JP2009199507A - Similar partial sequence detecting method, similar partial sequence detection program, and similar partial sequence detecting device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To suppress an increase in computational complexity and the amount of memory usage when detecting a pair similar partial sequences from two data streams. <P>SOLUTION: This similar partial sequence detecting device 1 can suppress an increase in computational complexity and the amount of memory usage by using a single time warping matrix when detecting a pair of similar partial sequences from two data streams by using the time warping matrix showing a similarity score of the two partial sequences with each other. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a technique for detecting similar partial sequence pairs in stream mining.

  A data stream (hereinafter also simply referred to as a “stream”) is a large amount of data flowing from a network at high speed. Stream mining is a technique for quickly finding useful information from a data stream expressed as a time series. Stream mining is not just a technique for analyzing large-scale data stored in a database, but a technique for analyzing and monitoring an increasing flow of data in real time. In order to analyze ever-increasing large-scale data and to provide information to users in real time, it is necessary to increase the speed and memory saving of stream mining technology.

  In stream monitoring, a sequence matching technique is required. In sequence matching, the similarity between two data sequences is expressed as a distance value, and the similarity is determined using this distance value. In addition, the sampling rate of each data stream may be different or the data transmission / reception cycle may change. However, it is important to consider time warping so as to flexibly cope with these. As a distance function considering this time warping, dynamic time warping (DTW) is widely used.

  DTW is a distance function that is used for the stored sequence. The DTW is extended in the time axis direction so as to minimize the distance between the two sequences, and the distance value is obtained by calculation that matches each element. Whether or not they are similar is determined by the distance value and the threshold value ε. This distance value is called a DTW distance, is represented by the total value of the distance after optimally adjusting the sequence length, and is calculated by a matrix (time warping matrix) based on dynamic programming. The smaller the value of the DTW distance, the higher the similarity between the two sequences, and 0 means that they are completely matched.

FIG. 14 is an explanatory diagram of DTW. As shown in FIG. 14A, two sequences X = (x ₁ , x ₂ ,..., X _n ) and sequence Y = (y ₁ , y ₂ ,..., Y _m ) obtain a DTW distance. At this time, the association is performed so that the DTW distance is minimized. Whether the two sequences have the same length or different lengths, the DTW can associate each element appropriately.

  As shown in FIG. 14B, in the matrix (time warping matrix) used for calculating the DTW distance, the combination (set) associated between the two sequences is called a time warping path. It is shown as a (blacked) cell.

  DTW will be further described with reference to FIG. FIG. 15 is a diagram illustrating a time warping matrix by DTW. In FIG. 15, a sequence Y is data of a fixed length m (4 in this case) and is data that is a source of sequence similarity determination. The sequence X, which is a data stream, is a sequence that is constantly expanding (the amount of data is increasing), and is data that is subjected to similarity determination with respect to the sequence Y.

The DTW distance can be calculated based on a time warping matrix. Here, the length n sequence _{X = (x 1, x 2} , ..., x n) and length sequence _{Y = (y 1, y 2} , ..., y m) of the m in, these DTW distance D ( X, Y) is defined as follows. Note that i = 1, 2,..., N, j = 1, 2,.

D (X, Y) = f (n, m) (9)
f (i, j) = ‖x _i −y _j ‖ + min {f (i, j−1), f (i−1, j),
f (i-1, j-1)} Expression (10)
f (0,0) = 0 Expression (11)
f (i, 0) = f (0, j) = ∞ (12)

Equation (9) is a definition of the DTW distance. Formula (10) is a specific calculation formula. In the formula (10), ‖x _i -y _j ‖ is representative of the distance of the two numbers _{(x i} and _{y j),} for example, Euclidean distance or the Manhattan distance (L1 distance), and the like. In the n-dimensional space, the coordinates of two points a and b are a (a ₁ , a ₂ ,..., a _n ), b (b ₁ , b ₂ ,..., b _n ), and (1 ≦ k ≦ n), the Euclidean distance is √ (Σ (a _k −b _k ) ² ), and the Manhattan distance is a distance represented by Σ | a _k −b _k |. In the following specific example, a square value of the Euclidean distance is used as ‖x _i -y _j ‖ for easy calculation. Note that the present invention is not limited to the case where the square value of the Euclidean distance is used, and other distances may be used.

  In equation (10), min {f (i, j-1), f (i-1, j), f (i-1, j-1)} is the smallest of the three values in {}. Means to adopt. Equations (11) and (12) are boundary conditions in the time warping matrix used when calculating these three values. According to the time warping matrix using this DTW distance, a partial sequence of sequence X similar to sequence Y can be detected.

  For example, if the DTW distance between the sequence Y = (11, 6, 9, 4) and the sequence X = (12, 6, 10, 6, 5, 1,...) Is calculated, the time warping matrix of FIG. It becomes the value shown in. Here, the hatched portion of the time warping matrix in FIG. 15 is a route (time warping path) followed to calculate the DTW distance “6”, and the start position of the calculation of the DTW distance by following this route. I understand. That is, by finding a time warping path in which the DTW distance values are relatively small, a sequence Y = (11, 6) from the sequence X = (12, 6, 10, 6, 5, 1,...). , 9, 4) can be detected (partial sequence (12, 6, 10, 6) here).

