JP2005258599A - Method for visualization of data, apparatus for visualization of data, program for visualization of data, and storage medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To appropriately visually detect predetermined data such as an outlier in given arbitrary multidimensional data. <P>SOLUTION: An outlier visualization apparatus A is used to visualize predetermined data in a plurality of data y forming object data Y by means of a mixed autoregressive model mixing a K number of autoregressive models. In the outlier visualization apparatus A, a model parameter estimation part 11 reads the object data Y into memory, and pairs the data y with input vectors x created from the data y to create a plurality of data D into memory, then an extended probability vector estimation part 12 estimates joint probabilities of the stored data D and classes k into memory, and combines a mean 2 sigma value to the probability vectors to create extended probability vectors into memory, and an outlier visualization part 13 uses the extended probability vectors to visually display the predetermined data. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a method and apparatus for visualizing predetermined data included in, for example, given data such as economic time series data, text data, and biological data.

In recent years, a large amount of data has been accumulated electronically. Knowing major past events and preparing for future crises by detecting outliers from electronically stored data are important research issues.
As a main method for detecting an abnormal value, there is a method in which a model is constructed using data in a normal state, and data having a large error from the model is abnormal (Non-Patent Document 1). As a method of outputting an abnormal value, there is a method of plotting data on the horizontal axis and the degree of abnormality on the vertical axis.
Early statistical detection of anthrax outbreaks by tracking over-the-counter medication sales, A. Goldenberg et.al.Proceedings of the National Academy of Sciences of the United States of America, 99 (8): 5237-5240,2002

  However, if a model in a normal state is constructed, and data with a large error from the constructed model is regarded as abnormal, it is regarded as an abnormal value even though it is not an abnormal value due to the lack of the ability to express the model. Sometimes. To accurately detect outliers, the model needs to be more expressive.

Furthermore, in the conventional abnormal value output method, it is possible to know the degree of abnormality, but it is difficult to know the nature of each abnormality.

  Therefore, the present invention provides a data visualization method, a data visualization device, and the like, which can appropriately detect and detect predetermined data such as an abnormal value from given arbitrary data. The main object is to provide a data visualization program and a storage medium.

  The present invention that has solved the above problems constructs a mixed model described by a linear sum of a plurality of probability models having different parameters included in the probability model based on given arbitrary data, and simultaneously combines the data and each probability model. By displaying the combination of the probability and the average 2 sigma value, predetermined data such as an abnormal value is visualized.

  That is, the present invention uses a computer having a calculation means for performing calculation using a memory for storing information as a work area, and converts predetermined data among a plurality of data y constituting target data Y into K probability models. The present invention relates to a method for visualizing data that is visualized using a mixed model described by a linear sum. In the data visualization method of the present invention, the calculation means reads the target data Y and stores it in the memory, and sets the probability of the data y and each probability model as a vector as a probability vector. Storing in the memory, creating an expanded probability vector by combining the probability vector with an average probability density that is a probability density in a predetermined random variable of all probability models, storing the expanded probability vector in the memory, and The coordinate data for visualizing the predetermined data is created and stored in the memory.

  Here, although the probability model is an autoregressive model in the embodiment described later, a normal distribution model, a multinomial distribution model, or the like can be applied. In the embodiment described later, the mixed model is an autoregressive mixed model, but may be another mixed model corresponding to the probability model. In addition, the average probability density is an average 2 sigma value in the embodiment described later, but other average probability density may be used. Detailed solution means will be described in detail in an embodiment described later.

  According to the present invention, predetermined data such as an abnormal value can be appropriately visualized and detected from given data.

  The best mode (hereinafter referred to as “embodiment”) for carrying out the “data visualization method, data visualization device, data visualization program, and storage medium” of the present invention will be described in detail below. In the embodiment described below, the principle of the visualization method (data visualization method) (“basic concept of visualization method” / “principle of visualization method / description of mathematical formula”) is explained first, and then visualization is performed. The “abnormal value visualization device” embodying the method will be specifically described.

≪Basic concept of visualization method≫
First, the basic concept of the visualization method will be described with reference to formulas (1) to (5).

(Estimation of expansion probability vector)
In the present embodiment, the data to be visualized is D ^* having the structure of the following formula (1).
In this equation (1), D (i) is the i-th data, and N is the total number of given data. This D (i) is a pair of data y (t) to be described later and an input vector x (t) to be described later. Supplementally, D (i) is “data consisting of input vector x (i) and data y (i)”.
Incidentally, i and t in parentheses in data D (i) and data y (t) are indexes that specify data defined as array variables. Even if the index names are different, the same data can be specified as long as the index values are the same.

