JP2009276913A - Clustering analysis device, clustering analysis method, and clustering analysis program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve the problem that it is difficult to understand the behavior of multivariate data by static display with the position of a leaf or the like fixed therefor when displaying the result of hierarchical clustering analysis by a dendrogram. <P>SOLUTION: In a clustering analysis method, multivariate data associated with an analytic object are successively obtained according to time series (S30) to execute hierarchical clustering analysis concerning prescribed analytic object data among the multivariate data (S32). On the basis of the result of this analysis, a three-dimensional dendrogram is constructed on a basic surface, and a projection image thereof is generated. The basic face is defined by associating prescribed coordinate data among the multivariate data with a coordinate axis in a three-dimensional space, and an analytic object is arranged as a leaf at a position corresponding to the coordinate data on the basic surface, and a branch corresponding to each leaf is erected on the basic surface to obtain a three-dimensional dendrogram. The processing is repeated according to a time series, so that the analytic result of hierarchical clustering analysis can be presented as the image of a dynamic three-dimensional dendrogram. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a clustering analysis apparatus, a clustering analysis method, and a clustering analysis program for performing cluster analysis and displaying an image of the analysis result as a dendrogram.

  In recent years, positioning technology using a GPS function or a wireless LAN mounted on a mobile phone has become widespread. According to such a technique, it is possible to obtain a large number of positions of the object at the same time. Accordingly, for example, it may be necessary to present information on a large number of objects on an image in an easily understandable format to a system administrator or the like. However, when the number of objects is large, it is difficult to grasp global information existing between objects in an image in which each object is displayed as one object such as a point.

  Clustering analysis exists as a method that enables such a large number of objects to be grasped globally. In hierarchical clustering, which is one of them, the similarity between a plurality of analysis objects is obtained based on the Euclidean distance related to multivariate data associated with the analysis objects, and the analysis objects are grouped based on the similarity. . A dendrogram is known as a method for displaying the result of this hierarchical clustering.

The dendrogram is a dendrogram (tournament diagram) in which distances between clusters are calculated using definition formulas such as the Ward method and nearest neighbor method, and clusters with small distances, that is, clusters with high similarity are sequentially collected. FIG. 8 is a diagram illustrating an example of a dendrogram. Analysis objects S _{01 to} S _{08 which} are leaves (terminal nodes) of the tree diagram are arranged along the horizontal direction of the figure. The vertical axis in the figure represents the distance between clusters. Here, it is assumed that each analysis target is a cluster composed of one analysis target. A branch (branch) 2 is extended upward from each cluster. Branches of clusters closer to each other than other clusters are connected at a height corresponding to the distance to form a node (non-terminal node) 4. The clusters joined at the node 4 form a new cluster, and the branch 2 extends upward from the node 4. Cluster example, in FIG. _{8, S 01} and _{S 02} are coupled at node _{N 01} form a cluster _{C 01} of one level higher in the hierarchy, the cluster _{C 01 then the S 03} and _{S 04} are coupled C ₀₂ and node N _{02 are} combined to form a higher layer cluster C ₀₃ .

The dendrogram is generally represented by a two-dimensional structure as shown in FIG. 8, but it can also be expressed as a three-dimensional structure as shown in Patent Document 1.
JP 2006-163894 A

  The conventional hierarchical clustering method is used for static data, and the dendrogram for displaying the analysis result is a still image. Therefore, there is a problem that it is difficult to grasp the behavior of multivariate data obtained in time series such as positioning data of a moving body.

  The present invention has been made to solve the above-described problems, and the analysis result of the hierarchical clustering for the analysis target associated with the data obtained in time series can be intuitively understood by the user. It is an object to provide a clustering analysis device, a clustering analysis method, and a clustering analysis program that can be presented.

  The clustering analysis apparatus according to the present invention relates to a plurality of analysis objects associated with a plurality of types of element data represented in time series, and the similarity between the analysis objects with respect to predetermined analysis object data among the element data And the analysis unit that sequentially performs hierarchical clustering analysis at each time according to the time series, and the analysis target is associated with a position corresponding to predetermined coordinate data in the element data in a three-dimensional space The analysis result of the hierarchical clustering analysis is a three-dimensional dendrogram in which each of the analysis objects arranged on the base surface is defined as a leaf and a branch for each leaf is erected on the base surface. And a dendrogram image generation unit that generates a projection image of the dendrogram that changes in accordance with the time series. It is intended.

  A preferred aspect of the present invention is a clustering analysis apparatus in which the coordinate data includes the analysis object data as a part thereof.

