understand the characteristics and structure of the entire space.

[0003] For example, Patent Document 1 discloses a multidimensional data visualization device that visualizes multidimensional data in a low-dimensional parallel coordinate plot. Patent Document 2 discloses an information presentation device that plots each value of multidimensional data on each axis and generates visual information that makes it possible to identify the number of values ​​plotted in each interval of each axis. Patent Document 3 discloses a multidimensional data selection device that extracts multiple combinations of m-dimensional data from n-dimensional data and outputs m-dimensional data selected based on the importance of each combination. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2013-161226 A [Patent Document 2] JP 2018-160034 A [Patent Document 3] JP 2011-28483 A Summary of the Invention [Problem to be solved by the invention]

[0005] However, it is not easy to visualize the distribution of multidimensional data with four or more dimensions. It is easy to visualize a space with up to three dimensions, including blank areas, but it is difficult to visualize a space with four or more dimensions in a way that humans can perceive.

[0006] In view of the above technical problems, one embodiment of the present disclosure aims to visualize the distribution of multidimensional data of four or more dimensions. [Means for solving the problem]

[0007] The present disclosure has the following configuration.

[0008] <1> an axis point acquisition unit configured to acquire N-dimensional coordinates of an axis point in an N-dimensional space, where N is an integer equal to or greater than 4; a distance calculation unit configured to calculate a distance matrix indicating distances for each combination of the axis points; a dimensionality reduction unit configured to transform the N-dimensional coordinates of the axis points into three-dimensional coordinates based on the distance matrix; a model generation unit configured to generate a transformation model that learns a relationship between the N-dimensional coordinates of the axis points and the three-dimensional coordinates of the axis points; a data conversion unit configured to convert a plurality of N-dimensional data into three-dimensional data based on the conversion model; a visualization unit configured to arrange the N-dimensional data and the axis points in a three-dimensional space based on the N-dimensional data, the three-dimensional data, the N-dimensional coordinates of the axis points, and the three-dimensional coordinates of the axis points; A visualization device comprising:

[0009] <2> the above <1> The visualization device according to the present invention comprises: a lattice point acquisition unit configured to acquire N-dimensional coordinates of lattice points in the N-dimensional space; a lattice point transformation unit configured to transform N-dimensional coordinates of the lattice points into three-dimensional coordinates based on the transformation model; Further equipped with The visualization unit is configured to arrange the lattice points in the three-dimensional space based on N-dimensional coordinates of the lattice points and three-dimensional coordinates of the lattice points. Visualization device.

[0010] <3> the above <2> The visualization device according to the present invention comprises: The visualization unit is configured to change a display mode of the axis points or the lattice points according to a degree of complexity of the N-dimensional coordinates of the axis points or the N-dimensional coordinates of the lattice points. Visualization device.

[0011] <4> the above <2> or <3> The visualization device according to the present invention comprises: The visualization unit is configured to change a display mode of an origin and a farthest point among the axis points. Visualization device.

[0012] <5> the above <2> from <4> The visualization device according to any one of the preceding claims, a normalization unit that normalizes each element of the N-dimensional data; an inverse normalization unit that performs an inverse transformation of the normalization on the N-dimensional coordinates of the axis points and the N-dimensional coordinates of the lattice points; The visualization device further comprises:

[0013] <6> the above <1> from <5> The visualization device according to any one of the preceding claims, The distance is a non-Euclidean distance. Visualization device.

[0014] <7> the above <6> The visualization device according to the present invention comprises: The non-Euclidean distance is a Dice distance. Visualization device.

[0015] <8> the above <1> from <7> The visualization device according to any one of the preceding claims, The dimensionality reduction unit is configured to convert the N-dimensional coordinates of the axis points into three-dimensional coordinates based on a multidimensional scaling method. Visualization device.

[0016] <9> The computer obtaining N-dimensional coordinates of an axis point in N-dimensional space, where N is an integer equal to or greater than 4; calculating a distance matrix indicating distances for each combination of the axis points; transforming the N-dimensional coordinates of the axis points into three-dimensional coordinates based on the distance matrix; generating a transformation model that learns a relationship between the N-dimensional coordinates of the axis points and the three-dimensional coordinates of the axis points; converting a plurality of N-dimensional data into three-dimensional data based on the conversion model; A step of arranging the N-dimensional data and the axis points in a three-dimensional space based on the N-dimensional data, the three-dimensional data, the N-dimensional coordinates of the axis points, and the three-dimensional coordinates of the axis points; A visualization method to perform.

[0017] <10> On the computer, obtaining N-dimensional coordinates of an axis point in N-dimensional space, where N is an integer equal to or greater than 4; calculating a distance matrix indicating distances for each combination of the axis points; transforming the N-dimensional coordinates of the axis points into three-dimensional coordinates based on the distance matrix; generating a transformation model that learns a relationship between the N-dimensional coordinates of the axis points and the three-dimensional coordinates of the axis points; converting a plurality of N-dimensional data into three-dimensional data based on the conversion model; A step of arranging the N-dimensional data and the axis points in a three-dimensional space based on the N-dimensional data, the three-dimensional data, the N-dimensional coordinates of the axis points, and the three-dimensional coordinates of the axis points; A program for executing the above. Effect of the Invention

[0018] According to one embodiment of the present disclosure, the distribution of multidimensional data of four or more dimensions can be visualized. [Brief description of the drawings]

