JP2006244389A - Similar time series data calculating device, and its method and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To more efficiently divide a multi-dimensional space when finding similar candidates of time series data flowing in sequentially. <P>SOLUTION: A center point determining part 33 in a space index part 3 determines the center point of a concentric hypersphere in the multi-dimensional space. A candidate searching part 34 divides the multi-dimensional space into concentric hypersphere structures with the center point as a center. Thus, multi-dimensional space is divided using all axes, which is more efficient. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a similar time-series data calculation apparatus, a similar time-series data calculation method, and a similar time-series data calculation program for obtaining a similar one among a plurality of time-series data.

  Until now, time-series data streams have been applied to services in various fields such as stock trading, climate observation, media processing, and medical care. One of the problems that has been studied extensively in the field of time series data processing is to obtain a similar one from accumulated time series data. Examples of applications of this technology include the following.

  ・ Find stocks with the same stock price transition.

  • Find years that have shown similar temperature patterns in the past.

  -Find similar videos from the stored videos.

  In recent years, as sensors for detecting time-series data have become smaller and cheaper, services using a large amount of time-series sensor data streams are becoming possible. For this reason, it is considered that the importance of processing technology for time-series data output from sensors will increase in the future. One of the features of the sensor data stream is that a large amount of time-series data sequentially flows.

  The following example is given as an application of a technique for obtaining similar data from time-series data that sequentially flows.

  -Find products with the same sales pattern in real time.

  ・ Find the same place of shaking when an earthquake occurs.

  ・ Find a person who is moving the same time.

In the present application, the problem of obtaining similar time series data is defined as follows. “Among the m time-series data, a combination of time-series data whose distance in the past certain period (n data points) from the current time T is within the threshold ε is obtained.”
The time series data handled here includes discrete values such as stock prices and continuous values such as movement trajectories. In the case of discrete values, whether the time-series data is similar may be determined by checking whether the distance between the time-series data is within the threshold using the discrete values. In the case of continuous values, the time-series data is sampled at the time of processing and becomes discrete values, so that eventually a discrete value processing method is used.

The following Euclidean distance is used as a distance function between the two time series data S ^u and S ^v .

  By defining the distance between the time series data using the Euclidean distance, as shown in FIG. 15, the problem of obtaining similar time series data can be replaced with the problem of obtaining a close point in a multidimensional space.

Further, by determining the distance between the time series data using the Euclidean distance, the problem in the present application is to obtain a set of combinations of time series data satisfying the following condition when the threshold is ε.

There is GEMINI (GEneric Multimedia INdex Ing method) as a framework for obtaining similar time-series data at high speed (see Non-Patent Document 1). In GEMINI, first, time-series data is dimensionally compressed, a spatial index such as R ^* -tree (see Non-Patent Document 2) is constructed using the feature quantity of the time-series data after this dimension compression, and the spatial index is used. Narrow the distance of similar time series data. Then, for the narrowed candidates, the distance of time series data before dimension compression is calculated, and similar time series data is accurately obtained.

  Conventionally, GEMINI has been widely used for accumulated time series data. In this case, it can take time to construct a spatial index. However, when time-series data that sequentially flows in is targeted, it is necessary to construct a spatial index at high speed.

  When similar time series data is obtained using a spatial index, attention must be paid to the occurrence of errors. Here, there are two types of error, false negative and false positive. False negative means that similar time-series data is not similar, and false positive is that similar time-series data is determined to be similar. is there. Of these two errors, it is more important that no false negative occurs. This is because false positives can be removed by examining the results of similarity judgments, and the occurrence of false negatives affects the accuracy of the results.

There is a grid structure as a spatial index method for time-series data that does not generate false negatives and flows sequentially (see Non-Patent Document 3). As shown in FIG. 16, the grid structure is a technique for dividing a multi-dimensional space in which time-series data exists into a plurality of regions using a grid structure and narrowing down combinations of similar time-series data without oversight. The grid structure divides a multidimensional space that is N-dimensionally compressed by discrete Fourier transform into a grid structure having a constant width by using the first few coefficients of the discrete Fourier transform. Then, combination candidates similar to certain time-series data are limited to an area to which the time-series data belongs and an area adjacent thereto. Thereby, since it is not necessary to calculate the combination of all the time series data, the number of calculations can be reduced. FIG. 16 shows an example in which a three-dimensional space is divided into a two-dimensional grid structure.
R. Agrawl, C. Faloutsos, and ANSwami, "Efficient Similarity Search In Sequence Databases", In Proc. FODO, 1993 N. Bechmann, HPKriegel, R. Schneider, B. Seeger, "R * -tree: An Efficient and Robust Access Method for Points and Rectangles", In Proc. SIGMOD, 1990 Y.zhu, D.Shasha, "State Stream: Statistical Monitoring of Thousands of Data Streams in Real Time", In Proc.VLDB, 2002

  By the way, a problem of the grid structure is that the multidimensional space cannot be divided effectively. This is because in the grid structure, a multidimensional space is divided based on a single axis. Since the distance between the time series data is also a distance in the multidimensional space, the accuracy is low even if the multidimensional space is divided based on a single axis. In addition, the grid structure has no significant effect unless a dimensional compression method in which a large amount of energy is collected in the first few coefficients such as discrete Fourier transform is used. In addition, the grid structure has to calculate the distance after dimensional compression for all the time-series data existing in the candidate area, and calculate whether or not they are similar candidates.