  In another preferred aspect of the present invention, the projection image when the dendrogram image generation unit defines a cluster with a set clustering threshold value has a structure of a portion corresponding to the cluster in the dendrogram. Then, an image replaced with an extension line of a branch connected to the cluster is generated.

  In still another preferred aspect of the present invention, the dendrogram image generation unit is a tertiary having a size corresponding to the number of the analysis objects included in the cluster at a position corresponding to the cluster on the basic surface. The original object is displayed as an image. In this aspect, the three-dimensional object can be a hemisphere. In addition, the three-dimensional object may be formed by stacking element objects having a predetermined size from the base surface in a number corresponding to the number of analysis objects included in the cluster.

  In the clustering analysis method according to the present invention, for a plurality of analysis objects associated with a plurality of types of element data represented in time series, the similarity between the analysis objects related to predetermined analysis object data among the element data An analysis step for performing a hierarchical clustering analysis, and defining a basic plane in which the analysis target is associated with a position corresponding to predetermined coordinate data of the element data in a three-dimensional space, and A three-dimensional dendrogram in which each analysis object arranged on a plane is a leaf and a branch for each leaf is erected on the base plane is obtained based on the analysis result of the hierarchical clustering analysis, and the dendrogram A dendrogram image generating step for generating a projection image, and sequentially performing the dendrogram motion according to the time series. To generate the image.

  Further, the clustering analysis program according to the present invention provides a plurality of analysis objects associated with a plurality of types of element data represented in time series, between the analysis objects related to predetermined analysis object data among the element data. Based on the similarity, an analysis step for performing a hierarchical clustering analysis, and in the three-dimensional space, define a basic plane in which the analysis target is associated with a position according to predetermined coordinate data of the element data, A three-dimensional dendrogram in which each analysis object arranged on the base plane is a leaf and a branch for each leaf is erected on the base plane is obtained based on the analysis result of the hierarchical clustering analysis. A dendrogram image generation step for generating a projected image of the gram, and sequentially in a computer according to the time series Is the line, and generates a moving image of the dendrogram.

  According to the present invention, the analysis result of the hierarchical clustering with respect to the analysis target associated with the element data represented in time series such as positioning data is displayed as an image as a dynamic and three-dimensional dendrogram. By displaying a part of the element data constituting the multivariate data as the position on the basic surface as the coordinate data, the user's intuitive understanding is improved. In particular, when the coordinate data is analysis target data, it is possible to intuitively understand the similarity between clusters based on the distance on the basic surface.

  Hereinafter, embodiments of the present invention (hereinafter referred to as embodiments) will be described with reference to the drawings.

  FIG. 1 is a schematic block diagram of a clustering analysis apparatus 10 according to the embodiment. The clustering analysis apparatus 10 includes a processing unit 12, a display unit 14, a storage unit 16, and an operation unit 18. The processing unit 12 includes an analysis unit 20 and a dendrogram image generation unit 22. For example, the clustering analysis apparatus 10 can be configured using a computer, the CPU configures the processing unit 12, and the analysis unit 20 and the dendrogram image generation unit 22 can be realized by a program executed by the CPU. The storage unit 16 includes a hard disk built in the computer, the display unit 14 includes an image display device such as a liquid crystal monitor, and the operation unit 18 includes a keyboard and a mouse.

  The clustering analysis apparatus 10 performs, for example, hierarchical clustering processing on analysis target data (analysis target data) among multivariate data related to a mobile object to be analyzed according to a time series, thereby obtaining a three-dimensional dendrogram. Animate the image. The processing unit 12 may perform online processing on the analysis purpose data observed in real time, and may perform off-line processing on the analysis purpose data stored in the storage unit 16.

  The analysis unit 20 obtains the similarity between the analysis targets based on the distance regarding the analysis target data, and performs hierarchical clustering analysis on the analysis target based on the distance. The analysis unit 20 performs hierarchical clustering for each time constituting the time series.

  The dendrogram image generation unit 22 defines a base plane in a virtual three-dimensional space, and uses the structure of the dendrogram arranged on the base plane as an analysis result of the analysis unit 20 and a display parameter to be described later. Ask based. Then, for example, according to the line-of-sight direction specified by the user, the three-dimensional space in which the base plane and the dendrogram are constructed is projected and converted to generate image data of the projected image.

  The display unit 14 receives image data sequentially generated by the dendrogram image generation unit 22 in time series, and displays a projected image on which a three-dimensional dendrogram is displayed as a moving image.

  The operation unit 18 allows the user to set and change display parameters and the like. For example, the user can manipulate the types of projection transformation such as parallel projection and perspective projection, the line-of-sight direction, the dendrogram clustering threshold, the type of object representing the cluster, and the like as display parameters.