  Thus, the time warping matrix holds the value of the DTW function (that is, the value of f (i, j) in equation (10)), which forms the basis of DTW. When the distance between the sequence X having the length n and the sequence Y having the length m is to be obtained, the DTW requires a time of O (nm). This is because the DTW performs the calculation by associating all elements of the two sequences, and the calculation cost is significantly increased particularly when a long sequence is handled.

  In other words, when using this conventional method, when detecting a similar partial sequence from the data stream, it is necessary to compare with a partial sequence of any pattern, so every time data in the data stream arrives after the time has passed. It is necessary to add a time warping matrix. That is, FIG. 15 shows only one time warping matrix, but it is necessary to add similar time warping matrices one after another as time passes. Therefore, there has been a problem that the amount of calculation and the amount of memory used increase as the number of data streams increases.

  Many algorithms for sequence matching using DTW have been proposed, but many of them detect sequences similar to a query sequence prepared in advance. Non-Patent Document 1 and Non-Patent Document 2 propose methods for reducing calculation costs in sequence matching using DTW. However, these methods are methods for accumulated data sets and are not suitable for stream processing.

  Regarding the sequence matching of streams using DTW, Non-Patent Document 3 proposes a method for detecting a partial sequence similar to an inquiry sequence. However, this conventional method for sequence matching is merely to detect a partial sequence similar to a prepared inquiry sequence.

  On the other hand, a technique that does not prepare a specific inquiry sequence and continues to detect similar partial sequence pairs from an ever-increasing stream is also regarded as important. Non-Patent Literature 4 and Non-Patent Literature 5 focus on real-time stream monitoring and propose a method for detecting correlation between streams. However, these use distance scales without adjustment in the time axis direction and do not support time warping.

  The present invention deals with the problem of detecting a similar partial sequence pair from a data stream. Specifically, “when two data streams are given, a similar partial sequence pair is converted into a method based on DTW (DTW and DTW). Equivalent method) ”. This problem will be described with reference to FIG. FIG. 13 is an example of a data stream (sequence) used for detecting similar partial sequence pairs.

  As shown in FIGS. 13A and 13B, sequence # 1 is data with small spikes (projections) at # 11, # 12, and # 14, and sequence # 2 is at # 22 and # 23. is there. The amplitude of each spike is substantially the same, but the period (time width) is different. In addition, these sequences include three large spikes (# 13, # 21, # 24), which have different periods.

  The problem to be solved by the present invention is to find a partial similarity between two sequences. For example, partial sequence pairs # 11 and # 22, # 11 and # 23, # 13 and # 21, and # 13 and # 24 are similar partial sequence pairs of sequences # 1 and # 2. Since the periods of these pairs are different, it is difficult to detect accurately when time warping is not considered.

Here, the data stream X, the time _{I = i 1, i 2,} ..., i n, x 1, x 2 collected ... in, ..., _{x n,} denoted as a semi-infinitely long sequence of ... the value of it can. x _n is the latest data in i _n , and n increases with time. Let X [i _s : i _e ] be a partial sequence from i _s to i _e . Likewise, Y _{is, y 1, y 2, ...} , a sequence of values of _{y m,} Y: a _[j s _{j e]} a is a partial sequence from _{j s} to _{j e.} For example, if sequence # 1 is data stream X and sequence # 2 is data stream Y, partial sequence # 11 can be expressed as X [1155: 2712], and # 22 can be expressed as Y [6111: 8361]. At this time, the similar partial sequence pair detection problem is defined as follows.

[Similar partial sequence pair detection]
Given two data streams X and Y, a threshold value ε for similarity determination, and a lower limit value ζ of similar partial sequence lengths, similar partial sequence pairs X [i _s : i _e ] and Y [ j _s : j _e ] is detected.
1. The average distance value between X [i _s : i _e ] and Y [j _s : j _e ] is ε or less.
2. The sequence lengths of X [i _s : i _e ] and Y [j _s : j _e ] are both ζ or more.
Here, the average distance value means a distance value per element of the partial sequences X [i _s : i _e ] and Y [j _s : j _e ], and X [i _s : i _e ] and Y [j The distance value of _s : j _e ] / (time warping path length of X [i _s : i _e ] and Y [j _s : j _e ]).

  The threshold value ε and the lower limit value ζ of the similar partial sequence length are designated (set) by the user, and a similar partial sequence pair is detected based on these conditions.

Consider solving this problem using DTW, which is the prior art. When detecting similar partial sequence pairs X [i _s : i _e ] and Y [j _s : j _e ] from the data stream using DTW, O (nm) matrices are required. This is because it is necessary to create a matrix starting from each starting point that varies in the range of 1 ≦ i _s ≦ n−ζ + 1 and 1 ≦ j _s ≦ m−ζ + 1. This is the conventional general method. In this specification, this method is called a naive method.

In the i, j-th matrix (that is, the matrix starting from time i and time j), let the distance of element (k, l) be d _{i, j} (k, l). In the naive method, the partial sequence matching distance between X and Y is obtained as follows. Note that i = 1, 2,..., N, k = 1, 2,..., N−i + 1, j = 1, 2,.