  The present invention has been made in view of the above, and an object of the present invention is to more efficiently divide a multidimensional space when obtaining similar candidates for time-series data that sequentially flows.

  The similar time-series data calculation apparatus according to the first aspect of the present invention is a data receiving means for receiving time-series data that sequentially flows in and storing it in the first memory; and time-series data read from the first memory. Dimension compression means for dimensional compression and storing in the second memory, center point determination means for determining the center point of the concentric hypersphere in the multi-dimensional space and storing it in the third memory, and the center read from the third memory Candidate search means for dividing a multidimensional space into concentric hypersphere structures centered on a point, narrowing down candidates for similar combinations of time-series data read from the second memory, and storing them in the fourth memory; It is characterized by having.

  In the present invention, the center point of the concentric hypersphere in the multidimensional space is determined, and the multidimensional space is divided into the concentric hypersphere structure centered on the center point, so that the multidimensional space using all the axes is obtained. Since space can be divided, it is more efficient.

  In the similar time series data calculation apparatus, the center point determination means uses clustering means for clustering the time series data after dimension compression and storing it in the fifth memory, and a clustering result read from the fifth memory. Center point position calculating means for determining the position of the center point in the multidimensional space and storing it in the third memory.

  In the present invention, clustering is performed for all time-series data, and the center point is determined using the clustering result, whereby the center point can be appropriately arranged.

  In the similar time-series data calculation apparatus, the center point determination unit includes a sample unit that randomly selects a sample from the time-series data after dimension compression before the clustering.

  In the present invention, clustering is performed on randomly sampled time-series data, and the center point is determined using the clustering result, whereby the center point can be calculated at high speed.

  In the similar time series data calculation apparatus, the center point determination means includes center point position calculation means for randomly determining the position of the center point in the multidimensional space for the time series data after dimension compression and storing the position in the third memory. It is characterized by having.

  In the present invention, the center point can be calculated at higher speed by randomly determining the center point.

  In the similar time series data calculation device, the candidate search means includes: a space dividing means for dividing the multidimensional space into concentric hypersphere structures in increments of a threshold for judging similarity of time series data from the center point; Candidate area determining means for determining candidate areas in which similar time-series data exists from the results of the above, and narrowing down similar candidates of the time-series data after dimension compression from the determined candidate areas, and a combination of the similar candidates in the fourth memory And a candidate determination means for storing the data.

  In the present invention, by dividing the multidimensional space into a concentric hypersphere structure in steps of a threshold for determining the similarity of time series data from the central point, candidate regions where similar time series data exist are obtained. Only the region to which the time-series data belongs and the region directly adjacent to this region can be limited, and the number of candidate regions can be reduced.

  In the similar time-series data calculation apparatus, the space dividing unit divides a multidimensional space in increments of values smaller than the threshold instead of the threshold.

In the present invention, by dividing the multidimensional space in increments of a value ε / c (c> 1) smaller than the threshold value ε, the region is divided finely, so that the candidate region can be reduced. It becomes. Thus, each ^R _Oi u from the center _{O ^i,} series data together when belonging to ^{R Oi} _v number of _^regions, without having to calculate the distance after dimensionality reduction if the relationship _{^{R Oi u + R Oi v ≦}} c Can be candidates for similar time-series data.

  The similar time series data calculation method according to the second aspect of the present invention includes a step of receiving time series data that sequentially flows in and storing the time series data in the first memory, and dimension compressing the time series data read from the first memory. Storing in the second memory, determining the central point of the concentric hypersphere in the multidimensional space and storing it in the third memory, and concentric super centering the central point read from the third memory Dividing the multidimensional space into a spherical structure, narrowing down candidates for similar combinations of time-series data read from the second memory, and storing them in the fourth memory.

  A similar time-series data calculation program according to a third aspect of the present invention includes a process of receiving time-series data that sequentially flows in and storing the time-series data in the first memory, and dimensionally compressing the time-series data read from the first memory Processing to be stored in the second memory, processing to determine the central point of the concentric hypersphere in the multidimensional space and store it in the third memory, and concentric super centering the central point read from the third memory Dividing the multidimensional space into a spherical structure, narrowing down candidates for similar combinations of time-series data read from the second memory and storing them in the fourth memory, and causing the computer to execute the processing .