Data D ^* (that is, data D (i)) is generated by a mixed model of the following equation (2) described by a weighted linear sum of K probability models. That is, the mixed model is defined by a linear sum of a plurality of probability models as shown in Expression (2). As will be described later, K is the total number of probability models.

Note that ΣP (k) = 1, P (k) ≧ 0, and Θ are unknown parameters. Here, Θ of the unknown parameter corresponds to at least one of A and σ described later.
The unknown parameter is estimated by maximizing the probability that the data D ^* is generated under the unknown parameter Θ. That is, Θ of the unknown parameter is estimated by maximizing the following equation (3). Here, the left side of Expression (3) indicates that Θ is an estimated value. Further, the right side of Equation (3) means that Θ that maximizes the right side is an estimated value. Incidentally, Expression (3) corresponds to Expression (11) to Expression (17) described later.

A probability vector z ^* (i) represented by the following equation (4) is a vector obtained by using the simultaneous probability of the data D (i) and each probability model (k = 1,..., K) as a vector. Here, i in parentheses is an index for designating any one of probability vectors that are array variables.
Here, the equation (4) is obtained by “setting a probability vector of the joint probability of the data y and the probability model as a probability vector”.

The probability vector z ^* (i) combined with (added to) an average 2-sigma value (α˜) is defined as an expanded probability vector z (i) in the following equation (5).

  The average 2 sigma value is an average of probability density in the 2 sigma value (twice the standard deviation) of the entire probability model. Incidentally, Expression (4) corresponds to Expression (19) described later, and Expression (5) corresponds to Expression (18) described later.

(Visualization of abnormal values by visualization of expansion probability vector)
Next, a method for visualizing an abnormal value by visualizing an expansion probability vector will be described. The expansion probability vector is visualized by, for example, dimensional compression into a two-dimensional or three-dimensional vector. Many methods such as a classical multidimensional scaling method and a CoPE method have been proposed as a dimensional compression method, and any method may be used. What will be described later is the CoPE method.

In the expansion probability vector, it can be said that data having a relatively high average 2 sigma value has a large degree of abnormal value (differing from other data is large). Therefore, by visualizing the expansion probability vector, an axis representing the degree of the abnormal value is formed, and the abnormal value can be visually detected. Since the probability vector represents the probability belonging to each probability model, by visualizing the expanded probability vector, it is possible to know not only the magnitude of the abnormal value but also the nature of the abnormal value. it can.
Supplementally, since it is possible to verify which of the plurality of probability models the displayed data was generated by, for example, know which probability model generated the data determined to be an abnormal value, and the probability If you check the parameters of the model, you can know what kind of properties the outliers have.
By the way, by displaying the data to be displayed, for example, by color coding for each probability model, the data processed by one probability model and the data processed by another probability model with different parameters are displayed in an identifiable manner, It is possible to visually know which probability model has generated the data determined to be an abnormal value.

≪Principle of visualization method ・ Explanation of mathematical expression≫
Next, a principle of a visualization method for visualizing an abnormal value included in given arbitrary data using a mixed model and a mathematical expression to be used will be described. Note that the description order of the mathematical expressions does not necessarily match the description order of the processing in a flowchart (FIG. 3 and the like) described later.

(data)
First, given arbitrary data (that is, target data Y) will be described. The target data Y that is an application target of the visualization method of the present embodiment has a structure of the following formula (6).
For example, y (1) is the economic time series data for January 1983, y (2) is the economic time series data for the next month, and y (T) is the economic time series data for the Tth month counted from January 1983. It is. If T is 240, y (T) is economic time series data of December 2002. That is, data y (t) is economic time series data at time t, and T is the total number of time series given. By the way, this economic time series data is from “January base of Japan”, “International interest rate”, “Wholesale price index”, “Machine orders”, “Industrial production index”, “Yen” “Dollar exchange rate” is assumed to be 6-dimensional time series data for each month (time t = January 1983 to December 2002, variable dimension number d = 6, total number of time series T = 240) . The target data Y in Expression (6) corresponds to “arbitrary target data Y composed of a plurality of data y”. Here, six-dimensional data is shown as the target data Y, but the dimension may be one or more dimensions.

(Input vector to autoregressive model)
When the abnormal value included in the target data Y is visualized, an input vector x (t) from the target data Y to the autoregressive model having the structure shown by the equation (7) is created. Note that x (t) is abbreviated as “input vector” as appropriate. Incidentally, the “abnormal value” included in the target data Y to be visualized corresponds to “predetermined data”.