_{D (X [i s: i} e], Y [j s: j e]) = d is, js (i e -i s + 1, j e -j s +1) ··· formula (13)
d _{i, j} (k, l) = ‖x _{i + k−1} −y _{j + l−1} ‖ + min {d _{i, j} (k, l−1), d _{i, j} (k−1, l), d _{i, j} (k-1, l-1)} Expression (14)
d _{i, j} (0,0) = 0 Expression (15)
d _{i, j} (k, 0) = d _{i, j} (0, l) = ∞ (16)

Further, the average distance d ′ for evaluating the similarity between X [i _s : i _e ] and Y [j _s : j _e ] is obtained as follows. W is the length of the time warping path between the partial sequence X [i _s : i _e ] and the partial sequence Y [j _s : j _e ].
d ′ = d _{i, j} (k, l) / W (17)

E. J. Keogh: “Exact Indexing of Dynamic Time Warping,” In Proceedings of the 28th International Conference on Very Large Data Base (VLDB2002), pp.406-417, 2002. S. W. Kim, S. Park, W. W. Chu: “An Index-based Approach for Similarity Search Supporting Time Warping in Large Sequence Database,” In Proceedings of IEEE 17th International Conference on Data Engineering (ICDE2001), pp.607-614, 2001. Y. Sakurai, C. Faloutsos, and M. Yamamuro: “Stream Monitoring under the Time Warping Distance,” In Proceedings of IEEE 23rd International Conference on Data Engineering (ICDE 2007), pp.1046-1055, 2007. S. Papadimitriou, J. Sun, and C. Faloutsos: “Streaming Pattern Discovery in Multiple Time-Series,” In Proceedings of the 31th International Conference on Very Large Data Bases (VLDB2005), pp.697-708, 2005. Y. Zhu, D. Shasha: “StatStream: Statistical Monitoring of Thousands of Data Streams in Real Time,” In Proceedings of the 28th International Conference on Very Large Data Bases (VLDB2002), pp.358-369, 2002.

However, since DTW is a sequence matching technique for detecting a sequence similar to a fixed-length query sequence, the use of this technique increases the number of matrices required for calculation. Therefore, the value that needs to be updated every hour is O (nm ² ) or O (n ² m) (since the number of matrices is O (nm)), and the amount of calculation and memory usage increase significantly. There is.

  The present invention has been made in view of the above problems, and an object of the present invention is to suppress an increase in the amount of calculation and memory usage when detecting a pair of similar partial sequences from two data streams.

  In order to solve the above-described problem, the present invention detects a similar partial sequence detection from two data streams using a time warping matrix indicating a similarity score between the two partial sequences. A similar partial sequence detection method by an apparatus, wherein the similar partial sequence detection device includes a storage unit that stores the time warping matrix, and a processing unit, wherein the processing unit is configured to store the two data streams. When one element of data of any one of the data streams is received, a similarity score between the partial sequence in the data stream including the element and the partial sequence in the other data stream is calculated, The calculated similarity score and the two partial sequences used to calculate the similarity score A pair of similar partial sequences using the similarity score stored in the time warping matrix of the storage unit in association with the start position and the end position of the storage unit stored in the time warping matrix of the storage unit Is detected and output.

  According to this invention, when detecting a pair of similar partial sequences from two data streams, since only a single time warping matrix is used, an increase in calculation amount and memory usage can be suppressed.

Further, according to the present invention, when the processing unit calculates the similarity score between the partial sequences of the two data streams, the two partial sequences X [i _s : i _e ] and Y [j _s : j _e ] Similarity score S (X [i _s : i _e ], Y [j _s : j _e ]) is calculated by the following equations (1) to (5),
S (X [i _s : i _e ], Y [j _s : j _e ]) = s (i _e , j _e ) (1)
s (i, j) = max {0, 2ε−‖x _i −y _j ‖ + s _best } Expression (2)
s _best = max {s (i, j-1), s (i-1, j), s (i-1, j-1)}
... Formula (3)
s (i, 0) = 0 Formula (4)
s (0, j) = 0 Formula (5)
The partial sequence _X stored in the time warping matrix _[i s: i _e] and the start position _{i s} of the partial sequence _Y: p indicating the start position _{j s} of _{[j s j e] (i} , j) Is calculated by the following equation (7),
p (i, j) = {p (i, j-1) (if s _best = s (i, j-1)),
p (i-1, j) (if s _best = s (i-1, j)),
p (i-1, j-1) (if s _best = s (i-1, j-1)),
(I, j) (if s _best = 0)} (7)
It is desirable to calculate the start position i _s , j _s by the following equation (8).
(I _s , j _s ) = p (i _e , j _e ) (8)
However, i = 1,2, ..., shown n, j = 1,2, ..., m, the distance between the ‖x _i -y _j ‖ the _{x i} and _{y j.}

  According to this invention, the similarity score is specifically calculated appropriately, and the similarity score is associated with the start position and the end position of the two partial sequences used for the calculation of the similarity score. It can be stored in the time warping matrix.

In the present invention, when the processing unit detects and outputs a pair of similar partial sequences using the similarity score stored in the time warping matrix of the storage unit,
The average value s ′ of the similarity score is calculated by the following equation (6),
s ′ = s (i, j) / W (6)
When the average value s ′ of the calculated similarity score is equal to or greater than a predetermined threshold ε, and the lengths of the two partial sequences used for calculating the similarity score are both equal to or greater than the predetermined length ζ It is desirable to detect and output these two partial sequences as pairs of similar partial sequences.
Here, W indicates the length of the time warping path between the partial sequence X [i _s : i _e ] and the partial sequence Y [j _s : j _e ].

  According to this invention, a pair of similar partial sequences can be detected more accurately by using the average value obtained by dividing the similarity score by the length of the corresponding time warping path.