  According to the present invention, it is possible to more efficiently divide a multidimensional space when obtaining similar time-series data.

  Hereinafter, the best mode of the present invention will be described with reference to the drawings.

  As shown in the block diagram of FIG. 1, the similar time-series data calculation apparatus 1 according to the present embodiment includes a data reception unit 2, a spatial index unit 3, a similarity determination unit 4, and a calculation result transmission unit 5. The processing in each part is executed by a computer program installed in the similar time series data calculation apparatus 1. A detailed description of the processing of each unit will be described later, but the outline is as follows.

  The data receiving unit 2 receives time-series data that sequentially flows and stores it in an internal memory.

  The spatial index unit 3 receives the time-series data read from the memory of the data receiving unit 2, narrows down similar time-series data candidates for the time-series data using the spatial index, and stores them in the internal memory.

  The similarity determination unit 4 reads the time series data before narrowing down corresponding to the candidate of the similar time series data read from the memory of the spatial index unit 3 from the memory of the data reception unit 2, and the time series data before the narrowing down Is obtained and stored in an internal memory, and time-series data having this distance within a certain range is determined to be similar.

  The calculation result transmission unit 5 transmits the combination of time series data determined to be similar to the outside.

  The spatial index unit 3 employs a CS structure (Concentric hyper Sphere structure) method. In this method, a multidimensional space is divided into concentric hypersphere structures to narrow down combinations of similar time series data. Specifically, as shown in FIG. 2, a plurality of center points are set on the multi-dimensional space, and the multi-dimensional space is divided with a width equal to or smaller than a predetermined threshold ε according to the distance from the center point. This threshold value ε is a threshold value used for determining similarity between time-series data. In this way, when dividing with a width equal to or smaller than the threshold ε, candidate regions similar to certain time-series data are limited to a region to which the time-series data belongs and a plurality of regions adjacent to this region within a certain range. In FIG. 2, when two concentric spheres are overlapped on a three-dimensional space and the multidimensional space is divided by the width of the threshold ε, similar time-series data candidate areas are the areas to which the time-series data belongs and An example is shown in which this region is limited to a plurality of regions adjacent to each other in a range of up to two. Hereinafter, the configuration of the space index unit 3 will be described.

  As shown in the block diagram of FIG. 3, the spatial index unit 3 includes a data reception unit 31, a dimension compression unit 32, a center point determination unit 33, a candidate search unit 34, and a data transmission unit 35. Processing in each unit is executed by a computer program.

  The data receiving unit 31 receives time-series data read from the memory of the data receiving unit 2.

  The dimension compression unit 32 dimensionally compresses the received time series data and stores it in an internal memory. As this dimensional compression method, for example, discrete Fourier transform is used, and the coefficient is used as a result of dimensional compression. Of course, other dimensional compression methods may be used.

  The center point determination unit 33 determines the center point of the concentric hypersphere in the multidimensional space and stores it in the internal memory. Details of this processing will be described later.

  The candidate search unit 34 divides the multidimensional space into a concentric hypersphere structure centered on the center point read from the memory of the center point determination unit 33, narrows down candidates for combinations of similar time-series data, and performs internal search. Store in memory. Details of this processing will also be described later.

  The data transmission unit 35 outputs similar time-series data combination candidates to the similarity determination unit 4.

  As shown in the block diagram of FIG. 4, the center point determination unit 33 includes a data reception unit 331, a sample unit 332, a clustering unit 333, a center point calculation unit 334, and a data transmission unit 335. Processing in each unit is executed by a computer program.

  The data receiving unit 331 receives the time-series data after dimension compression read from the memory of the dimension compressing unit 32 and stores it in the internal memory.

  The sample unit 332 selects a sample at random from the time-series data after dimension compression stored in the memory of the data reception unit 331, and stores the sample in the internal memory.

  The clustering unit 333 reads the time-series data after dimensional compression selected as a sample from the memory of the sample unit 332, clusters the data, and stores it in the internal memory.

  The center point calculation unit 334 determines the position of the center point in the multidimensional space using the result of clustering read from the memory of the clustering unit 333 and stores it in the internal memory.

  The data transmission unit 335 outputs the position of the center point read from the memory and the time-series data after dimension compression selected as a sample to the candidate search unit 34 of the spatial index unit 3.

  As illustrated in the block diagram of FIG. 5, the candidate search unit 34 includes a data reception unit 341, a space division unit 342, a candidate area determination unit 343, a candidate determination unit 344, and a data transmission unit 345. Processing in each unit is executed by a computer program.

  The data receiving unit 341 receives the transmitted center point position and time-series data after dimension compression, and stores them in an internal memory.