[0019] [Figure 1] FIG. 13 is a diagram illustrating an example of a scatter plot matrix. [Diagram 2] FIG. 1 is a diagram showing an example of a parallel plot. [Diagram 3] 1 is a block diagram showing an example of an overall configuration of an analysis system. [Figure 4] FIG. 2 is a block diagram showing an example of a hardware configuration of a computer. [Diagram 5] FIG. 2 is a block diagram illustrating an example of a functional configuration of the analysis system. [Figure 6] 1 is a flowchart illustrating an example of a visualization method. [Figure 7] FIG. 2 is a diagram illustrating an example of multidimensional data. [Figure 8] FIG. 13 is a diagram illustrating an example of multidimensional data after normalization. [Figure 9] FIG. 11 is a diagram illustrating an example of axial point cloud data. [Figure 10] FIG. 13 is a diagram illustrating an example of lattice point group data. [Figure 11] FIG. 13 is a diagram illustrating an example of a distance matrix. [Figure 12] FIG. 13 is a diagram illustrating an example of axis point cloud data after dimension reduction. [Figure 13] FIG. 13 is a diagram illustrating an example of multidimensional data after dimension reduction. [Figure 14] FIG. 13 is a diagram illustrating an example of lattice point cloud data after dimensionality reduction. [Figure 15] FIG. 13 is a diagram illustrating an example of axis point cloud data after inverse normalization. [Figure 16] FIG. 13 is a diagram showing an example of lattice point cloud data after inverse normalization. [Figure 17] FIG. 11 is a diagram illustrating an example of a visualization result according to an embodiment. [Figure 18] FIG. 13 is a diagram showing an example of a visualization result according to Comparative Example 1. [Figure 19] FIG. 11 is a diagram showing an example of a visualization result according to Comparative Example 2. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. In this specification and the drawings, components having substantially the same functional configurations are denoted by the same reference numerals, and redundant description will be omitted.

[0021] [Embodiment] An embodiment of the present disclosure is an analysis system for analyzing multidimensional data. The analysis system has a function of visualizing a distribution of multidimensional data to be analyzed. The multidimensional data to be analyzed may be, for example, composition information obtained by an experiment or the like.

[0022] In this embodiment, the multidimensional data is data with four or more dimensions. The distribution of multidimensional data with three or less dimensions can be easily visualized by arranging it in a three-dimensional space or the like. On the other hand, the distribution of multidimensional data with four or more dimensions is very difficult to visualize due to the limitations of human cognition. However, composition information and the like are generally multidimensional data with more than three dimensions, and in order to analyze them, it is required to visualize multidimensional data with four or more dimensions.

[0023] In this embodiment, a visualization method that satisfies all of the following criteria is proposed. The first criterion is that visualization including blank areas is possible. The second criterion is that a reference point (e.g., the origin) exists. The third criterion is that the direction from the reference point (axis direction) is clear. The fourth criterion is that there is no overlap of axes (in other words, the number of axes does not exceed the number of dimensions). The fifth criterion is that there is no overlap of data when visualized (in other words, the coordinates of the data can be determined centrally). The sixth criterion is that there is no overlap of blank areas when visualized (in other words, the coordinates of the blank areas can be determined centrally).

[0024] Although various visualization methods for multidimensional data have been proposed, no visualization method satisfies all six of the above criteria.

[0025] Here, an example of a conventional visualization method will be described. The first visualization method is a scatter plot matrix. The scatter plot matrix is ​​disclosed in, for example, Reference 1.

[0026] [Reference 1] DF Andrews, "Plots of High-Dimensional Data," Biometrics, vol. 28, pp. 125-136, 1972.

[0027] Fig. 1 is a diagram showing an example of a scatter plot matrix. As shown in Fig. 1, when there are multiple variables, a scatter plot matrix is ​​created for all combinations of two variables and arranged in a matrix. The scatter plot matrix allows the correlation between multiple variables to be visually grasped.

[0028] Figure 1 is a scatter plot matrix that visualizes the Iris dataset, which is publicly available as a dataset for machine learning. The sepal length (cm), sepal width (cm), petal length (cm), and petal width (cm) shown in Figure 1 are attributes included in the Iris dataset.

[0029] In the scatter plot matrix, the fifth and sixth indicators among the six indicators above are not satisfied. In other words, in the scatter plot matrix, when visualized, data and blank areas cannot be determined centrally.

[0030] The second visualization method is parallel plotting, which is disclosed in, for example, Reference 2.

[0031] [Reference 2] A. Inselberg and B. Dimsdale, "Parallel coordinates: a tool for visualizing multi-dimensional geometry," Proceedings of the First IEEE Conference on Visualization, pp. 361-378, 1990.

[0032] FIG. 2 is a diagram showing an example of a parallel plot. As shown in FIG. 2, a parallel plot is a diagram that expresses the relationship between variables in parallel. In a parallel plot, coordinates with each variable on the vertical axis are arranged in parallel, and coordinates of the same element are connected by lines. Note that, like FIG. 1, FIG. 2 is a parallel plot that visualizes the Iris dataset.

[0033] In the parallel plot, the sixth of the six indicators above is not satisfied. In other words, in the parallel plot, the blank area cannot be determined centrally when it is visualized.

[0034] An embodiment of the present disclosure aims to visualize the distribution of multidimensional data of four or more dimensions. In particular, the present embodiment proposes a visualization method that can satisfy all of the above six indicators. According to one aspect, the present embodiment allows a user to easily understand the distribution of multidimensional data, and enables efficient analysis of a large amount of multidimensional data.

[0035] <Overall composition> The overall configuration of the analysis system in this embodiment will be described with reference to Fig. 3. Fig. 3 is a block diagram showing an example of the overall configuration of the analysis system in this embodiment.

[0036] 3, the analysis system 1000 in this embodiment includes a visualization device 10 and a terminal device 20. The visualization device 10 and the terminal device 20 are connected to each other so as to be able to communicate data with each other via a communication network N1 such as a LAN (Local Area Network) or the Internet.

[0037] The visualization device 10 is an information processing device such as a personal computer, a workstation, or a server that visualizes the distribution of four or more dimensional multidimensional data in a three-dimensional space. The visualization device 10 receives multidimensional data to be analyzed from a terminal device 20, and transmits to the terminal device 20 a visualization result in which the distribution of the multidimensional data is visualized in a three-dimensional space.

[0038] The terminal device 20 is an information processing terminal such as a personal computer, a smartphone, or a tablet terminal operated by a user of the analysis system 1000. The terminal device 20 transmits multidimensional data to be analyzed to the visualization device 10 in response to an operation by the user. The terminal device 20 outputs the visualization result received from the visualization device 10 to the display device 506.

[0039] A user of analysis system 1000 can refer to the visualization results output to terminal device 20 and analyze the characteristics and structure of the data based on the distribution of the multidimensional data displayed in the three-dimensional space.