  Further, according to the present invention, the processing unit has an average value s ′ of the calculated similarity score that is equal to or greater than a predetermined threshold value ε, and the lengths of the two partial sequences used for the calculation are both predetermined. If the length ζ is greater than or equal to ζ, the two partial sequences are stored in the storage unit as similar partial sequence pair candidates, and among the similar partial sequence pair candidates stored in the storage unit, at least the time warping path When there is an overlapping part, the similar partial sequence pair candidate with the longest time warping path is selected from the overlapping similar partial sequence pair candidates, and the selected similar partial sequence pair candidate is selected. It is desirable to output the two partial sequences that are as pairs of similar partial sequences.

  According to this invention, when there are a plurality of similar partial sequence pairs in which at least a part of the time warping path overlaps, the similar partial sequence pair with the longest time warping path among them is output, so that redundancy is provided to the user. It is possible to provide more useful information without giving unnecessary information.

  The present invention also provides a similar partial sequence detection program which causes a computer to execute a similar partial sequence detection method. According to such a program, it is possible to cause a general computer to execute the similar partial sequence detection method.

  According to the present invention, it is possible to suppress an increase in calculation amount and memory usage when detecting a pair of similar partial sequences from two data streams.

  Hereinafter, the best mode for carrying out the present invention (hereinafter referred to as an embodiment) will be described by dividing it into a first embodiment and a second embodiment. Thereafter, three experimental results will be described.

<< First Embodiment >>
FIG. 1 is a configuration diagram of a similar partial sequence detection apparatus according to the first embodiment. The similar partial sequence detection device 1 is a computer device, and includes an input unit 11, a processing unit 12, a storage unit 13, and an output unit 14.

  The input unit 11 receives data stream input from an external device (not shown) or a sensor (not shown) via the Internet or a LAN (Local Area Network), or a similar part from an input device (not shown) such as a keyboard or a mouse. An input of a similar partial sequence detection condition for detecting a sequence pair (hereinafter also simply referred to as “similar partial sequence”) is accepted. The similar partial sequence detection conditions are, for example, the lower limit value ζ of the partial sequence length when detecting a similar partial sequence from the data stream, the threshold value ε of the average value of similarity scores, and the like (details will be described later). The input unit 11 is realized by a communication interface for transmitting / receiving data via the Internet or a LAN, and an input / output interface for inputting / outputting various data to / from an external device such as an input device.

  Such an input unit 11 includes a detection condition input unit 111 that receives an input of a similar partial sequence detection condition used when detecting a similar partial sequence from two data streams, and a data stream input unit 112 that receives an input of a data stream. It is comprised including.

  The processing unit 12 performs various arithmetic processes for detecting a similar partial sequence pair from two data streams, and is realized, for example, by a CPU (Central Processing Unit) executing a program in the storage unit 13. . The processing unit 12 includes a data stream processing unit 121, and uses the time warping matrix (matrix) of the time warping data storage unit 132 of the storage unit 13 for the data stream received by the data stream input unit 112, and a similar partial sequence A pair is detected and output to the outside via a similar partial sequence output unit 141 (described later) of the output unit 14. The data stream processing unit 121 uses a scoring function when calculating the average value of similarity scores between partial sequences from two data streams.

  The scoring function is similarity determination means for detecting similar partial sequence pairs. The degree of similarity between partial sequences is calculated as a score after optimal expansion in the time axis direction in order to match each element between two sequences. Similar to DTW, the scoring function is an approach based on dynamic programming, but differs from DTW in the following two points.

  The first is to obtain a similar partial sequence pair using the maximum value of the cumulative score. On the other hand, the DTW obtains a similar partial sequence pair using the minimum cumulative distance.

  The second is the introduction of “zero-resetting” for scoring functions. This means that if the cumulative score s (i, j) of the matrix becomes a negative value, this value is replaced with 0 (zero). This approach has been proposed in the field of bioinformatics and is implemented in the Smith-Waterman algorithm and the like. The sequence in the bioinformatics field is intended for symbol sequences, but the scoring function in this embodiment is different in that it is intended for numerical sequences.

Replacing the score with 0 means that the partial sequences X and Y at the end point (i, j) no longer meet the definition of similar partial sequence detection, i.e. are not at all similar. Therefore, in the section where 0 continues, the partial sequence pairs in this section are not similar at all. Assess the similarity between the partial sequence pair X [i _s : i _e ] (length is L _x ) and Y [j _s : j _e ] (length is L _y ) by “zero-resetting” Can do.

Hereinafter, the scoring function and the like will be described more specifically. The scoring function is similar to one data stream X = (x ₁ , x ₂ ,..., X _n ,...) And the other data stream Y = (y ₁ , y ₂ ,..., Y _m ,. It is a function for calculating the average value of the degree score. The data stream processing unit 121 uses the scoring function to generate a partial sequence X [i _s : i _e ] of the data stream X and a partial sequence of the data stream Y each time one piece of data of any data stream arrives. The similarity score of Y [j _s : j _e ] is calculated (calculated).

  The similarity score calculated by this scoring function is added when the similarity is high and subtracted when the similarity is low, as shown in equations (1) to (5). This means that partial sequences having a similarity score equal to or greater than the threshold ε are similar partial sequences. The similarity score is calculated by the data stream processing unit 121 by associating the elements of the partial sequence X and the partial sequence Y with each other using a time warping matrix (see FIGS. 3 to 6).

The similarity score S (X [i _s : i _e ], Y [j _s : j _e ]) between the two partial sequences X [i _s : i _e ] and Y [j _s : j _e ] is (1) to (5). Note that i = 1, 2,..., N, j = 1, 2,.