FIG. 2 is a flowchart showing a schematic operation of the processing unit 12 of the clustering analysis apparatus according to the embodiment. Processing unit 12 as a processing by the analyzing unit 20, the time series _T k (k is an integer and _{T k} + 1> _{T k} for any k.) Multivariate that observed input at time _{T n} of the Data or multivariate data at time T _n stored in advance in the storage unit 16 is acquired (S30), and hierarchical clustering analysis is performed on the acquired multivariate data (S32). By the clustering analysis, a set of lower clusters that are combined with each other to form an upper cluster and a distance d between the lower clusters are obtained.

  The dendrogram image generation unit 22 generates a projection image of a three-dimensional dendrogram based on the analysis result (S34). At that time, the dendrogram image generation unit 22 generates an image with reference to the set display parameter. The generated image data is output to the display unit 14. The generation of the three-dimensional dendrogram image will be described later.

When the image generation of the dendrogram time _{T n} is completed (S34), the time series of multivariate data next time _{T n + 1} is acquired (S30), the above processing S32, S34 are repeated. Thus, as long as there is multivariate data to be processed (S36), the clustering process S32 and the dendrogram image generation process S34 are basically repeated, and the generated images are sequentially displayed on the display unit 14. Thus, a three-dimensional dendrogram is dynamically displayed.

  When there is no more multivariate data to be processed (S36), the processing unit 12 ends the clustering process S32 and the dendrogram image generation process S34.

  Next, generation of a projection image of a three-dimensional dendrogram will be described. When generating the projection image, the coordinates of each node (terminal node and non-terminal node) of the dendrogram with respect to the base plane are obtained. 3 and 4 are schematic diagrams for explaining a method of determining coordinates of each node of the dendrogram. These drawings show the lowermost layer portion of the three-dimensional dendrogram. For convenience, for example, an orthogonal coordinate system xyz in which the base plane is z = 0 is defined, and the direction in which the branch extends is perpendicular to the base plane (z Axis direction).

The dendrogram image generation unit 22 generates, as basic dendrograms, terminal nodes (terminal nodes) N _T1 and N _T2 arranged on the base plane are leaves, that is, a single analysis target. FIG. 3 is a diagram for explaining this case. As described above, _NT1 and _NT2 are arranged on the base plane, so their z coordinate is z = 0. On the other hand, the x and y coordinates of N _T1 and N _T2 are set according to predetermined element data e _C1 and e _C2 defined as coordinate data among the multivariate data to be analyzed. The branches B ₁ and B ₂ connected to N _T1 and N _T2 extend to a height corresponding to the distance d ₁ between the analysis target S ₁ arranged at N _T1 and the analysis target S ₂ arranged at N _T2. . S ₁ and S ₂ are combined at this height d ₁ , and one layer forms the upper cluster C ₁ . Node _{N M} corresponding to C ₁ is non-terminal node is set between the upper end _{P U1, P U2} branch _B 1, _{B 2.} Specifically _{d 1} is the z coordinate of _{N M,} also x, y coordinates are set at the midpoint of the _{N T1, N T2} (or _{P U1, P U2).} Branch _B is connected to C _{1 3} extends from _{N M,} up to a height _{d 2} corresponding to the distance between the mating cluster combined with _{C 1.} In this way, the coordinates of the upper layer nodes are sequentially determined. In the example shown in FIG. 3, since the cluster _{C 1} contains only two analytes, the node _{N M} corresponding to _{C 1} x, y coordinate two corresponding to their analyte of _{N T1, N T2} and the midpoint, but more numerous analyzes of the node N _M corresponding to the cluster including the target x, the y-coordinate is preferred to the center of gravity of the analyte of coordinates included in the cluster.

In addition, the dendrogram image generation unit 22 can generate a dendrogram showing a clustered state as one cluster when the distance between the analysis objects is equal to or less than the set clustering threshold γ. FIG. 4 is a diagram for explaining this case, and shows a case where γ satisfying d ₁ <γ <d ₂ is set in the example shown in FIG. In this case, gamma following structure abridged dendrogram is generated one branch B _R, thereby representing a state of being clustered. B _R is a branch B ₃ which are connected to the cluster C ₁ present at the level γ that extends from the node N _M to basal plane. In other words, the lower structure of C ₁ is replaced by B _R is an extension of the B _3, in that the B ₃ and the base surface is in contact, terminal node N _T3 representative of the position of the cluster C ₁ is set .