  The space dividing unit 342 divides the multidimensional space into concentric hypersphere structures with a predetermined threshold value centered on the center point read from the memory of the data receiving unit 341. The threshold value is set to a value ε / c (c> 1) smaller than the threshold value ε for determining whether time series data are similar.

  The candidate area determination unit 343 determines candidate areas for selecting similar time-series data candidates in the divided multidimensional space. In this determination, the region to which the division result or time-series data after dimension compression belongs is used.

  Candidate determination unit 344 narrows down similar candidates of time-series data after dimension compression from the determined candidate region, and stores the combination of similar candidates in an internal memory.

  The data transmission unit 345 outputs a combination of similar candidates of time-series data read from the memory of the candidate determination unit 344 to the data transmission unit 35 of the spatial index unit 3.

  Next, conditions that must be satisfied by the dimensional compression method used by the dimensional compression unit 32 of the spatial index unit 3 will be described.

  In the dimension compression unit 32, false negatives should not occur even if dimension compression is performed. The lower bounding lemma is known as a theorem to guarantee this. This is a theorem that false negative does not occur if the following expression (lower bounding condition) holds.

Ddigest (S ′ ^u , S ′ ^v ) ≦ Dreal (S ^u , S ^v ) (3)
Here, the definition of each function is as follows.

Dreal (S ^u , S ^v ): distance between time series data S ^u , S ^v before dimension compression Ddigest (S ′ ^u , S ′ ^v ): distance between time series data S ′ ^u , S ′ ^v after dimension compression Therefore, the dimension compression unit 32 uses a technique such as a discrete Fourier transform method, a discrete weblet transform method, or a singular value decomposition method that satisfies this lower bounding condition. Here, the distance between the time-series data before dimension compression is the Euclidean distance, but is not limited to this.

  Next, a method for determining the center point of the concentric hypersphere in the center point determination unit 33 will be described.

  In the CS structure, if a plurality of center points are gathered at close positions in a multidimensional space, as shown in FIG. 6, the wide candidate areas of the plurality of center points overlap. However, in order to perform efficient narrowing down, it is desirable that the center points are uniformly distributed in the multidimensional space. Therefore, in order to uniformly distribute the center points in the multidimensional space, here, a clustering unit 333 is provided and a clustering method based on the K-means method is used. The algorithm of the K-means method is as follows.

  Step 1 (determination of initial value): Initial division of K clusters (K is an arbitrary positive integer) is set at random.

  Step 2 (assignment of individual): Assign each individual to the nearest representative point.

  Step 3 (Update of representative points): The process ends if the centers of all the clusters have not changed. If not, the representative point of each cluster is calculated and the process returns to Step 2.

  Here, it is assumed that the time series data is an individual, and the center of each cluster (the average of the elements of each cluster) is replaced with the center point of the hypersphere.

  In the present embodiment, since time series data that sequentially flows in is an object, it is desirable that the center point can be calculated at high speed. Therefore, it is necessary to keep the calculation cost in the K-means method low. It is known that the calculation cost of the K-means method is S × M × r × d. Here, S is the number of clusters (center points), M is the number of individuals (time-series data), r is the number of iterations until calculation of the K-means method converges, and d is the number of dimensions when calculating the distance. It is. In the present embodiment, the number M of individuals is reduced as follows.

M = m × k (4)
Here, m is the total number of time-series data, and k is a sample rate (0 to 1) that determines how many of the time-series data are used to perform the K-means method. As the value of k is smaller, the center point is determined from fewer data points. Therefore, the multidimensional space can be divided at high speed, but an inappropriate position may be the center point.

Next, a method for determining candidates for similar time series data in the candidate search unit 34 will be described. In the present embodiment, the multidimensional space is divided by the width of ε / c (c> 1), but whether the time series data is dissimilar is determined based on the region to which the time series data belongs. As illustrated in FIG. 7, the time series data S ′ ^u after dimension compression from the center point O _i is in the R ^Oi _u (> 0) region, and the time series data S ′ ^v is R ^Oi _v (> 0) When it is in the area, it is determined that the time series data belonging to the area represented by the following expression (5) may be similar, and the time series data belonging to the area represented by the following expression (6) is Judged as dissimilar.

| R ^Oi _u -R ^Oi _v | <c + 1 (5)
| R ^Oi _u -R ^Oi _v | ≧ c + 1 (6)
For time-series data with similar possibility, the distance after dimension compression is calculated, and it is determined whether or not it is a candidate for similar time-series data depending on whether this distance is within a certain range. In the example of FIG. 7, c = 1.5, R ^Oi _u = 2, R ^Oi _v = 4, or R ^Oi _v = 5. If R ^Oi _v = 4, the time series data is likely to be similar, and if R ^Oi _v = 5, the time series data is dissimilar.