[0040] The overall configuration of the analysis system 1000 shown in Fig. 3 is an example, and various system configuration examples are possible depending on the application and purpose. For example, the analysis system 1000 may include a plurality of visualization devices 10 and one or more terminal devices 20. For example, the visualization device 10 may be realized by a plurality of computers, or may be realized as a cloud computing service. The division of devices such as the visualization device 10 and the terminal device 20 shown in Fig. 3 is an example.

[0041] <Hardware configuration> The hardware configuration of the analysis system 1000 in this embodiment will be described with reference to FIG.

[0042] <Computer hardware configuration> The visualization device 10 and the terminal device 20 in this embodiment are realized by, for example, a computer. Fig. 4 is a block diagram showing an example of the hardware configuration of a computer 500 in this embodiment.

[0043] 4, the computer 500 includes a CPU (Central Processing Unit) 501, a ROM (Read Only Memory) 502, a RAM (Random Access Memory) 503, a HDD (Hard Disk Drive) 504, an input device 505, a display device 506, a communication I / F (Interface) 507, and an external I / F 508. The CPU 501, the ROM 502, and the RAM 503 form a so-called computer. Each piece of hardware of the computer 500 is connected to each other via a bus line 509. The input device 505 and the display device 506 may be connected to the external I / F 508 for use.

[0044] The CPU 501 is a calculation device that reads out programs and data from a storage device such as a ROM 502 or a HDD 504 onto a RAM 503 and executes processes, thereby realizing overall control and functions of the computer 500 .

[0045] The ROM 502 is an example of a non-volatile semiconductor memory (storage device) that can retain programs and data even when the power is turned off. The ROM 502 functions as a main storage device that stores various programs and data required for the CPU 501 to execute various programs installed in the HDD 504. Specifically, the ROM 502 stores boot programs such as a Basic Input / Output System (BIOS) and an Extensible Firmware Interface (EFI) that are executed when the computer 500 is started, and data such as an Operating System (OS) setting and a network setting.

[0046] The RAM 503 is an example of a volatile semiconductor memory (storage device) in which programs and data are erased when the power is turned off. The RAM 503 is, for example, a dynamic random access memory (DRAM) or a static random access memory (SRAM). The RAM 503 provides a working area in which various programs installed in the HDD 504 are expanded when the CPU 501 executes them.

[0047] The HDD 504 is an example of a non-volatile storage device that stores programs and data. The programs and data stored in the HDD 504 include an OS, which is basic software that controls the entire computer 500, and applications that provide various functions on the OS. Note that the computer 500 may use a storage device that uses a flash memory as a storage medium (e.g., an SSD (Solid State Drive) or the like) instead of the HDD 504.

[0048] The input device 505 includes a touch panel, operation keys or buttons, a keyboard or mouse, a microphone for inputting sound data such as voice, etc., which are used by the user to input various signals.

[0049] The display device 506 is composed of a display such as a liquid crystal display or an organic EL (Electro-Luminescence) display for displaying a screen, a speaker for outputting sound data such as voice, and the like.

[0050] The communication I / F 507 is an interface that connects to a communication network and enables the computer 500 to perform data communication.

[0051] The external I / F 508 is an interface with external devices, such as a drive device 510.

[0052] The drive device 510 is a device for setting the recording medium 511. The recording medium 511 here includes media that record information optically, electrically, or magnetically, such as a CD-ROM, a flexible disk, or a magneto-optical disk. The recording medium 511 may also include semiconductor memories that record information electrically, such as a ROM or a flash memory. This allows the computer 500 to read and / or write data from and to the recording medium 511 via the external I / F 508.

[0053] The various programs to be installed in the HDD 504 are installed, for example, by setting the distributed recording medium 511 in a drive device 510 connected to the external I / F 508 and reading out the various programs recorded in the recording medium 511 by the drive device 510. Alternatively, the various programs to be installed in the HDD 504 may be installed by being downloaded from a network different from the communication network via the communication I / F 507.

[0054] <Functional configuration> The functional configuration of the analysis system in this embodiment will be described with reference to Fig. 5. Fig. 5 is a block diagram showing an example of the functional configuration of the analysis system in this embodiment.

[0055] ≪Visualization device≫ As shown in Figure 5, the visualization device 10 in this embodiment includes a data acquisition unit 101, a normalization unit 102, an axis point acquisition unit 103, a lattice point acquisition unit 104, a distance calculation unit 105, a dimension reduction unit 106, a model generation unit 107, a model memory unit 108, a data conversion unit 109, a lattice point conversion unit 110, an inverse normalization unit 111, and a visualization unit 112.

[0056] The data acquisition unit 101, normalization unit 102, axis point acquisition unit 103, lattice point acquisition unit 104, distance calculation unit 105, dimension reduction unit 106, model generation unit 107, data conversion unit 109, lattice point conversion unit 110, inverse normalization unit 111 and visualization unit 112 are realized by processing executed by the CPU 501 of a program loaded from the HDD 504 shown in Fig. 4 onto the RAM 503. The model storage unit 108 is realized by the HDD 504 shown in Fig. 4.

[0057] The data acquisition unit 101 acquires a plurality of data to be analyzed. The number of pieces of data is arbitrary. The data acquisition unit 101 may acquire data by receiving the data from the terminal device 20. The data acquisition unit 101 may acquire data input by a user to the input device 505. Hereinafter, the number of dimensions of the data is N, and the data is referred to as "N-dimensional data." Here, N is an integer equal to or greater than 4.

[0058] The normalization unit 102 normalizes each element of the N-dimensional data input to the data acquisition unit 101. Specifically, the normalization unit 102 normalizes each element of the N-dimensional data to a maximum of 1 and a minimum of 0.

[0059] The axis point acquisition unit 103 acquires N-dimensional coordinates of an axis point in the N-dimensional space. An axis point is a point that is an end of the N-dimensional space. Specifically, an axis point is a point where each element of the N-dimensional data takes the value 0 or 1, and the combination of 0 and 1 in each element does not overlap. The number of dimensions of the N-dimensional space is the same as the number of dimensions of the N-dimensional data acquired by the data acquisition unit 101. There are 2 to the Nth power of axis points in the N-dimensional space.