  As described above, each node and branch is obtained, and a dendrogram in the three-dimensional space is defined based on this. The dendrogram image generation unit 22 performs coordinate conversion according to the line-of-sight vector and the type of projection, and displays an image display target such as a dendrogram represented in the xyz coordinate system, for example, with the line-of-sight direction as the Z axis and the screen vertical This is expressed in an XYZ coordinate system in which the direction is the Y axis and the horizontal direction is the X axis. Image data to be displayed on the screen of the display unit 14 is generated by projecting the XYZ space in the Z-axis direction.

  FIG. 5 is a schematic diagram illustrating an example of an image of a three-dimensional dendrogram. This image 40 is a perspective projection image in which the viewpoint is set obliquely above the base surface 42, and is displayed so that the width of the base surface 42 set to a rectangle narrows toward the back in the line-of-sight direction. A three-dimensional dendrogram 44 standing on the base surface 42 is displayed as an image.

As a simple specific example, a case where the analysis object data is the coordinate data e _C1 and e _C2 of the analysis object S will be described. In this case, since the similarity between clusters is related to the distance of the clusters on the base plane, for example, the similarity is calculated from the distance between the end nodes _NT of the three-dimensional dendrogram shown in FIG. It becomes possible to understand intuitively.

For example, the coordinate data e _C1 and e _C2 are the positions on the ground surface of the moving object to be analyzed. In this case, an aerial photograph or CG image of the ground surface can be texture-mapped on the base surface 42. This makes it easy to grasp the movement of the analysis target and the positional relationship between the clusters, and makes it easy to understand the clustering analysis result represented by the dendrogram. The display unit 14 displays a moving image of how the analysis target moves on the ground. When displaying the result of clustering by setting the threshold value γ, the state of clusters joining and separating with the movement of the analysis target is close to the branches standing on the base plane and reduced to one branch. It is expressed as being contracted or conversely separated.

  Further, the dendrogram image generation unit 22 is configured to display an image of a three-dimensional object having a size corresponding to the number of analysis targets S included in the cluster at a position corresponding to the cluster on the base surface 42. You can also.

FIG. 6 is a schematic diagram illustrating an image example of a three-dimensional dendrogram displaying a hemisphere as a three-dimensional object. This image 50 is a perspective projection image of a dendrogram formed on the base surface 42 as in FIG. A hemisphere 56 is displayed at the terminal node _NT of the dendrogram 54 arranged on the base surface 42. The hemisphere 56 is, for example, proportional to the number of analysis objects S (cluster size, size) whose center coincides with the end node _NT and whose radius, area on the base surface 42, or volume is included in the cluster. Set to change. Further, the size of the hemisphere 56 may be set according to the size of the distribution range on the basic surface 42 of the analysis target S included in the cluster.

  Furthermore, the color of the hemisphere 56 may be gradually changed in conjunction with the size of the cluster, and this makes it easy to compare the sizes of clusters displayed in perspective by perspective projection, for example.

FIG. 7 is a schematic diagram illustrating an example of a three-dimensional dendrogram image in which element objects having a predetermined shape and size are stacked on the base surface 42 as a three-dimensional object. This image 60 is a perspective projection image of a dendrogram formed on the base surface 42 as in FIG. A sphere 66 is stacked as an element object along the branch 65 from the terminal node _NT of the dendrogram 64 arranged on the base surface 42. The number of balls 66 to be stacked is determined according to the size of the cluster.

  When the analysis purpose data includes data other than coordinate data, the distance on the base surface 42 does not necessarily correspond to the distance between clusters. Therefore, for example, by reflecting the distance between clusters in the color attributes (hue, saturation, brightness) of a three-dimensional object, it is easy to intuitively understand the distance between clusters in a three-dimensional dendrogram image. It can be.

  Further, as described above, the clustering analysis apparatus 10 can display the result of clustering with the threshold value γ in a form in which the structure below the threshold value is reduced. Therefore, it may be displayed as a three-dimensional object whether the result of clustering the three-dimensional dendrogram displayed in the image is displayed and what level the threshold value γ is set to. For example, a cylinder extending along a branch can be used as a three-dimensional object for that purpose. The presence / absence of the cylinder indicates whether the threshold γ is set, and the height of the cylinder indicates the size of the threshold γ. be able to.

  Further, when displaying the clustered result, the distribution range of the analysis target S included in each cluster on the basic surface 42 is displayed by a three-dimensional object extending in the range, color coding on the basic surface 42, or the like. May be.