  When using a spatial index, it is necessary that false negatives do not occur. Therefore, the candidate search unit 34 introduces a theorem contractive transform lemma that guarantees this.

  Contractive transform lemma means that false negative does not occur if the following expression (contractive transform condition) is satisfied.

^{Dcontractive (S 'u, S'} v) <Ddigest (S 'u, S' v) ≦ Dreal (S u, S v) (7)
Here, the definition of each function is as follows.

Dreal (S ^u , S ^v ): distance between time series data S ^u , S ^v before dimension compression Ddigest (S ′ ^u , S ′ ^v ): distance between time series data S ′ ^u , S ′ ^v after dimension compression Dcontractive (S ′ ^u , S ′ ^v ): distance of time series data S ′ ^u , S ′ ^v after dividing the multidimensional space and setting a new metric space
The contractive transform lemma can be proved as follows. For false negative to ensure that does not ^{occur, Dreal (S u, S v} ) if ^{≦ ε Dcontractive (S 'u,} S' v) must be ≦ epsilon. Here, from the contractive transform condition, the following formula holds, so that the contractive transform lemma can be proved.

^{Dcontractive (S 'u, S'} v) <Ddigest (S 'u, S' v) ≦ Dreal (S u, S v) ≦ ε (8)
Here, Dcontractive (S ′ ^u , S ′ ^v ) is (| R ^Oi _u −R ^Oi _v | −1) · (ε / c) when the central point is Oi.

Next, it will be described that Dcontractive (S ′ ^u , S ′ ^v ) satisfies the contractive transform condition. First, the following equation holds according to the lower bounding condition.

Ddigest (S ′ ^u , S ′ ^v ) ≦ Dreal (S ^u , S ^v ) (9)
Subsequently, it is shown that the following equation holds.

^{Dcontractive (S 'u, S'} v) <Ddigest (S 'u, S' v) (10)
[I]: When S ′ ^u , S ′ ^v , and O _i are not on the same straight line The plane S ′ ^u S ′ ^v O _i is a triangle as shown in FIG. In the figure, the following equation holds from the conditions for establishing the triangle S ′ ^u S ′ ^v O _i .

_{^{S 'u O i + S'}} v O i> S 'u S' v and _{^{S 'v O i + S'}} u S 'v>S' u O i and ^{S 'u S' v + S} 'u O i>S' ^v O _i (11)
From this equation, S ′ ^u S ′ ^v > | S ′ ^u O _i −S ′ ^v O _i | _{^{Moreover, | S 'u O i -S}} ' v O i |> (| R Oi u -R Oi v | -1) is a · (ε / c). ^{Here, S 'u S' v =} Ddigest (S 'u, S' v) ^{_{is, (| R Oi u -R Oi}} v | -1) · (ε / c) = Dcontractive (S 'u, S Since ' ^v ), equation (10) holds.

[Ii-1]: When S ′ ^u , S ′ ^v and O _i are on the same straight line and O _i is inside the line segment S ′ ^u S ′ ^{v As} shown in FIG. | S ′ ^u O _i −S ′ ^v O _i | <S ′ ^u S ′ ^v . _{^{Moreover, | S 'u O i -S}} ' v O i |> (| R Oi u -R Oi v | -1) is a · (ε / c). ^{Here, S 'u S' v =} Ddigest (S 'u, S' v) _{^{is, (| R Oi u -R Oi}} v | -1) · (ε / c) = Dcontractive (S 'u, S Since ' ^v ), equation (10) holds.

[Ii-2]: S ′ ^u , S ′ ^v , O _i are on the same straight line and O _i is not inside the line segment S ′ ^u S ′ ^{v As} shown in FIG. | S ′ ^u O _i −S ′ ^v O _i | = S ′ ^u S ′ ^v . _{^{Moreover, | S 'u O i -S}} ' v O i |> (| R Oi u -R Oi v | -1) is a · (ε / c). ^{Here, S 'u S' v =} Ddigest (S 'u, S' v) _{^{is, (| R Oi u -R Oi}} v | -1) · (ε / c) = Dcontractive (S 'u, S Since ' ^v ), equation (10) holds.

Therefore, Dcontractive (S ′ ^u , S ′ ^v ) <Ddigest (S ′ ^u , S ′ ^v ) holds in any case of [i], [ii-1], and [ii-2].

^{Here, Dcontractive (S 'u, S} ' v) = (| R Oi u -R Oi v | -1) · (ε / c) < becomes a epsilon, this equation, | ^{R _Oi} u ^-R _{Oi v} | <c + 1. Therefore, time-series data satisfying the relationship of | R ^Oi _u −R ^Oi _v | <c + 1 may be similar. ^{Further, ε ≦ Dcontractive (S 'u} , S' v) = (| R Oi u -R Oi v | -1) · (ε / c) (<Dreal (S u, S v)) if dissimilar However, this equation becomes | R ^Oi _u -R ^Oi _v | ≧ c + 1. Therefore, time-series data ^satisfying | R ^Oi _u −R ^Oi _v | ≧ c + 1 are dissimilar.