[0060] The lattice point acquisition unit 104 acquires N-dimensional coordinates of lattice points in an N-dimensional space. A lattice point is a point that divides a line connecting two axis points into M equal intervals. The number of divisions M is arbitrary, but may be, for example, M=10. There are M+1 to the Nth power of lattice points in the N-dimensional space.

[0061] The distance calculation unit 105 calculates a distance matrix indicating the distance for each combination of axis points acquired by the axis point acquisition unit 103. The distance measure indicated in the distance matrix may be Euclidean distance or non-Euclidean distance. When the distance measure is non-Euclidean distance, it may be Dice distance. An example of the Dice distance is the Mahalanobis distance.

[0062] When the dice distance is used as the distance measure, the distance calculation unit 105 updates the values ​​in the upper region of the anti-diagonal component of the distance matrix after generating the distance matrix with values ​​that are in line symmetrical positions with respect to the anti-diagonal component. In other words, the upper region is overwritten with the lower region across the anti-diagonal component of the distance matrix.

[0063] The dimension reduction unit 106 converts the N-dimensional coordinates of the axis points acquired by the axis point acquisition unit 103 into three-dimensional coordinates based on the distance matrix calculated by the distance calculation unit 105. Specifically, the dimension reduction unit 106 converts the N-dimensional coordinates of the axis points into three-dimensional coordinates based on multi-dimensional scaling (MDS).

[0064] The model generation unit 107 learns the relationship between the N-dimensional coordinates of the axis points acquired by the axis point acquisition unit 103 and the three-dimensional coordinates of the axis points converted by the dimension reduction unit 106, thereby generating a transformation model.

[0065] The conversion model in this embodiment is a neural network. The number of nodes in the input layer of the neural network is the number of dimensions (=N) of the N-dimensional space, and the number of nodes in the output layer is the number of dimensions (=3) of the three-dimensional space. The number of nodes in the intermediate layer is arbitrary, and may be, for example, 512. The activation function of the neural network can be the ReLU function.

[0066] The trained conversion model is stored in the model storage unit 108. The trained conversion model is generated by the model generation unit 107.

[0067] The data conversion unit 109 converts the N-dimensional data normalized by the normalization unit 102 into three-dimensional data based on the conversion model read from the model storage unit 108. Specifically, the data conversion unit 109 inputs the normalized N-dimensional data to the trained conversion model and acquires the three-dimensional data output from the conversion model.

[0068] The lattice point conversion unit 110 converts the N-dimensional coordinates of the lattice points acquired by the lattice point acquisition unit 104 into three-dimensional coordinates based on the conversion model read out from the model storage unit 108. Specifically, the lattice point conversion unit 110 inputs the N-dimensional coordinates of the lattice points to a trained conversion model and acquires the three-dimensional coordinates output from the conversion model.

[0069] The inverse normalization unit 111 inversely normalizes the N-dimensional coordinates of the axis points acquired by the axis point acquisition unit 103 and the N-dimensional coordinates of the lattice points acquired by the lattice point acquisition unit 104. The inverse normalization is the inverse conversion of the normalization performed on the N-dimensional data by the normalization unit 102. By performing the inverse normalization on the axis points and lattice points, the scale of the axis points and lattice points coincides with the scale of the N-dimensional data.

[0070] The visualization unit 112 arranges the N-dimensional data, the axis point cloud data, and the lattice point cloud data in a three-dimensional space. Specifically, the visualization unit 112 arranges the three-dimensional data obtained from the N-dimensional data by the data conversion unit 109, the three-dimensional coordinates of each axis point obtained by the dimension reduction unit 106, and the three-dimensional coordinates of each lattice point obtained by the lattice point conversion unit 110 in a three-dimensional space based on the multidimensional element construction method.

[0071] The visualization unit 112 may combine the N-dimensional data obtained by the data acquisition unit 101, the normalization unit 102, and the data conversion unit 109. The visualization unit 112 may also combine the axial point cloud data obtained by the axis point acquisition unit 103, the dimension reduction unit 106, and the inverse normalization unit 111. The visualization unit 112 may also combine the lattice point cloud data obtained by the lattice point acquisition unit 104, the lattice point conversion unit 110, and the inverse normalization unit 111.

[0072] The visualization unit 112 may change the display mode of the axis points and the grid points according to the complexity of the N-dimensional coordinates of the axis points and the grid points. The complexity of the N-dimensional coordinates is the number of elements that take a value other than 0 in the N-dimensional coordinates. The visualization unit 112 may plot the axis points and the grid points in different colors for each complexity, or may plot the axis points and the grid points in different shapes for each complexity.

[0073] The visualization unit 112 may display the axis points with emphasis. The visualization unit 112 may further display the origin and the farthest point among the axis points with emphasis. The farthest point is a point (i.e., an axis point where all elements are 1) that is the longest distance from the origin (i.e., an axis point where all elements are 0) among the axis points. For example, the visualization unit 112 may plot the axis points at points larger than the lattice points and the N-dimensional data. Also, for example, the visualization unit 112 may plot the farthest point in a color different from other axis points.

[0074] Terminal Device As shown in FIG. 5, the terminal device 20 in this embodiment includes a data input unit 201 and a result display unit 202.

[0075] The data input unit 201 and the result display unit 202 are realized by processing that is executed by the CPU 501 according to a program loaded onto the RAM 503 from the HDD 504 shown in FIG.

[0076] The data input unit 201 receives input of a plurality of N-dimensional data to be analyzed in response to a user operation. The data input unit 201 transmits the input N-dimensional data to the visualization device 10.

[0077] The result display unit 202 outputs the visualization result received from the visualization device 10 to the display device 506. The visualization result shows the distribution of the N-dimensional data to be analyzed in a three-dimensional space. Specifically, the three-dimensional data includes three-dimensional coordinates of axis points, three-dimensional coordinates of lattice points, and three-dimensional data corresponding to the multidimensional data to be analyzed.