S (X [i _s : i _e ], Y [j _s : j _e ]) = s (i _e , j _e ) (1)
s (i, j) = max {0, 2ε−‖x _i −y _j ‖ + s _best } Expression (2)
s _best = max {s (i, j-1), s (i-1, j), s (i-1, j-1)}
... Formula (3)
s (i, 0) = 0 Formula (4)
s (0, j) = 0 Formula (5)

Further, the average value s ′ of the similarity score is calculated by the following equation (6).
s ′ = s (i, j) / W (6)

Here, ε is a threshold value for similarity determination. Formula (1) is the definition of the similarity score. Formula (2) is a specific calculation formula. In Expression (2), ‖x _i −y _j ‖ represents a distance between two numerical values (x _i and y _j ), and examples thereof include a Euclidean distance and a Manhattan distance (L1 distance). Here, the square value of the Euclidean distance is used.

In formulas (2) and (3), max {} means that the maximum value among the values in {} is adopted. Expressions (4) and (5) are boundary conditions in the time warping matrix. W represents the length of the time warping path between the partial sequence X [i _s : i _e ] and the partial sequence Y [j _s : j _e ]. By using the time warping matrix using the similarity score and the average value s ′ of the similarity score, a pair of similar partial sequences in sequence X and sequence Y can be detected more accurately (details will be described later). .

As shown in the equation (2), when s (i, j) is calculated, when the value of “2ε−‖x _i −y _j ‖ + s _best ” becomes smaller than 0, s (i, j j) = 0. By doing in this way, even when the similarity score becomes smaller than 0, it is possible to prevent the similarity score of the subsequent partial sequences from being affected. That is, it is possible to calculate a similarity score that reflects the connection between partial sequences having higher similarity scores.

The time warping matrix subsequence _X to store _[i s: i _e] and the start position _{i s} of the partial sequence _Y: p showing the _[j s j _e] start position _{j s} (i, _j) Can be calculated by the following equation (7).

p (i, j) = {p (i, j-1) (if s _best = s (i, j-1)),
p (i-1, j) (if s _best = s (i-1, j)),
p (i-1, j-1) (if s _best = s (i-1, j-1)),
(I, j) (if s _best = 0)} (7)

Then, the start position i _s , j _s can be calculated by the following equation (8).
(I _s , j _s ) = p (i _e , j _e ) (8)

  That is, this time warping matrix holds the similarity score for each element and the start positions of the partial sequences X and Y used to calculate the similarity score, so that the start position of the corresponding time warping path is stored in the past. Can be recognized without going back to the past (without holding past data).

  The storage unit 13 stores various data for performing similar partial sequence detection from two data streams. The storage unit 13 is realized by, for example, a RAM (Random Access Memory) and an HDD (Hard Disk Drive). The storage unit 13 includes a detection condition storage unit 131 and a time warping data storage unit 132. The similar partial sequence candidate storage unit 133 indicated by a broken line will be described separately in the second embodiment.

  The detection condition storage unit 131 stores similar partial sequence detection conditions. The similar partial sequence detection condition is information indicating the lower limit value ζ of the partial sequence length when detecting a pair of similar partial sequences from two data streams, the threshold value ε of the average value of similarity scores, and the like.

  The time warping data storage unit 132 stores the above-described time warping matrix (see FIGS. 3 to 6). One feature of the similar partial sequence detection apparatus 1 is that this time warping matrix is single. In other words, since a similar partial sequence pair can be detected by using one time warping matrix, an increase in the amount of calculation and memory usage is greatly suppressed as compared to the case of using a large number of time warping matrices. Can do. Further, it is not necessary to hold the original data stream, and an increase in memory usage can be further suppressed.

  3 to 6 show the time warping matrix of all elements of the received data stream, the time warping matrix prepared in the time warping data storage unit 132 is outside (new data side). There should be data for 2 rows and 2 columns (in the matrix of FIG. 3, data for i = 3, 4, j = 4, 5).

  The output unit 14 includes a similar partial sequence output unit 141 that outputs a similar partial sequence detected by the data stream processing unit 121. The output unit 14 is realized by the communication interface described above and an input / output interface for inputting / outputting various data to / from an external device such as an output device.

Next, processing of the similar partial sequence detection device 1 will be described. FIG. 2 is a flowchart showing processing of the similar partial sequence detection device 1 of the first embodiment. Here, each of the two data streams X (= x ₁ ,..., X _i ,..., X _n ,...) And the data stream y (= y ₁ ,..., Y _j ,..., Y _m ,. Assume that elements are given sequentially.

First, the data stream processing unit 121, via the data stream input unit 112, receives the data _{x i} at time i (step S11).
Next, the data stream processing unit 121 resets the value of j to 0 (step S12).

  Thereafter, the data stream processing unit 121 repeats the processes of steps S13 to S16 while incrementing (increasing by 1) the value of j until the value of j becomes m.

In step S13, the data stream processing unit 121 calculates the similarity score s (i, j) between x _i and y _j , the average value s ′ of the similarity score, and the start position p (i, j) using the above formula. Calculate using (1) to (7).

In step S14, the data stream processing unit 121 determines whether or not the conditions of s ′ ≧ ε, L _x ≧ ζ, and L _y ≧ ζ are satisfied, that is, the average value s ′ of the similarity score is equal to or greater than a predetermined threshold value ε. In addition, it is determined whether or not the lengths of the two partial sequences used for calculating the similarity score s (i, j) are equal to or greater than a predetermined length ζ.