The candidate determination unit 344 of the candidate search unit 34 calculates the distance between time series data after dimension compression with respect to time series data that may be similar, and selects those whose distances are within a certain range as similar candidates. Refine as. However, there are cases where similar candidates can be obtained without calculating the distance after dimension compression. For example, as shown in FIG. 11, when 'there ^u is from the center point _{O i} to ^{R Oi} _u-th region, S' series data S ^{when v} is from the center point _{O i} to ^{R Oi} _v-th region, Time series data belonging to the region where R ^Oi _u + R ^Oi _v ≦ c can be narrowed down as similar candidates without calculating the distance. On the other hand, for time-series data belonging to a region where R ^Oi _u + R ^Oi _v > c, a distance after dimension compression is calculated, and similarity is determined based on this distance. In the example of FIG. 11, c = 5.5, R ^Oi _u = 2, R ^Oi _v = 3, or R ^Oi _v = 4. If R ^Oi _v = 3, it is a similar candidate, and if R ^Oi _v = 4, the distance after dimension compression is calculated. Hereinafter, the process at this time will be described in detail.

  The candidate determination unit 344 obtains time series data that satisfies the following expression as a similar candidate.

Ddigest (S ′ ^u , S ′ ^v ) <Dexpanded (S ′ ^u , S ′ ^v ) ≦ ε (12)
Here, Dexpanded (S ′ ^u , S ′ ^v ) is (R ^Oi _u + R ^Oi _v ) · (ε / c). In the following, it is shown that the following equation holds.

^{Ddigest (S 'u, S'} v) <Dexpanded (S 'u, S' v) (13)
[I]: When S ′ ^u , S ′ ^v , and O _i are not on the same straight line The plane S ′ ^u S ′ ^v O _i is a triangle as shown in FIG. In the figure, than satisfied the conditions of the triangle _{^{S 'u S' v O i}} , S 'u O i + S' v O i> S 'u S' v holds. Further, it is _{^{S 'u O i + S'}} v O i <(R Oi u + R Oi v) · (ε / c). Here, S ′ ^u S ′ ^v = Ddigest (S ′ ^u , S ′ ^v ), and (R ^Oi _u + R ^Oi _v ) · (ε / c) = Dexpanded (S ′ ^u , S ′ ^v ). Therefore, Formula (13) is materialized.

[Ii-1]: S ′ ^u , S ′ ^v , O _i are on the same straight line and O _i is inside the line segment S ′ ^u S ′ ^{v As} shown in FIG. the ^{S 'u S' v = S} 'u O i + S' v O i. Further, it is _{^{S 'u O i + S'}} v O i <(R Oi u + R Oi v) · (ε / c). Here, S ′ ^u S ′ ^v = Ddigest (S ′ ^u , S ′ ^v ), and (R ^Oi _u + R ^Oi _v ) · (ε / c) = Dexpanded (S ′ ^u , S ′ ^v ). Therefore, Formula (13) is materialized.

[Ii-2]: When S ′ ^u , S ′ ^v , O _i are on the same straight line and O _i is not inside the line segment S ′ ^u S ′ ^{v As} shown in FIG. the _{^{S 'u O i + S'}} v O i> S 'u S' v. Further, it is _{^{S 'u O i + S'}} v O i <(R Oi u + R Oi v) · (ε / c). Here, S ′ ^u S ′ ^v = Ddigest (S ′ ^u , S ′ ^v ), and (R ^Oi _u + R ^Oi _v ) · (ε / c) = Dexpanded (S ′ ^u , S ′ ^v ). Therefore, Formula (13) is materialized.

Therefore, Ddigest (S ′ ^u , S ′ ^v ) <Dexpanded (S ′ ^u , S ′ ^v ) holds in any case of [i], [ii-1], and [ii-2]. If Ddigest (S ′ ^u , S ′ ^v ) <Dexpanded (S ′ ^u , S ′ ^v ) = (R ^Oi _u + R ^Oi _v ) · (ε / c) ≦ ε, similar candidates are obtained. This equation becomes _{^{R Oi u + R Oi v ≦}} c, determines as candidates for similar time-series data that satisfies the relationship of _{^{R Oi u + R Oi v ≦}} c.

On the other hand, if ε <Dexpanded (S ′ ^u , S ′ ^v ) = (R ^Oi _u + R ^Oi _v ) · (ε / c), it is not immediately a similar candidate. Since this equation is R ^Oi _u + R ^Oi _v > c, a distance is calculated for time series data satisfying the relationship of R ^Oi _u + R ^Oi _v > c, and those whose distance is within a certain range are similar candidates. Judge as. For this distance, for example, the Euclidean distance is used.