  Further, depending on the setting of the threshold value γ in the analysis process and the movement status of the analysis target, a plurality of analysis targets may be clustered into one, or the analysis target itself may temporarily become one. In this case, a hemisphere having a radius, an area on the base surface, and a volume corresponding to the number of one or more analysis objects included in the cluster is displayed, or a corresponding number of balls are stacked and displayed. The dendrogram may be displayed at the time of separation into a plurality of clusters.

In the above-described specific example, the case where the analysis target data is the coordinate data e _C1 and e _C2 has been described. However, the analysis target data may be a combination of coordinate data and other data, Only data other than data may be used.

1 is a schematic block diagram of a clustering analysis apparatus according to an embodiment of the present invention. It is a flowchart which shows the operation | movement of the outline | summary of the process part of the clustering analyzer which concerns on embodiment of this invention. It is a schematic diagram which shows the lowest layer part of a basic three-dimensional dendrogram. It is a schematic diagram which shows the lowest layer part of the three-dimensional dendrogram in the case of showing the result clustered. It is a schematic diagram which shows the example of an image of a three-dimensional dendrogram. It is a schematic diagram which shows the image example of the three-dimensional dendrogram which displayed the hemisphere as a three-dimensional object. FIG. 6 is a schematic diagram illustrating an example of a three-dimensional dendrogram image in which element objects having a predetermined shape and size are stacked on a basic surface as three-dimensional objects. It is a figure which shows an example of the conventional general dendrogram.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 10 Clustering analyzer, 12 processing part, 14 display part, 16 memory | storage part, 18 operation part, 20 analysis part, 22 dendrogram image generation part, 42 base plane, 44,54,64 three-dimensional dendrogram.

Claims (8)

For a plurality of analysis objects associated with a plurality of types of element data represented in time series, based on the similarity between the analysis objects with respect to predetermined analysis object data of the element data, the hierarchical structure for each time An analysis unit that sequentially performs clustering analysis according to the time series;
In a three-dimensional space, a base plane is defined in which the analysis target is associated with a position according to predetermined coordinate data of the element data, and each analysis target placed on the base plane is defined as a leaf. A dendrogram for obtaining a three-dimensional dendrogram in which a branch for each leaf is erected on the base plane based on the analysis result of the hierarchical clustering analysis, and generating a projection image of the dendrogram that changes according to the time series An image generator;
A clustering analysis apparatus characterized by comprising: The clustering analysis apparatus according to claim 1,
A clustering analysis apparatus characterized in that the coordinate data includes the analysis object data in a part thereof. In the clustering analysis apparatus according to claim 1 or 2,
The dendrogram image generation unit, as the projection image when a cluster is defined with a set clustering threshold, the structure of a portion corresponding to the cluster in the dendrogram, an extension line of a branch connected to the cluster A clustering analysis device characterized by generating an image replaced with. In the clustering analysis apparatus according to claim 3,
The dendrogram image generation unit displays a three-dimensional object having a size corresponding to the number of the analysis targets included in the cluster at a position corresponding to the cluster on the basic surface. Clustering analyzer. In the clustering analysis apparatus according to claim 4,
A clustering analysis apparatus, wherein the three-dimensional object is a hemisphere. In the clustering analysis apparatus according to claim 4,
The three-dimensional object is a clustering analysis apparatus characterized in that element objects having a predetermined size are stacked from the base plane in a number corresponding to the number of analysis objects included in the cluster. For multiple analysis targets that are associated with multiple types of element data represented in time series,
An analysis step of performing a hierarchical clustering analysis based on the similarity between the analysis objects with respect to predetermined analysis object data of the element data;
In a three-dimensional space, a base plane is defined in which the analysis target is associated with a position according to predetermined coordinate data of the element data, and each analysis target placed on the base plane is defined as a leaf. A dendrogram image generation step of obtaining a three-dimensional dendrogram in which a branch for each leaf is erected on the base plane based on the analysis result of the hierarchical clustering analysis, and generating a projection image of the dendrogram;
The clustering analysis method is characterized in that the dynamic image of the dendrogram is generated in order according to the time series. For multiple analysis targets that are associated with multiple types of element data represented in time series,
An analysis step of performing a hierarchical clustering analysis based on the similarity between the analysis objects with respect to predetermined analysis object data of the element data;
In a three-dimensional space, a base plane is defined in which the analysis target is associated with a position according to predetermined coordinate data of the element data, and each analysis target placed on the base plane is defined as a leaf. A dendrogram image generation step of obtaining a three-dimensional dendrogram in which a branch for each leaf is erected on the base plane based on the analysis result of the hierarchical clustering analysis, and generating a projection image of the dendrogram;
A clustering analysis program that causes a computer to sequentially execute in accordance with the time series to generate a moving image of the dendrogram.

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