  In this equation (7), τ represents the order of the autoregressive model. For example, if the order τ is 2, the input vector x (t at time t is based on the data y (t−1) at the time retroactive to January from the time t and the data y (t−2) at the retroactive time in February. ) Will be created. Note that “′” in Equation (7) is a transpose of a matrix. Incidentally, the input vector x (t) is data having a vector of dτ. Here, d is the number of dimensions of variables (here, 6) as described above. For example, when the order τ is 2, dτ is 12.

(Autoregressive model)
The autoregressive model is given by the following equation (8). That is, in the autoregressive model, the data y (t) at time t is described as the sum of the weighted linear sum of the data in the past τ period and the error. That is, the data y (t) at time t is expressed by the following equation (8).
In Equation (8), A is a parameter of an autoregressive model of dτ × d matrix (referred to as “parameter” as appropriate), and ε is an error term of white noise.

(Autoregressive mixed model)
In the autoregressive mixed model, it is considered that the data y (t) at time t is generated by a weighted linear sum of K autoregressive models as in the following equation (9) (K is 1 or more). Note that k is an index for specifying (designating) an autoregressive model and takes values 1, 2,..., K).

  Here, the left side of Equation (9) is the probability density of the data y (t) when the input vector x (t) is known. Further, P (k) on the right side of Equation (9) is a weight when the autoregressive model is kth. Similarly, p (y (t) | x (t), k) on the right side is the probability density of the input data y (t) when the input vector x (t) and the autoregressive model are understood to be k-th. That is, this equation (9) can also be said to indicate a weighted linear sum of K probability models.

In estimating the parameters, p (y (t) | x (t), k) on the right side of the equation (9) is obtained by the following equation (10). In other words, since the error is assumed to be a normal distribution in the autoregressive model, the probability distribution of the data y (t) at time t when it belongs to the kth autoregressive model among the K autoregressive models. (In other words, the input vector x (t) and the probability density of the input data y (t) when the autoregressive model is solved) are obtained by the following equation (10).
Incidentally, A _k is a parameter of the k-th autoregressive model, sigma _k ² is the variance of the k th autoregressive model. Here, it is assumed that the variance of all variables is constant and independent.

(Model parameter estimation)
The unknown parameter of the autoregressive mixed model is estimated as follows.

Step 1; First, assuming that K ^* = 1, the parameter A ₁ is estimated by minimizing the square error E ₁ of the autoregressive model expressed by the following equation (11).
This calculation is performed by the least square method. At time t, the initial value is τ + 1 and the final value is T. As described above, τ is the order of the autoregressive model. K ^* is a loop counter.

Step 2; s satisfying 1 ≦ s ≦ K ^* is selected, and parameters are set as shown in the following equations (12) and (13). s is an index for selecting the parameter A. ΔA is, for example, a random number. Incidentally, when Step 2 is executed for the first time, s becomes 1 since K ^* = 1 at Step 1. When Step 2 is executed after the second time, s may become 1 again.

Step 3; Increment K ^* of the loop counter by one.

Step 4: The parameters (A, σ, P) are estimated by maximizing L _K ^* in the following equation (13) that is a logarithm of the likelihood of data. Note that the probability density of the second term in Σ on the right side corresponds to Equation (10).

Step5; K ^* <If K, i.e. of the loop counter K ^* is, if less than K is the total number of autoregressive model returns to Step2, performs processing after Step2.

By the way, in Step 4, the parameter that maximizes L _K ^* cannot be calculated analytically. Therefore, a parameter that approximately maximizes L _K ^* is calculated by repeating the EM algorithm, that is, by repeating the following E-Step and M-Step.

  E-Step; The weight P (k | x (t), y (t) of the kth autoregressive model when x (t) and y (t) are known using the following equation (14) ) Is calculated.

M-Step; The following parameters, P (k), A _k , and σ _k ² are estimated by the following equations (15) to (17). Note that P (k), A _k , and σ _k ² are probability density, parameter, and variance, respectively, when the autoregressive model is kth.

(Estimation of expansion probability vector)
When parameter estimation is complete, an autoregressive mixture model is constructed. Thereafter, z (t) of the expansion probability vector is estimated. z (t) is estimated (defined) by the following equation (18).
Note that the expansion probability vector z (t) in the equation (18) is an average 2 sigma value (α˜) of the autoregressive mixed model in the following equation (20) to the probability vector z ^* (t) in the following equation (19). ) Is added. Incidentally, equation (18) corresponds to equation (5), and equation (19) corresponds to equation (4).

In Expressions (18) and (19), k takes values up to 1, 2,..., K for both weight P and probability density p. Further, the probability vector z ^* (t) and the expanded probability vector z (t) are estimated at each time t (t = 1 to T), respectively. Incidentally, in the equation (20), the dispersion σ _k ² can use the equation (17).
Here, the equation (19) is set as “the probability vector is a vector in which the simultaneous probability of the data D composed of the input vector x and the data y corresponding to the input vector x and each autoregressive model is set”. Is.