When Yes in step S14, in step S15, the data stream processing unit 121 assigns p (i _e , j _e ) to (i _s , j _s ), i to i _e , and j to j _e , respectively. To do.

In step _S < _b > 16, the data stream processing unit 121 outputs the values of i _s , i _e , j _s , j _e , and s ′ to the user via the similar partial sequence output unit 141.

  When No in step S14, step S15 and step S16 are skipped.

When the data stream processing unit 121 receives the data y _j at time j via the data stream input unit 112 (step S21), the data stream processing unit 121 performs the processing of step S22 to step S26 in the same manner as the processing of step S12 to step S16. Do.

  After the processes of steps S13 to S16 or after the processes of steps S23 to S26, the data stream processing unit 121 determines whether or not the reception of the two data streams has been completed (step S31). If not completed (No in step S31), the data stream processing unit 121 returns to step S11 or step S21, and if completed (Yes in step S31), ends the process.

  Next, a specific example of the processing of the flowchart of FIG. 2 will be described. 3-6 is explanatory drawing of the specific example. In this example, for two data streams X = (5, 12, 6, 10, 6, 5, 1), y = (11, 6, 9, 4, 13, 8, 5), ε = 3, Assume that similar partial sequence pairs are detected under the condition of ζ = 4. As described above, the matrix (time warping matrix) holds, for each element (cell), the similarity score and the start positions of the partial sequences X and Y used to calculate the similarity score. However, in the following, for ease of explanation, each element (cell) is assumed to hold the average value of the similarity score and the start position.

  When one element of the data stream X or Y arrives, processing by the similar partial sequence detection device 1 is executed. First, when i = 4, j = 5, that is, when the data of X = (5, 12, 6, 10) and y = (11, 6, 9, 4, 13) has already been received, the matrix is shown in FIG. It becomes like 3. Each cell holds the average value s ′ of the similarity score and the information of the calculation start point p (i, j), the average value s ′ of the similarity score in the upper part, and the starting point information in the lower part. Is shown. For example, the average value s ′ of the similarity score of the cell (4, 3) is 4, meaning that it is the average value of the similarity scores of the partial sequences X [2: 4] and Y [1: 3]. .

When x ₅ = 6 arrives at time i = 5, the processing in steps S11 to S16 in FIG. 2 is executed, and the values of the colored (shaded) cells in FIG. 4 are calculated. FIG. 4 is a matrix at the time point when i = 5 and j = 5. At this time, in the cells (5, 4) surrounded by the circles, the partial sequences X [2: 5], Y [whose average score is equal to or greater than ε (= 3) and whose length is equal to or greater than ζ (= 4). 1: 4] is detected as a similar partial sequence pair.

  When the element of the data stream Y arrives, the processing of steps S21 to S26 in FIG. 2 is executed. These processes are repeated when the elements of the data streams X and Y arrive, and the final matrix is as shown in FIG. FIG. 5 is a matrix at the time point of i = 7 and j = 7 (the description of each numerical value is omitted). As shown in FIG. 5, finally, partial sequence pairs corresponding to the five cells surrounded by circles are detected as similar partial sequence pairs.

The naive approach uses a memory amount of O (nm ² + n ² m) to detect similar partial sequence pairs, and O (nm ² ) (when an element of X arrives) or O (n ² m) It is necessary to update the distance value (when the element Y arrives). On the other hand, in the present embodiment, similar partial sequence pairs can be detected using only a single matrix. Therefore, a memory amount of O (m + n) is used, and O (m) per unit time (when an element of X arrives) Alternatively, only the value of O (n) (when the element Y arrives) needs to be updated. Therefore, it is possible to achieve a significant reduction in the calculation amount (calculation time) and memory usage.

<< Second Embodiment >>
Next, a second embodiment will be described. According to the similar partial sequence detection device 1 of the first embodiment described above, the similar partial sequence pairs output by the similar partial sequence pair detection include those in which at least a part of the time warping path overlaps. For example, the similar partial sequence pairs detected in FIG. 5 are a pair of X [1: 5] and Y [4: 7], a pair of X [1: 6] and Y [4: 7], and X [2: 5] and Y [1: 4], X [2: 6] and Y [1: 4], and X [2: 7] and Y [1: 4]. The time warping path is as shown in FIG. FIG. 6 is a diagram showing a time warping path of similar partial sequence pairs detected in FIG.

  As described above, the time warping path indicates which elements of the two partial sequences are matched with each other. As can be seen from FIG. 6, the five sequence pairs can be broadly classified into two groups, that is, the five time warping paths can be classified into two different groups. Therefore, the similar partial sequence detection apparatus 1 according to the second embodiment selects and detects one similar partial sequence pair with the longest time warping path from a plurality of similar partial sequence pairs with overlapping time warping paths. By notifying the user (data output) only by using the similar partial sequence pair having the longest selected time warping path, it is possible to avoid a situation where the user receives duplicate information. In the example of FIG. 5, the pair of X [1: 6], Y [4: 7] and the pair of X [2: 7], Y [1: 4] has the longest output time warping path. Similar partial sequence pairs.