[0078] <Processing Procedure> The processing procedure of the visualization method executed by analysis system 1000 in this embodiment will be described with reference to Fig. 6. Fig. 6 is a flowchart showing an example of the visualization method in this embodiment.

[0079] In step S1, the data input unit 201 of the terminal device 20 accepts input of a plurality of N-dimensional data to be analyzed in response to a user operation. Next, the data input unit 201 transmits the input N-dimensional data to the visualization device 10.

[0080] In the visualization device 10, the data acquisition unit 101 acquires a plurality of N-dimensional data to be analyzed. Next, the data acquisition unit 101 stores the acquired N-dimensional data in a storage unit such as the HDD 504. In addition, the data acquisition unit 101 sends the number of dimensions N of the N-dimensional data to the axis point acquisition unit 103.

[0081] Fig. 7 is a diagram showing an example of N-dimensional data. As shown in Fig. 7, the N-dimensional data in this embodiment is four-dimensional data having four attributes (attributes A to D) as elements. Fig. 7 shows an example of N-dimensional data with a dimension number N of 4, but the dimension number N may be 5 or more. In the case of N-dimensional data with 5 or more dimensions, the number of columns of the N-dimensional data increases to the dimension number N.

[0082] Returning to Fig. 6, in step S2, the normalization unit 102 of the visualization device 10 reads out the N-dimensional data from the storage unit. Next, the normalization unit 102 normalizes each element of the N-dimensional data. Then, the normalization unit 102 sends the normalized N-dimensional data to the data conversion unit 109 and the visualization unit 112. In addition, the normalization unit 102 sends information indicating the content of normalization performed on each element of the N-dimensional data to the denormalization unit 111.

[0083] Fig. 8 is a diagram showing an example of N-dimensional data after normalization. As shown in Fig. 8, in the N-dimensional data after normalization, each attribute of the N-dimensional data shown in Fig. 7 is normalized to a range of 0 to 1.

[0084] Returning to Fig. 6, in step S3, the axis point acquisition unit 103 of the visualization device 10 receives the number of dimensions N of the N-dimensional data from the data acquisition unit 101. Next, the axis point acquisition unit 103 acquires N-dimensional coordinates of the axis points in the N-dimensional space. Then, the axis point acquisition unit 103 stores the axis point cloud data indicating the acquired axis points in a storage unit such as the HDD 504.

[0085] Fig. 9 is a diagram showing an example of axis point cloud data. As shown in Fig. 9, the axis point cloud data is 2 to the power of N data, in which each element takes 0 or 1 and the combination of values ​​of each element does not overlap. Since the N-dimensional data shown in Fig. 7 is four-dimensional data, the axis point cloud data shown in Fig. 9 includes 16 axis points h_0 to h_15.

[0086] Returning to Fig. 6, in step S4, the lattice point acquisition unit 104 of the visualization device 10 reads out the axial point cloud data stored in the storage unit. Next, the lattice point acquisition unit 104 acquires N-dimensional coordinates of lattice points in the N-dimensional space based on the axial point cloud data. Then, the lattice point acquisition unit 104 stores the lattice point cloud data indicating the acquired lattice points in a storage unit such as the HDD 504.

[0087] Fig. 10 is a diagram showing an example of lattice point cloud data. As shown in Fig. 10, the lattice point cloud data is M+1 N pieces of data in which each element takes one of values ​​obtained by dividing 0 to 1 into M parts, and the combinations of values ​​of each element do not overlap. In the lattice point cloud data shown in Fig. 10, each element is divided into 5 increments of 0.2, so the lattice point cloud data includes 1296 (6 to the fourth power) lattice points t_0 to t_1295.

[0088] Note that the N-dimensional coordinates included in the lattice point cloud data shown in Fig. 10 include those that overlap with the N-dimensional coordinates included in the axis point cloud data shown in Fig. 9. In the subsequent processing, the coordinates that overlap between the lattice point cloud data and the axis point cloud data will be treated as axis points.

[0089] Returning to FIG. 6, in step S5, the distance calculation unit 105 of the visualization device 10 reads out the axis point cloud data stored in the storage unit. Next, the distance calculation unit 105 calculates the distance between two axis points for each combination of axis points shown in the axis point cloud data. Next, the distance calculation unit 105 generates a distance matrix indicating the distance for each combination of axis points. Then, the distance calculation unit 105 sends the generated distance matrix to the dimension reduction unit 106.

[0090] Fig. 11 is a diagram showing an example of a distance matrix. As shown in Fig. 11, the distance matrix is ​​a matrix in which each matrix indicates an axis point, and the distance between the axis points is set for each combination of axis points. Therefore, the diagonal matrix of the distance matrix is ​​1.0 because it is the distance between the same axis points, and two distances that are in line symmetrical positions with respect to the diagonal matrix have the same value.

[0091] Returning to FIG. 6, in step S6, the dimension reduction unit 106 of the visualization device 10 receives the distance matrix from the distance calculation unit 105. Next, the dimension reduction unit 106 reads out the axis point cloud data stored in the storage unit. Next, the dimension reduction unit 106 converts the N-dimensional coordinates of the axis points indicated in the axis point cloud data into three-dimensional coordinates based on the distance matrix. Then, the dimension reduction unit 106 sends the axis point cloud data indicating the axis points after dimension reduction to the model generation unit 107 and the visualization unit 112.

[0092] Fig. 12 is a diagram showing an example of axial point cloud data after dimension reduction. As shown in Fig. 12, the axial point cloud data after dimension reduction is data obtained by reducing the axial point cloud data shown in Fig. 9 to three dimensions by the multidimensional element construction method. Each element y0 to y2 in the axial point cloud data after dimension reduction corresponds to each axis of the three-dimensional space generated by the multidimensional element construction method.

[0093] Returning to FIG. 6, in step S7, the model generation unit 107 of the visualization device 10 receives the axis point cloud data after dimension reduction from the dimension reduction unit 106. Next, the dimension reduction unit 106 reads out the axis point cloud data (i.e., the axis point cloud data before dimension reduction) stored in the storage unit. Next, the model generation unit 107 learns the relationship between the N-dimensional coordinates and the three-dimensional coordinates of the axis points based on the axis point cloud data before dimension reduction and the axis point cloud data after dimension reduction, thereby generating a conversion model. Then, the model generation unit 107 stores the learned conversion model in the model storage unit 108.