  Therefore, according to the present embodiment, the center point determination unit 33 in the space index unit 3 determines the center point of the concentric hypersphere in the multidimensional space, and the candidate search unit 34 sets the concentric super center around the center point. By dividing the multidimensional space into spherical structures, it becomes possible to divide the multidimensional space using all the axes, so that more efficient division can be realized.

  According to the present embodiment, the clustering unit 333 performs time-series data clustering, and the center point calculation unit 334 determines the center point using the clustering result, thereby appropriately arranging the center point. be able to.

  According to the present embodiment, the clustering unit 333 performs clustering on the time-series data randomly sampled by the sample unit 332, and the center point calculation unit 334 determines the center point using the clustering result. Thus, the center point can be calculated at high speed.

According to the present embodiment, the space dividing unit 342 divides the multidimensional space in increments of a value ε / c (c> 1) smaller than the threshold value ε for determining the similarity of time series data. Since the area is finely divided, the candidate area can be reduced. Thus, each ^R _Oi u from the center _{O ^i,} series data together when belonging to ^{R Oi} _v number of _^regions, without having to calculate the distance after dimensionality reduction if the relationship _{^{R Oi u + R Oi v ≦}} c Can be candidates for similar time-series data.

  In the present embodiment, the Euclidean distance is used as the distance function. However, the present invention is not limited to this, and any distance function that satisfies the following four properties can be applied.

1. d (x, y) ≧ 0 (reflection law)
2. d (x, y) = 0⇔x = y (separation rule)
3. d (x, y) = d (y, x) (Symmetry)
4). d (x, y) + d (y, z) ≧ d (x, z) (trigonometric rule)
In addition, since various modifications can be considered for the present embodiment, modifications thereof will be described below.

[Example 1]
The center point determination unit 33 randomly determines the center point of the concentric hypersphere in the multidimensional space and stores it in the internal memory. Since the center point is determined randomly, there is an advantage that it can be calculated at high speed. On the other hand, there is a disadvantage that the center point may be arranged at an inappropriate position.

[Example 2]
Without adopting the sample unit 332, the clustering unit 333 performs clustering on all time series data in the multidimensional space. Thereby, there is a merit that the center point calculation unit 334 can arrange the center point more appropriately. On the other hand, there is a demerit that requires time for calculation because clustering is performed on all time series data.

[Example 3]
The space dividing unit 342 divides the multidimensional space from the center point in increments of the threshold ε. Compared to the case where the threshold value ε / c is used, the candidate area where similar time-series data exists is limited to the area to which the time-series data belongs and the area directly adjacent to this area. There is an advantage that the number is reduced. On the other hand, there is a demerit that it is necessary to calculate the distance after dimension compression for all the time series data existing in the candidate area.

It is a block diagram which shows the structure of the similar time series data calculation apparatus in one embodiment. It is a figure for demonstrating CS strucutre. It is a block diagram which shows the structure of the space index part in the said similar time series data calculation apparatus. It is a block diagram which shows the structure of the center point determination part in the said space index part. It is a block diagram which shows the structure of the candidate search part in the said space index part. It is a figure which shows the state which the several center point has gathered in the position close in the multidimensional space of CS strucutre. It is a figure for demonstrating the area | region which judges dissimilar time series data. ^{Dcontractive (S 'u, S'} v) S 'u, S' in ^v, _{O i} is a diagram illustrating a case not collinear. Figure for ^{Dcontractive (S 'u, S'} v) in ^{S 'u, S' v,} O i is collinear and _{O i} is described a case where the interior of the line segment S ^'u S' ^v It is. A diagram for explaining a case where S ′ ^u , S ′ ^v , and O _i are on the same straight line in Dcontractive (S ′ ^u , S ′ ^v ) and O _i is not inside the line segment S ′ ^u S ′ ^v . It is. It is a figure for demonstrating the area | region which judges similar time series data. ^{Dexpanded (S 'u, S'} v) S 'u, S' in ^v, _{O i} is a diagram illustrating a case not collinear. A diagram for explaining a case where S ′ ^u , S ′ ^v , and O _i are on the same straight line and O _i is inside the line segment S ′ ^u S ′ ^v in Dexpanded (S ′ ^u , S ′ ^v ). It is. The figure for explaining the case where S ′ ^u , S ′ ^v , O _i are on the same straight line and O _i is not inside the line segment S ′ ^u S ′ ^v in Dexpanded (S ′ ^u , S ′ ^v ) It is. The diagram on the left shows two time-series data, and the diagram on the right shows the distance between the time-series data when using the Euclidean distance. It is a figure for demonstrating grid structure.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Similar time series data calculation apparatus 2 ... Data reception part 3 ... Spatial index part 4 ... Similarity determination part 5 ... Calculation result transmission part 31 ... Data reception part 32 ... Dimension compression part 33 ... Center point determination part 34 ... Candidate search part 35 ... Data transmission unit 331 ... Data reception unit 332 ... Sample unit 333 ... Clustering unit 334 ... Center point calculation unit 335 ... Data transmission unit 341 ... Data reception unit 342 ... Spatial division unit 343 ... Candidate area determination unit 344 ... Candidate determination unit 345 ... Data transmission unit