(Abnormal value detection by visualization)
When the parameters are estimated from the given target data Y, the construction of the autoregressive mixed model, and the estimation of the expansion probability vector are completed, the abnormal value is detected by visualization. In this embodiment, the abnormal value is visualized in two or three dimensions by the CoPE method (Connectivity Preserving Embedding method) based on the expansion probability vector z (t) at each time (t = 1 to T). .
The CoPE method is described in detail in “Embedding Network Data Based on Cross-Entropy Minimization”, Transactions of Information Processing Society of Japan, 44 (9): 1234-1231, 2003.

In the CoPE method, first, the similarity s _{i, j} between the data D (i) when the time t is i and the data D (j) when the time t is j is used as an expansion probability vector z between the time i and the time j. (I) Calculated by the cosine similarity of z (j). The mathematical formula used at this time is the following formula (21). The data D (i) is data having the input vector x (i) as an input and the data y (i) as an output (data in which y and x are paired). Similarly, data D (j) is data having input vector x (j) as input and data y (j) as output.

  In this equation (21), z (i) ′ of the numerator indicates the transposition of the expansion probability vector z (i) of equation (18) at time i. The denominator represents the product of the absolute value of the expansion probability vector z (i) and the absolute value of z (j).

Here, let r _{i be} the coordinates of the data D (i). Coordinates (i is all coordinates to tau + 1 to T), and r _i and r _j the probability density p (r _i, r _j) and the similarity s _i, a regularization term to the sum of the cross-entropy of _j added following This is calculated by minimizing the equation (22).

At time i, the initial value is τ + 1 and the final value is T-1. The time j has an initial value of τ + 2 and a final value of T. μ is the weight of the regularization term, and is appropriately set based on the visualization result, for example. ‖R _i ‖ ² is the distance from the origin of the coordinate r _i.

Here, the cross entropy of p (r _i , r _j ) is calculated by the following equation (23), and p (r _i , r _j ) required in this equation (23) is calculated by the following equation (24). Calculated.

The coordinates r _i are visualized by graphing them in two or three dimensions. Thereby, the abnormal value can be visually discriminated.

≪Configuration of abnormal value visualization system≫
Next, based on the principle described above, an abnormal value visualization apparatus that visualizes an abnormal value included in given data (target data Y) by a computer will be specifically described.
FIG. 1 is a configuration diagram of an abnormal value visualization apparatus according to an embodiment of the present invention.

  As shown in FIG. 1, the abnormal value visualization apparatus A has a configuration in which an arithmetic device 1, an input device 2, a storage device 3, and a display device 4 are connected to a bus. In terms of hardware, the arithmetic device 1 includes a CPU (Central Processing Unit) as arithmetic means and a RAM (Random Access Memory) as a memory for storing information. The arithmetic device 1 includes a model parameter estimation unit 11, an expansion probability vector estimation unit 12, and an abnormal value visualization unit 13 as a software configuration. The function of each part 11, 12, 13 will be described in detail later. The model parameter estimator 11, the expansion probability vector estimator 12, and the abnormal value visualization unit 13 have their base programs stored in the storage device 3, and are stored by the CPU when the abnormal value visualization device A is activated. It is assumed that the data is read from the device 3 onto the RAM and functions as the respective units 11, 12, and 13. The CPU performs various calculations while storing the calculation results and calculation progress in the RAM as needed using a RAM, which is a memory for storing various information, as a work area. Of course, the CPU performs various calculations while using the cache memory built in the CPU as a work area.

  The input device 2 is an input means composed of a keyboard, a network interface card, a disk drive device such as an FDD, and the like, the target data Y (economic time series data), the order τ of the autoregressive model, the self It is used to input various data such as the total number K of regression models to the abnormal value visualization apparatus A. The storage device 3 is a storage means configured from a hard disk device or the like. In the present embodiment, it is assumed that various data input from the input device 2 is stored in the storage device 3. Further, as described above, it is assumed that the storage device 3 stores a program that is the basis of the units 11, 12, and 13. The display device 4 is, for example, a graphic board and a liquid crystal monitor connected thereto, and visually displays data visualized by the abnormal value visualization unit 13.

  Next, functions of the model parameter estimation unit 11, the expansion probability vector estimation unit 12, and the abnormal value visualization unit 13 configured in software on the arithmetic device 1 (as program modules) will be described.