[0094] In step S8, the data conversion unit 109 of the visualization device 10 receives the normalized N-dimensional data from the normalization unit 102. Next, the data conversion unit 109 reads out the trained conversion model from the model storage unit 108. Then, the data conversion unit 109 inputs the normalized N-dimensional data into the trained conversion model.

[0095] The conversion model converts the input N-dimensional data into three-dimensional data and outputs it. The data conversion unit 109 acquires the three-dimensional data output from the conversion model. The data conversion unit 109 then sends the N-dimensional data after dimension reduction to the visualization unit 112.

[0096] Fig. 13 is a diagram showing an example of N-dimensional data after dimension reduction. As shown in Fig. 13, the N-dimensional data after dimension reduction is data obtained by converting the normalized N-dimensional data shown in Fig. 8 into three dimensions.

[0097] Returning to Fig. 6, in step S9, the lattice point conversion unit 110 of the visualization device 10 reads out the lattice point cloud data stored in the storage unit. Next, the lattice point conversion unit 110 reads out the trained conversion model from the model storage unit 108. Next, the lattice point conversion unit 110 inputs the N-dimensional coordinates of the lattice points indicated in the lattice point cloud data into the trained conversion model.

[0098] The conversion model converts the input N-dimensional coordinates of the grid points into three-dimensional coordinates and outputs them. The grid point conversion unit 110 acquires the three-dimensional coordinates output from the conversion model. The grid point conversion unit 110 then sends the grid point group data after the dimension reduction to the visualization unit 112.

[0099] Fig. 14 is a diagram showing an example of lattice point cloud data after dimension reduction. As shown in Fig. 14, the lattice point cloud data after dimension reduction is data obtained by converting the lattice point cloud data shown in Fig. 10 into three dimensions.

[0100] Returning to FIG. 6, in step S10, the inverse normalization unit 111 of the visualization device 10 reads out the axis point cloud data stored in the storage unit. Next, the inverse normalization unit 111 receives information indicating the content of normalization from the normalization unit 102. Next, based on the information indicating the content of normalization, the inverse normalization unit 111 performs, on the axis point cloud data, an inverse transformation of the normalization performed on the N-dimensional data in step S2. Then, the inverse normalization unit 111 sends the axis point cloud data after the inverse transformation to the visualization unit 112.

[0101] Fig. 15 is a diagram showing an example of the axis point cloud data after denormalization. As shown in Fig. 15, the axis point cloud data after denormalization is data in which the scale of the axis point cloud data shown in Fig. 9 is matched with the scale of the N-dimensional data shown in Fig. 7.

[0102] Returning to Fig. 6, in step S11, the inverse normalization unit 111 of the visualization device 10 reads out the lattice point cloud data stored in the storage unit. Next, based on information indicating the content of normalization, the inverse normalization unit 111 performs an inverse transformation on the lattice point cloud data, which was performed on the N-dimensional data in step S2. Then, the inverse normalization unit 111 sends the lattice point cloud data after the inverse transformation to the visualization unit 112.

[0103] Fig. 16 is a diagram showing an example of lattice point cloud data after denormalization. As shown in Fig. 16, the lattice point cloud data after denormalization is data in which the scale of the lattice point cloud data shown in Fig. 10 is matched with the scale of the N-dimensional data shown in Fig. 7.

[0104] Returning to FIG. 6, in step S12, the visualization unit 112 of the visualization device 10 reads out N-dimensional data (N-dimensional data before dimension reduction) from the storage unit. The visualization unit 112 also receives the normalized N-dimensional data from the normalization unit 102. The visualization unit 112 also receives the dimension-reduced N-dimensional data from the data conversion unit 109. The visualization unit 112 then combines the N-dimensional data before dimension reduction, the normalized N-dimensional data, and the dimension-reduced N-dimensional data (three-dimensional data). Specifically, the visualization unit 112 combines the N-dimensional data into one multidimensional data by linking the N-dimensional data in the row direction (horizontal direction).

[0105] Next, the visualization unit 112 reads out the axis point cloud data (axis point cloud data before dimension reduction) from the storage unit. The visualization unit 112 also receives the axis point cloud data after dimension reduction from the dimension reduction unit 106. The visualization unit 112 also receives the axis point cloud data after denormalization from the denormalization unit 111. Then, the visualization unit 112 combines the axis point cloud data before dimension reduction, the axis point cloud data after dimension reduction, and the axis point cloud data after denormalization. Specifically, the visualization unit 112 combines each axis point cloud data in the row direction (horizontal direction) to combine them into one axis point cloud data.

[0106] Next, the visualization unit 112 reads out the lattice point cloud data (lattice point cloud data before dimension reduction) from the storage unit. The visualization unit 112 also receives the lattice point cloud data after dimension reduction from the lattice point conversion unit 110. The visualization unit 112 also receives the lattice point cloud data after denormalization from the denormalization unit 111. Then, the visualization unit 112 combines the lattice point cloud data before dimension reduction, the lattice point cloud data after dimension reduction, and the lattice point cloud data after denormalization. Specifically, the visualization unit 112 combines each lattice point cloud data in the row direction (horizontal direction) to combine them into one lattice point cloud data.

[0107] In step S13, the visualization unit 112 of the visualization device 10 arranges the dimension-reduced N-dimensional data, the dimension-reduced axis point cloud data, and the dimension-reduced lattice point cloud data acquired in step S12 in a three-dimensional space based on the multidimensional element construction method. At this time, the visualization unit 112 changes the display mode of the axis points and the lattice points according to the complexity of the axis points and the lattice points. The visualization unit 112 also highlights the axis points. The visualization unit 112 further highlights the origin and the farthest point.