Claims (15)

Data receiving means for receiving time-series data flowing in sequentially and storing them in the first memory;
Dimensional compression means for dimensionally compressing time-series data read from the first memory and storing it in the second memory;
Center point determination means for determining a center point of a concentric hypersphere in a multidimensional space and storing it in a third memory;
Dividing the multidimensional space into concentric hypersphere structures centered on the center point read from the third memory, and narrowing down candidates for similar combinations of time-series data read from the second memory Candidate search means to be stored in
A similar time-series data calculation device comprising: The center point determination means includes
Clustering means for clustering the time-series data after dimension compression and storing it in the fifth memory;
Center point position calculation means for determining the position of the center point in the multidimensional space using the result of the clustering read from the fifth memory and storing it in the third memory;
The similar time series data calculation apparatus according to claim 1, wherein: The center point determination means includes
3. The similar time series data calculation apparatus according to claim 2, further comprising sample means for randomly selecting a sample from the time series data after dimension compression before the clustering.   2. The similar time series data calculation apparatus according to claim 1, wherein the center point determination means includes center point position calculation means for randomly determining the position of the center point in the multidimensional space and storing it in a third memory. . The candidate search means includes:
Space dividing means for dividing a multidimensional space into concentric hypersphere structures in increments of a threshold for judging the similarity of time series data from the center point;
Candidate area determination means for determining candidate areas where similar time-series data exists from the result of the division;
Candidate determination means for narrowing down similar candidates of time-series data after dimension compression from the determined candidate area, and storing the combination of the similar candidates in the fourth memory;
5. The similar time series data calculation apparatus according to claim 1, comprising:   6. The similar time series data calculation apparatus according to claim 5, wherein the space dividing unit divides the multidimensional space in units of a threshold smaller than the threshold instead of the threshold. Receiving time-series data flowing in sequentially and storing them in the first memory;
Dimensionally compressing time-series data read from the first memory and storing it in the second memory;
Determining a center point of a concentric hypersphere in a multidimensional space and storing it in a third memory;
Dividing the multidimensional space into concentric hypersphere structures centered on the center point read from the third memory, and narrowing down candidates for similar combinations of time-series data read from the second memory Memorizing steps,
A similar time series data calculation method characterized by comprising: Determining the center point comprises:
Clustering time-series data after dimension compression and storing it in a fifth memory;
Determining the position of the center point in the multidimensional space using the result of clustering read from the fifth memory and storing it in the third memory;
The similar time series data calculation method according to claim 7, further comprising: Determining the center point comprises:
9. The similar time series data calculation method according to claim 8, further comprising a step of selecting a sample at random from the time series data after dimension compression before the clustering.   8. The similar time series data calculation method according to claim 7, wherein the step of determining the center point includes the step of randomly determining the position of the center point in the multidimensional space and storing it in a third memory. The step of narrowing down the candidates includes
Dividing a multidimensional space into concentric hypersphere structures in threshold increments to determine similarity of time series data from the center point;
Determining candidate areas where similar time-series data exists from the result of the division;
Narrowing down similar candidates of time-series data after dimension compression from the determined candidate area, and storing the combination of the similar candidates in the fourth memory;
The similar time series data calculation method according to claim 7, comprising: Receiving time-series data that sequentially flows in and storing it in the first memory;
A process of dimensionally compressing the time-series data read from the first memory and storing it in the second memory;
Determining the center point of the concentric hypersphere in the multidimensional space and storing it in the third memory;
Dividing the multidimensional space into concentric hypersphere structures centered on the center point read from the third memory, and narrowing down candidates for similar combinations of time-series data read from the second memory Processing to be stored in
A similar time series data calculation program characterized by causing a computer to execute. The process of determining the center point is:
Clustering the time-series data after dimension compression and storing it in the fifth memory;
Processing for determining the position of the center point in the multidimensional space using the result of clustering read from the fifth memory and storing it in the third memory;
The similar time series data calculation program according to claim 12, wherein: The process of determining the center point is:
14. The similar time series data calculation program according to claim 13, wherein a process of randomly selecting a sample from time series data after dimension compression is executed before the clustering. 15. The process of determining the center point includes executing a process of randomly determining the position of the center point in the multidimensional space and storing it in a third memory for time-series data after dimension compression. Similar time series data calculation program.