(Model parameter estimation unit)
The model parameter estimation unit 11 of the arithmetic device 1 has a function of estimating the parameters of the autoregressive mixed model represented by the equations (9) and (10) and constructing the autoregressive mixed model. For this reason, the model parameter estimation unit 11 (a) reads the target data Y and the order τ shown in the equation (6) stored in the storage device 3 into the arithmetic device 1, and (b) reads into the arithmetic device 1. From the target data Y and the order τ, a process for calculating an input vector to the autoregressive model of Expression (7), (c) From the target data Y and the input vector x (t), Expressions (11) to (17) ) And a process for estimating parameters (A, σ, P (k)) of the autoregressive mixed model. It should be noted that the read target data Y and the result of the calculation and the intermediate result are stored in a RAM (not shown) as appropriate, and used for processing in the subsequent expansion probability vector estimation unit 12. In the present embodiment, the weight P (k) will be described as one of the parameters.

(Expansion probability vector estimation unit)
The expansion probability vector estimation unit 12 uses the above-described equations (18) to (20), and appropriately uses the calculation results of the model parameter estimation unit 11 stored in the RAM and the progress of the expansion probability. It has a function of performing a process of estimating the vector z (t) at each time t (t = 1 to T).

(Abnormal value visualization part)
The abnormal value visualization unit 13 has a function of performing a process of visualizing the abnormal value included in the target data Y by the CoPE method using the equations (21) to (24).

≪Operation of abnormal value visualization system≫
Next, the operation of the abnormal value visualization apparatus A having the above-described configuration will be described using a flowchart.
FIG. 2 is a flowchart showing an outline of processing from the read data until the abnormal value is visualized. As shown in FIG. 2, the abnormal value visualization apparatus A reads the target data Y from the storage device 3 in step S <b> 100 and performs “autoregressive mixture model construction process”. This process is performed by the model parameter estimation unit 11 shown in FIG. Next, in step S200, “expansion probability vector estimation processing” is performed. This process is performed by the expansion probability vector estimation unit 12 shown in FIG. After the expansion probability vector estimation processing, “abnormal value visualization processing” is performed in S300. This process is performed by the abnormal value visualization unit 13 shown in FIG.

(Building an autoregressive mixed model)
Next, the “autoregressive mixture model construction process” in step S100 of FIG. 2 will be described in detail with reference to the flowchart of FIG. 3 (see FIG. 1 as appropriate). What is performed here is a process of constructing an autoregressive mixture model by estimating the parameters of the autoregressive mixture model represented by equations (9) and (10). The operating subject in the following description is the model parameter estimation unit 11. Note that the model parameter estimation unit 11 is a program module that functions in the arithmetic device 1 including a CPU, a RAM, and the like.
Incidentally, since the flowchart of FIG. 3 is expressed in consideration of the order of the arithmetic processing in the computer, it does not necessarily match the appearance order of the mathematical expressions described in “Principle of visualization method / Explanation of mathematical expressions”. This also applies to the subsequent flowcharts (FIGS. 4 and 5).

  First, as illustrated in FIG. 3, the model parameter estimation unit 11 reads the target data Y having the structure represented by Expression (6) from the storage device 3 to the arithmetic device 1 (S101). The target data Y is 6-dimensional economic time series data as described above. With respect to the read target data Y, input data x (t) to an autoregressive model having a structure represented by Expression (7) is created (S102). It is assumed that τ used in Equation (7) is the order of the autoregressive model as described above, and this τ is read into the arithmetic device 1 separately.

Next, the loop counter K ^* is initialized to 1 (S103). The loop counter K ^* takes an integer value from 1 to K. This step S103 is a preparation step for estimating the parameters of all autoregressive models.

Subsequently, by using the data y (t) included in the target data Y read in step S101 and the input vector x (t) created in step S102, the squared minimum error E ₁ of equation (11) is minimized. Thus, the parameter A ₁ is estimated (S104). Up to this point, the parameters of the autoregressive model are estimated, and the subsequent steps S105 and after are parameters of the autoregressive mixed model.

After the parameter A ₁ is estimated, an arbitrary index s satisfying 1 ≦ s ≦ K ^* is selected, and the parameters are set as shown in Expression (12) (S105). When K ^{* of} the loop counter is 1, s is always 1. _{A K * + 1 = As-} ΔA of formula (12), since you are K ^* +1 part of subscript, it means that by setting the value of the next A _K ^*.

When the parameter A is set as shown in equation (12), the loop counter K ^* is incremented by one (S106). Then, E-step of the EM algorithm described above is executed (S107). That is, the weight of the k-th autoregressive model when the data y (t) and the input vector y (t) are known is calculated from the equation (14) (S107).
Incidentally, in Eqs. (11) and (13), one E ₁ and one L _K ^* are calculated using values from time t = τ + 1 to T. On the other hand, for Equation (14), a plurality of P (k | x (t), y (t)) is calculated.