[0108] Fig. 17 is a diagram showing an example of a visualization result. As shown in Fig. 17, the visualization result in this embodiment includes a three-dimensional space generated by multidimensional scaling. In the visualization result, an origin 301, an furthest point 302, and N-dimensional data 303 after dimension reduction are arranged. Note that in Fig. 17, only representative N-dimensional data are labeled. All small black plots in Fig. 17 are N-dimensional data.

[0109] In the visualization result, axis points 311 to 313 are arranged. In addition, in the visualization result, lattice points 321 to 323 are arranged. Note that in Fig. 17, similar to the N-dimensional data, only representative axis points and lattice points are labeled. In Fig. 17, the larger plots are axis points and the smaller plots are lattice points.

[0110] In the visualization results, axis points and grid points are displayed in different colors depending on the complexity. In Fig. 17, axis points or grid points with a complexity of 1 (i.e., one non-zero element) are displayed in a first color (yellow), axis points or grid points with a complexity of 2 (i.e., two non-zero elements) are displayed in a second color (green), and axis points or grid points with a complexity of 3 (i.e., three non-zero elements) are displayed in a third color (orange).

[0111] In the visualization result shown in Fig. 17, axis points and lattice points with a complexity of 1 are arranged in region 331, axis points and lattice points with a complexity of 2 are arranged in region 332, and axis points and lattice points with a complexity of 3 are arranged in region 333. In other words, in the visualization result shown in Fig. 17, axis points and lattice points with the same complexity are displayed in close regions, and it can be seen that the axis points and lattice points are arranged in layers according to their complexity.

[0112] The visualization result shown in FIG. 17 satisfies all six of the above criteria. First, this visualization result visualizes the axial point group and the lattice point group, and thus visualizes the distribution of multidimensional data including blank areas. Therefore, the first criterion is met. Second, this visualization result uses the origin, the farthest point, and the axial point group as reference points. Therefore, the second criterion is met. Third, this visualization result allows the direction of the axis to be determined by the angle from the origin and the layer. Therefore, the third criterion is met.

[0113] Fourth, in this visualization result, the axis can be determined from the position of the axis point, so there is no concept of an axis and overlapping of axes cannot occur. Therefore, the fourth indicator is met. Fifth, in this visualization result, N-dimensional data can be determined centrally. Therefore, the fifth indicator is met. Sixth, in this visualization result, blank areas can be determined centrally from the axis point group and the lattice point group, so blank areas can be determined centrally. Therefore, the sixth indicator is met.

[0114] According to the visualization result by the visualization unit 112, the user can easily confirm what N-dimensional data the blank area corresponds to. For example, the user can select a desired point in the blank area shown in the visualization result. The visualization unit 112 holds multidimensional data combining the N-dimensional data before dimension reduction, the N-dimensional data after normalization, and the N-dimensional data after dimension reduction, and can therefore display the N-dimensional coordinates before dimension reduction that correspond to the three-dimensional coordinates of the selected blank area. Furthermore, the visualization unit 112 can display the N-dimensional coordinates after normalization that correspond to the three-dimensional coordinates of the selected blank area based on the multidimensional data.

[0115] For example, if the N-dimensional data is composition information obtained by an experiment or the like, the blank areas are areas where no experimental data exists, so the user can easily know the compositions for which no experimental data is available. In particular, the user can intuitively determine the relative relationship between the blank areas and other N-dimensional data, and therefore can efficiently consider the composition to be experimented next.

[0116] <Comparison with conventional technology> A visualization result according to the conventional technology will be described with reference to Fig. 18. Fig. 18 is a diagram showing an example of a visualization result according to Comparative Example 1. Comparative Example 1 is a visualization result when N-dimensional data, axis point cloud data, and lattice point cloud data are directly arranged in a three-dimensional space by the multidimensional scaling method.

[0117] 18, in the visualization result of Comparative Example 1, the multidimensional data, axis points, and lattice points are concentrated on the outer edge of the three-dimensional space, and the data cannot be displayed in a unified manner. In addition, in this visualization result, the data is concentrated at one point, so the distribution of the data cannot be visualized.

[0118] <Comparison of distance measures> In this embodiment, non-Euclidean distance is used as the distance measure, but Euclidean distance may be used. Differences in visualization results depending on the distance measure will be described with reference to Fig. 19. Fig. 19 is a diagram showing an example of a visualization result according to Comparative Example 2. Comparative Example 2 is a visualization result when a distance matrix is ​​calculated using Euclidean distance.

[0119] As shown in FIG. 19, in the visualization result of Comparative Example 2, N-dimensional data, axis points, and lattice points can be visualized. In the visualization result of Comparative Example 2, even if the display form is changed according to the complexity, the layers for each complexity are not separated, and mixed regions 401 to 403 are created. It can be seen that axis points or lattice points with different complexities are mixed in the regions 401 to 403. Therefore, although visualization that satisfies the above six indices is possible whether using Euclidean distance or non-Euclidean distance, using non-Euclidean distance (especially dice distance) makes it possible to visualize in layers according to the complexity, and visualization that is easier for analysts to understand can be realized.

[0120] <Effects of the embodiment> The visualization device 10 in this embodiment converts the N-dimensional coordinates of the axis points into three-dimensional coordinates based on the distance between the axis points in the N-dimensional space, converts a plurality of N-dimensional data into three-dimensional data based on a conversion model that has learned the relationship between the N-dimensional coordinates of the axis points and the three-dimensional coordinates of the axis points, and arranges the three-dimensional coordinates of the axis points and the three-dimensional data in the three-dimensional space. In the three-dimensional space, the axis points and data are visualized including blank areas. Therefore, according to this embodiment, the distribution of multidimensional data of four or more dimensions can be visualized.

[0121] The visualization device 10 may convert the N-dimensional coordinates of the lattice points into three-dimensional coordinates based on the conversion model, and further arrange the three-dimensional coordinates of the lattice points in a three-dimensional space. Therefore, according to this embodiment, the distribution of multidimensional data can be visualized in an easy-to-understand manner.

[0122] The visualization device 10 may change the display mode of the lattice points and the three-dimensional data according to the complexity of the N-dimensional coordinates. Therefore, according to this embodiment, it is possible to visualize the distribution by layer according to the complexity of the multidimensional data in an easy-to-understand manner.