  The similar partial sequence detection device 1 of the second embodiment will be described focusing on the differences from the case of the first embodiment. The similar partial sequence detection apparatus 1 according to the second embodiment is characterized by selecting and detecting one longest similar partial sequence pair from a plurality of similar partial sequence pairs in which at least a part of the time warping path overlaps. . In the following description, the same components as those in the first embodiment described above are denoted by the same reference numerals and description thereof is omitted.

As illustrated in FIG. 1, the similar partial sequence detection device 1 includes a similar partial sequence candidate storage unit 133 in the storage unit 13. The similar partial sequence candidate storage unit 133 records (accumulates) one or more pieces of information of similar partial sequence pairs that satisfy the conditions of s ′ ≧ ε, L _x ≧ ζ, and L _y ≧ ζ.

  The processing procedure of such a similar partial sequence detection apparatus 1 will be described with reference to FIG. FIG. 7 is a flowchart showing processing of the similar partial sequence detection device of the second embodiment.

After step S15, the data stream processing unit 121 stores the values of i _s , i _e , j _s , j _e , and s ′ as similar partial sequence pair candidates in the similar partial sequence candidate storage unit 133 of the storage unit 13. (Step S17). The same applies to step S27.

  After the loop of steps S13 to S17 or the loop of steps S23 to S27, the data stream processing unit 121 has a time warping path among a plurality of similar partial sequence pairs in which at least a part of the time warping path overlaps. It is determined whether the longest similar partial sequence pair has been determined (step S41). This determination can be performed by using the information on the start position of each cell in the time warping matrix. That is, for example, when there are a plurality of similar partial sequence pairs in which at least a part of the time warping path overlaps, the information on the start positions of all cells sequentially updated in the matrix is the time warping path of the plurality of similar partial sequence pairs. If it is after the end position, there are no more similar partial sequence pairs that overlap.

  When Yes in step S41, the data stream processing unit 121 outputs the similar partial sequence pair having the longest time warping path to the user via the similar partial sequence output unit 141 (step S42), and proceeds to step S31.

  In this way, according to the similar partial sequence detection device 1 of the second embodiment, when there are a plurality of similar partial sequence pairs in which at least a part of the time warping path overlaps, the similarity with the longest time warping path is among them. Since the partial sequence is output, more useful information (similar partial sequence with the longest time warping path) can be provided to the user without giving redundant information.

  If a similar partial sequence detection program for executing the similar partial sequence detection method of the first embodiment and the second embodiment is created, a general computer that executes the program operates as the similar partial sequence detection device 1. it can.

≪Experimental results≫
Next, experimental results of processing using the similar partial sequence detection device 1 of the first embodiment will be described. In order to visually grasp the experimental results, a scatter diagram is used here. For example, FIG. 8 is a scatter diagram showing the result of detecting similar partial sequence pairs from sequences # 1 and # 2 in FIG. The scatter diagram in FIG. 8 reflects the elements i _e and j _e in X [i _s : i _e ] and Y [j _s : j _e ], which are similar partial sequence pairs in sequences # 1 and # 2. That is, the horizontal axis in FIG. 8 represents an element of X, the vertical axis represents an element of Y, and when the partial sequence pair X [i _s : i _e ] and Y [j _s : j _e ] are similar, A point is plotted at the position of (i _e , j _e ) in the scatter diagram.

  In FIG. 8, a small spike in which each part surrounded by two solid lines is detected, and a region including a large spike in which a part surrounded by a broken line is detected are shown. In FIG. 8, the periodicity (appearance interval and appearance time width) of similar partial sequence pairs between two sequences can be confirmed.

For example, small spikes # 11 and # 22 are similar, and the relationship appears in the lower left corner of the part surrounded by the left solid line in the scatter diagram. In a portion surrounded by a solid line, six positions representing correspondences between small spikes are regularly plotted, and it can be seen that small spikes similar to # 11 and # 22 appear periodically. The sequence # 1 and # 2 have different large and small spike intervals, but the presence of a similar partial sequence pair and its periodicity can be confirmed.
Hereinafter, scatter diagrams can be created in the same manner for FIGS.

  Next, experimental results using actual data are shown. Each experiment was carried out on a computer equipped with a 2 GB memory and a 3 GHz CPU.

9, (a) and (b) are diagrams showing artificial data (Sines) composed of a plurality of sine waves having white noise (the vertical axis is a numerical value, the horizontal axis is time), and (c) is It is a scatter diagram of an experimental result.
As shown in FIGS. 9A and 9B, Sines 1 and Sines 2 have different periods of the sine wave and the period in which the sine wave appears. And as shown in FIG.9 (c), according to the similar partial sequence detection apparatus 1 of this embodiment, all the sine waves and the time change periodicity can be specified completely (representation). I understand. That is, there are six sine waves in Sines1, five sine waves in Sines2, and there are 30 (= 6 × 5) plot groups in the scatter diagram. Moreover, in the scatter diagram of FIG.9 (c), it can confirm that the difference in the period of each sine wave appears as the difference in inclination.

  10, (a) and (b) are diagrams showing measured values (Temperature) of the temperature sensor, and the temperature is expressed in Celsius (the vertical axis is temperature, the horizontal axis is time), and (c) is the experimental result. It is a scatter diagram.

  The data acquisition interval in FIGS. 10A and 10B is about 1 minute, and these data lack measurement values at many times. Temperature 1 and Temperature 2 each include two patterns in which two temperature changes that vary greatly from about 18 degrees to 32 degrees depending on the weather appear in succession (see the broken line portion). As shown in FIG. 10C, it can be seen that the similar partial sequence detection apparatus 1 of the present embodiment has succeeded in finding these two patterns. That is, there are four (= 2 × 2) plot groups in the scatter diagram of FIG.