Next, M-step of the above-described EM algorithm is executed (S108). That is, P (k) is estimated by Expression (15), σ _k ² is estimated by Expression (16), and A _k is estimated by Expression (17). Incidentally, since the equations (15) to (17) are executed using the weight P (k | x (t), y (t)) calculated in step S107, P (k), σ _k ² and A _k are estimated.

In step S109 and step S110, the estimated parameter is verified using equation (13). In the parameter verification, L _K ^* obtained by taking the logarithm of the data likelihood is calculated by the equation (13) (S109), and the parameter when this is maximized is adopted as the verified parameter. In the present embodiment, a maximum of L _K ^* L _K ^* is determined by whether or not convergence (S110). Therefore, if L _K ^* has converged (Yes in S110), the parameter estimation for the incremented K ^* is completed. On the other hand, if L _K ^* does not converge (No in S110), the process returns to step S107 and step S107 and subsequent steps are executed again, and new parameters are estimated and verified.

Incidentally, in the present embodiment, whether or not L _K ^* has converged is determined by comparing the previous value of L _K ^* calculated in step S109 with the current value, and the absolute value of the difference is less than a predetermined value (below). Then, it is judged that it has converged. Of course, determining whether or not L _K ^* has converged is an example for determining whether or not L _K ^* has been maximized, and how to determine whether or not L _K ^* has been maximized. May be a determination method other than this embodiment.

In step S111, the loop counter K ^* to determine whether small or (K ^* <K) judges than K is the total number of autoregressive model. If K ^* <K (Yes in step S111), the process returns to step S105, and step S105 and subsequent steps are executed. That is, the parameter for the next K ^* (next autoregressive model) is estimated. On the other hand, if K ^* <K, that is, if K ^* = K (No in step S111), all parameters (P (k), σ _k ² , A _k ) of the autoregressive mixture model have been estimated. Then, the process of the flowchart of FIG. Thereby, an autoregressive mixed model is constructed.

(Expansion probability vector estimation process)
Next, the “expansion probability vector estimation process” in step S200 of FIG. 2 will be described in detail with reference to the flowchart of FIG. The operation subject in the following description is the expansion probability vector estimation unit 12. The expansion probability vector estimation unit 12 is a program module that functions in the arithmetic device 1.

First, as illustrated in FIG. 4, the expansion probability vector estimation unit 12 initializes time t by setting t = 0 in step S201. This is a preparation for estimating the expansion probability vector for all times t from t = 1 to T. In step S202, the time t is incremented (because there is no data y (0)). In step S203, the simultaneous probability of “data y (t) and input vector x (t)” and “each autoregressive model (k = 1,..., K)” (that is, data D (t) and each probability A vector in which the joint probability with the model) is set as a vector is set as a probability vector z ^* (t) in Expression (18). Expression (18) is set based on the calculation result in step S100 described above.

Next, the average 2 sigma value of the autoregressive mixed model is calculated by the equation (20) using the calculation result in step S100 (S204). Then, the average 2 sigma value is added to the probability vector z ^* (t) to estimate the expansion probability vector z (t) of Expression (19) (S205). Next, it is determined whether time t is smaller than T which is the total number of time series (t <T) (S206). When t is less than T (Yes in S206), the process returns to Step S202 and executes Step S202 and subsequent steps. That is, the expansion probability vector z (t) at the next time t is estimated. On the other hand, if t = T in step S206 (Yes), the expansion probability vectors for all the times t have been estimated, and thus the processing of the flowchart of FIG. 4 ends.

(Abnormal value visualization processing)
Next, the “abnormal value visualization process” in step 300 of FIG. 2 will be described in detail with reference to the flowchart of FIG. 5 (see FIG. 1 as appropriate). The operation subject in the following description is the abnormal value visualization unit 13. The abnormality visualization unit 13 is a program module that functions in the arithmetic device 1 configured by a CPU, a RAM, and the like.

First, as shown in FIG. 5, the abnormal value visualization unit 13 determines the similarity s _{i, j} between the data D (i) at time i and the data D (j) at time j different from time i in step S301. The calculation is performed using the expansion probability vectors z (i) and z (j) at time i and time j calculated in step S200 described above (see formula (21)).

Next, in step S302, r _i is set as the coordinate of the data D (i) using the equations (22) to (24). The coordinates ri are obtained by minimizing the expression (22) obtained by adding the regularization term to the sum of the cross entropy with the probability density p (ri, rj) while using the expressions (23) and (24).

  As a result of the above, what is located away from other data is an abnormal value, and the abnormal value is visualized.