[0123] The visualization device 10 may normalize the N-dimensional data and perform an inverse transformation of the normalization on the N-dimensional coordinates of the axis points and the N-dimensional coordinates of the lattice points. Therefore, according to this embodiment, the positional relationship between the axis points and the lattice points and the data can be appropriately visualized.

[0124] The visualization device 10 may convert the N-dimensional coordinates of the axis points into three-dimensional coordinates based on the non-Euclidean distance. The non-Euclidean distance may be the Dice distance. By using these distances, the positional relationship between the axis points and the grid points and the data can be more appropriately visualized. Therefore, according to this embodiment, the distribution of multidimensional data can be appropriately visualized.

[0125] The visualization device 10 may convert the N-dimensional coordinates of the axis points into three-dimensional coordinates based on multidimensional scaling. The three-dimensional positions of the axis points can be appropriately converted using multidimensional scaling. Therefore, according to this embodiment, the distribution of multidimensional data can be appropriately visualized.

[0126] [supplement] Each function of the above-described embodiments can be realized by one or more processing circuits. Here, the term "processing circuit" in this specification includes a processor programmed to execute each function by software, such as a CPU (Central Processing Unit) or GPU (Graphics Processing Unit) implemented by an electronic circuit, and an ASIC (Application Specific Integrated Circuit), DSP (Digital Signal Processor), FPGA (Field Programmable Gate Array), conventional circuit module, and other devices designed to execute each function described above.

[0127] Although the embodiments of the present disclosure have been described in detail above, the embodiments disclosed herein are illustrative and not restrictive in all respects. The embodiments can be modified and improved in various forms without departing from the scope and spirit of the appended claims. The matters described in the above embodiments can be configured in other ways as long as they are not inconsistent, and can be combined as long as they are not inconsistent. [Explanation of symbols]

[0128] 10 Visualization device 20 Terminal Equipment 101 Data Acquisition Section 102 Normalization section 103 Axis point acquisition part 104 Grid point acquisition part 105 Distance calculation section 106 Dimensionality reduction part 107 Model Generation Unit 108 Model Memory Section 109 Data Conversion Section 110 Grid Point Conversion Unit 111 Denormalization part 112 Visualization section 201 Data Entry Department 202 Result display section 1000 Analysis System

Claims

1. an axis point acquisition unit configured to acquire N-dimensional coordinates of an axis point in an N-dimensional space, where N is an integer equal to or greater than 4; a distance calculation unit configured to calculate a distance matrix indicating distances for each combination of the axis points; a dimensionality reduction unit configured to transform the N-dimensional coordinates of the axis points into three-dimensional coordinates based on the distance matrix; a model generation unit configured to generate a transformation model that learns a relationship between the N-dimensional coordinates of the axis points and the three-dimensional coordinates of the axis points; a data conversion unit configured to convert a plurality of N-dimensional data into three-dimensional data based on the conversion model; a visualization unit configured to arrange the N-dimensional data and the axis points in a three-dimensional space based on the N-dimensional data, the three-dimensional data, the N-dimensional coordinates of the axis points, and the three-dimensional coordinates of the axis points; A visualization device comprising:

2. The visualization device according to claim 1 , a lattice point acquisition unit configured to acquire N-dimensional coordinates of lattice points in the N-dimensional space; a lattice point conversion unit configured to convert the N-dimensional coordinates of the lattice points into three-dimensional coordinates based on the conversion model; Further equipped with The visualization unit is configured to arrange the lattice points in the three-dimensional space based on N-dimensional coordinates of the lattice points and three-dimensional coordinates of the lattice points. Visualization device.

3. The visualization device according to claim 2, The visualization unit is configured to change a display mode of the axis points or the lattice points according to a degree of complexity of the N-dimensional coordinates of the axis points or the N-dimensional coordinates of the lattice points. Visualization device.

4. The visualization device according to claim 2, The visualization unit is configured to change a display mode of an origin and a farthest point among the axis points. Visualization device.

5. The visualization device according to claim 2, a normalization unit that normalizes each element of the N-dimensional data; an inverse normalization unit that performs an inverse transformation of the normalization on the N-dimensional coordinates of the axis points and the N-dimensional coordinates of the lattice points; The visualization device further comprises:

6. The visualization device according to any one of claims 1 to 5, The distance is a non-Euclidean distance. Visualization device.

7. The visualization device according to claim 6, The non-Euclidean distance is a Dice distance. Visualization device.

8. The visualization device according to any one of claims 1 to 5, The dimensionality reduction unit is configured to convert the N-dimensional coordinates of the axis points into three-dimensional coordinates based on a multidimensional scaling method. Visualization device.

9. The computer obtaining N-dimensional coordinates of an axis point in an N-dimensional space, where N is an integer equal to or greater than 4; calculating a distance matrix indicating distances for each combination of the axis points; converting the N-dimensional coordinates of the axis points into three-dimensional coordinates based on the distance matrix; A step of generating a transformation model that learns a relationship between the N-dimensional coordinates of the axis points and the three-dimensional coordinates of the axis points; converting a plurality of N-dimensional data into three-dimensional data based on the conversion model; a step of arranging the N-dimensional data and the axis points in a three-dimensional space based on the N-dimensional data, the three-dimensional data, the N-dimensional coordinates of the axis points, and the three-dimensional coordinates of the axis points; A visualization method to perform.

10. On the computer, obtaining N-dimensional coordinates of an axis point in an N-dimensional space, where N is an integer equal to or greater than 4; calculating a distance matrix indicating distances for each combination of the axis points; converting the N-dimensional coordinates of the axis points into three-dimensional coordinates based on the distance matrix; A step of generating a transformation model that learns a relationship between the N-dimensional coordinates of the axis points and the three-dimensional coordinates of the axis points; converting a plurality of N-dimensional data into three-dimensional data based on the conversion model; a step of arranging the N-dimensional data and the axis points in a three-dimensional space based on the N-dimensional data, the three-dimensional data, the N-dimensional coordinates of the axis points, and the three-dimensional coordinates of the axis points; A program for executing the above.

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