≪Visualization result≫
The effectiveness of the visualization method of the present invention will be shown in an embodiment using economic time series data with reference to FIG. 6 (see FIG. 1 as appropriate). FIGS. 6A to 6D are diagrams showing the results of visualizing abnormal values in three dimensions by the abnormal value visualization apparatus of the present embodiment (displayed in a plane in the drawing).

  As described above, the data used (target data Y) are “Japanese monetary base”, “international interest rate”, “wholesale price index”, “machine orders”, “industrial production index” from January 1983 to December 2002. ”,“ Yen-dollar exchange rate ”for each month, the number of variables d = 6 and the number of data T = 240. For this target data Y, the method of visualizing abnormal values of time series data using the autoregressive mixed model described above is adopted, the order of the autoregressive model is τ = 1, and the total number of autoregressive models is K = 1-4. As a visualization. Incidentally, the case where K is 1 is FIG. 6A, the case where K is 2 is FIG. 6B, the case where K is 3 is FIG. 6C, and the case where K is 4 is shown in FIG. It is FIG.6 (d). One point in each figure is one month. In addition, the abnormal value visualization apparatus A has a function of displaying different types of points for each autoregressive model, and even if there are a plurality of autoregressive models, the displayed autoregressive point is what number the autoregressive model is. It can be visually understood whether it is generated by the model. For example, in FIG. 6B, the first autoregressive model is indicated by a point with a circle, and the second autoregressive model is indicated with a point with an x mark. In FIG. 6C, the third autoregressive model is indicated by a triangle mark. In FIG. 6D, the fourth autoregressive model is indicated by □.

  As shown in Fig. 6, the Russian crisis in August 1998 is a major economic incident that occurred during this period. Looking at the results of abnormal value visualization, in all cases of autoregressive models K = 1 to 4, September 1998, the month following the Russian crisis, was far away from many other months. I understand that there is. However, when the total number K of autoregressive models is 1, other months are also located near September 1998, and there are a plurality of abnormal values. Even if the total number K of the autoregressive model is 2 or 3, there are a plurality of months that are regarded as abnormal values. However, when the total number K of the autoregressive model is 4, only an abnormal value is obtained in September 1998.

This is because when the total number K of autoregressive models is 1, the autoregressive mixed model is a linear model, and therefore cannot be appropriately modeled if the data has nonlinearity. For this reason, although it is not an abnormal value originally, it may be an abnormal value because the expression ability of the model is low. However, by increasing the total number K of autoregressive models, the model's ability to express increases, and the original abnormal value can be detected.
As described above, according to the present invention, since visualization is performed with a model having expressive power, it is possible to realize detection of abnormal values better than the conventional method.

  Further, the conventional abnormal value detection method is based on the deviation of the data from the average in the data space. However, in the present embodiment, by mapping each data to the parameter space of the model, in other words, by generating the data from a certain probability model as shown in the equations (2) and (9). The characteristics of the raw data such as the target data Y can be made clearer.

The abnormal value visualization apparatus executes a visualization method by a program, and a program for causing a computer to execute the visualization method is stored and distributed in a storage medium such as a CDR-ROM or a digital multipurpose disk. It is distributed via a communication line and is installed in a computer and functions. As an embodiment of this visualization method, a computer (that is, an abnormal value visualization device) in which a program for executing the visualization method is installed acquires target data via a communication line, visualizes the data, and the result is displayed on the communication line. You may make it answer via. Also, various methods other than the CoPE method can be applied to the abnormal value visualization process using the expansion probability vector (step S300 in FIG. 2).
In the above embodiment, an example using an autoregressive model has been described for the probability model. However, the present invention is not limited to this autoregressive model, and other probability models such as a normal distribution model and a multinomial distribution model are used. May be.
In the above-described embodiment, the abnormal value is visualized as an example of the predetermined data. However, for example, a preferable value may be visualized as the predetermined data.
That is, the present invention is not limited to the above-described embodiment, and can be widely modified within the scope of its technical idea.

It is a block diagram of the abnormal value visualization apparatus of one Embodiment of this invention. It is the flowchart which showed the outline | summary of the process until it visualizes an abnormal value from the read data. It is a flowchart which shows "the construction process of the autoregressive mixed model" of step S100 of FIG. It is a flowchart which shows the "expansion probability vector estimation process" of step S200 of FIG. It is a flowchart which shows the "abnormal value visualization process" of step S300 of FIG. It is a figure which shows the result of having visualized the abnormal value by the abnormal value visualization apparatus of FIG. 1, (a) shows the case where K is 1, (b) shows the case where K is 2, and (c) shows K being K. The case of 3 is shown, and (d) shows the case where K is 4.

Explanation of symbols

A Abnormal value visualization device 1 Arithmetic device (calculation means)
DESCRIPTION OF SYMBOLS 11 Model parameter estimation part 12 Expansion probability vector estimation part 13 Abnormal value visualization part 2 Input device 3 Memory | storage device 4 Display apparatus

Claims (9)

Using a computer having calculation means for performing calculation using a memory for storing information as a work area, predetermined data among a plurality of data y constituting target data Y is described by a linear sum of K probability models. In the data visualization method to visualize using the mixed model
The computing means is
Read the target data Y and store it in the memory;
A vector of the joint probability of the data y and each probability model is set as a probability vector and stored in the memory;
An expanded probability vector is created by combining the probability vector with an average probability density that is an average of the probability density in a predetermined random variable of all probability models, and stored in the memory.
Creating coordinate data for visualizing the predetermined data using the expansion probability vector and storing the coordinate data in the memory;
A method for visualizing data. Using a computer having calculation means for performing calculation using a memory for storing information as a work area, predetermined data among a plurality of data y constituting target data Y is linearized with K autoregressive models having different parameters. In the data visualization method that visualizes using the autoregressive mixed model described by the sum,
The computing means is
A procedure for reading the target data Y and storing it in the memory;
A step of creating a plurality of input vectors x to the autoregressive model based on a plurality of data y included in the target data Y and the order τ of the autoregressive model and storing the input vector x in the memory;
Using the plurality of data y and the plurality of input vectors x to calculate parameters of the autoregressive model and store them in the memory;
A step of sequentially storing the parameters of the autoregressive mixed model using the plurality of data y and the plurality of input vectors x by the number of the autoregressive model and storing the same in the memory;
A step of setting a vector of the simultaneous probability of the data D consisting of the input vector x and the data y corresponding to the input vector x and each autoregressive model as a probability vector and storing it in the memory;
Calculating an average probability density that is an average of probability densities in a predetermined random variable of the total autoregressive model and storing the average probability density in the memory;
Estimating an expanded probability vector by adding the average probability density to the probability vector and storing it in the memory;
A step of calculating coordinates for visual display using the expansion probability vector and storing them in the memory;
With
A method for visualizing data, wherein the predetermined data is visualized using the coordinates thus calculated. The calculation of the parameter is
Execute E-step and M-step of the EM algorithm repeatedly, calculate a judgment value that is a logarithm of the likelihood of data based on each calculated parameter, and verify the parameter that maximizes this judgment value The procedure to be adopted as
The data visualization method according to claim 2, wherein: As a procedure for visualization using the expansion probability vector,
A step of calculating a similarity between one data D of the plurality of data D and another data D different from the data D based on the expansion probability vector and storing the similarity in the memory;
A procedure for calculating coordinates of the plurality of data based on the similarity and storing them in the memory;
Using a CoPE method,
The data visualization method according to claim 2, wherein:   5. The data visualization method according to claim 1, wherein the target data Y is multidimensional time-series data. The probability density in the predetermined random variable is a 2 sigma value and the average probability density is a 2 sigma value;
The data visualization method according to claim 1, wherein the data visualization method is a data visualization method. Computation means for performing computation using a memory for storing information as a work area and a display device for displaying the computation results of the computation means, and predetermined data among a plurality of data y constituting the target data Y, In a data visualization apparatus for visualizing using an autoregressive mixed model described by a linear sum of K autoregressive models having different parameters,
The computing means is
A function of creating a plurality of input vectors x to the autoregressive model based on a plurality of data y included in the target data Y and the order τ of the autoregressive model;
A function of calculating parameters of the autoregressive model using the plurality of data y and a plurality of input vectors x;
A function of sequentially repeating the procedure of calculating the parameters of the autoregressive mixed model using the plurality of data y and the plurality of input vectors x by the number of the autoregressive models;
A model parameter estimator comprising:
A function of setting as a probability vector a set of simultaneous probabilities of a plurality of data D having the input vector x as an input and the corresponding data y as an output and each autoregressive model;
A function for calculating an average probability density that is an average of probability densities in a predetermined random variable of the total autoregressive model,
A function of estimating an expanded probability vector by adding the average probability density to the probability vector;
An expanded probability vector estimator comprising:
A function of calculating the similarity between one data D of the plurality of data D and another data D different from the data D based on the expansion probability vector;
A function for calculating coordinates of the plurality of data based on the similarity,
A function for instructing to display the calculated coordinates on the display device;
An abnormal value visualization unit comprising:
A data visualization device comprising:   7. A data visualization program for causing a computer having computation means for performing computation using the memory for storing information as a work area, the data visualization method according to claim 1. .   A data visualization method according to any one of claims 1 to 6, characterized in that a visualization program is stored that is executed by a computer having computing means for performing computation using a memory for storing information as a work area. Storage medium.

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