  In FIG. 11, (a) and (b) are diagrams showing motion capture data (Mocap), and (c) is a scatter diagram of experimental results. These two data (Mocap1 and Mocap2) are motion capture data obtained by attaching a marker to each part of the subject and measuring the angular velocity of the attached part at a sampling period of 120 times per second. “Sec.” In the table corresponds to the actual motion time, and indicates that the subject is performing a certain motion continuously.

  For example, in Mocap1, it means that the subject performed a motion in the order of walking-running-jumping-. In this experiment, eight pieces of angular velocity data acquired from markers attached symmetrically to the respective parts of the upper arm, the elbow, the thigh, and the calf are selected and used as eight-dimensional data. These data include walking motion (colored portion of the table), and the data length of each walking motion is different. As shown in FIG. 11C, in the similar partial sequence detection apparatus 1 of the present embodiment, it can be confirmed from the scatter diagram that all walking motions are detected. That is, there are three walkings in Mocap1, three walkings in Mocap2, and there are nine (= 3 × 3) plot groups in the scatter diagram.

  In addition, it seems that there is a part where a slight deviation occurs between the numerical value of “Time” in Mocap 1 and Mocap 2 and the position of the plot group in the scatter diagram. However, it detects both when the subject's motion switching is continuous (no pause) and discontinuous (temporary pause) until the next motion starts (ie, This is because when the next motion starts immediately after the end of a certain motion, and when the subject's movement stops once (1, 2 seconds), the rate of decrease in the similarity score is different). It has nothing to do with the accuracy of the method.

FIG. 12 is a comparison diagram regarding calculation time between the method according to the present embodiment and the naive method. Artificial data is used as data, and the sequence length (horizontal axis) n and m are changed. In FIG. 12, the total time of matrix update and similar partial sequence pair detection is averaged, and the vertical axis indicates the calculation time. From this experimental result, it can be seen that the method according to the present embodiment shows extremely high performance (higher processing speed is realized) than the naive method. In other words, the calculation amount is O (m + n) (since the matrix is single) as compared with the naive technique O (nm ² + n ² m) (since the number of matrices is O (nm)). ) And has achieved a significant reduction.

  As mentioned above, although embodiment of this invention was described, this invention is not limited to this, It can implement in the range which does not change the meaning.

  In addition, specific configurations of hardware and software can be appropriately changed without departing from the gist of the present invention.

  Data streams occur in various fields such as video, sensor networks, and finance. The present invention is applicable to all these fields.

It is a block diagram of the similar partial sequence detection apparatus of 1st Embodiment. It is a flowchart which shows the process of the similar partial sequence detection apparatus of 1st Embodiment. It is a figure which shows an example of a time warping matrix. It is a figure which shows an example of a time warping matrix. It is a figure which shows an example of a time warping matrix. It is a figure which shows an example of a time warping matrix. It is a flowchart which shows the process of the similar partial sequence detection apparatus of 2nd Embodiment. It is a scatter diagram showing the result of having detected the similar partial sequence pair from the sequence of FIG. (A) And (b) is a figure which shows the artificial data comprised from several sine waves with white noise, (c) is a scatter diagram of an experimental result. (A) And (b) is a figure which shows the measured value of a temperature sensor, (c) is a scatter diagram of an experimental result. (A) And (b) is a figure which shows motion capture data, (c) is a scatter diagram of an experimental result. It is a comparison figure regarding the calculation time of the method by this embodiment, and a naive method. It is an example of the data stream used for the detection of a similar partial sequence pair. It is explanatory drawing of DTW. It is the figure which illustrated the time warping matrix by DTW.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Similar partial sequence detection apparatus 11 Input part 12 Processing part 13 Storage part 14 Output part 111 Detection condition input part 112 Data stream input part 121 Data stream processing part 131 Detection condition storage part 132 Time warping data storage part 133 Similar partial sequence candidate memory | storage 141 Similar partial sequence output section

Claims (9)

A similar partial sequence detection method by a similar partial sequence detection device for detecting a pair of similar partial sequences from two data streams using a time warping matrix indicating a similarity score between the two partial sequences,
The similar partial sequence detection device includes a storage unit that stores the time warping matrix, and a processing unit.
The processor is
When one element of data of one of the two data streams is received, the degree of similarity between the partial sequence in the data stream including the element and the partial sequence in the other data stream Calculate the score,
The calculated similarity score and the start position and end position of the two partial sequences used for calculating the similarity score are stored in the time warping matrix of the storage unit in association with each other,
A similar partial sequence detection method, comprising: detecting and outputting a pair of similar partial sequences using the similarity score stored in the time warping matrix of the storage unit. The processor is
When calculating the similarity score between the partial sequences of the two data streams,
The similarity score S (X [i _s : i _e ], Y [j _s : j _e ]) between two partial sequences X [i _s : i _e ] and Y [j _s : j _e ] is expressed as Calculated by equations (1) to (5),
S (X [i _s : i _e ], Y [j _s : j _e ]) = s (i _e , j _e ) (1)
s (i, j) = max {0, 2ε−‖x _i −y _j ‖ + s _best } Expression (2)
s _best = max {s (i, j-1), s (i-1, j), s (i-1, j-1)}
... Formula (3)
s (i, 0) = 0 Formula (4)
s (0, j) = 0 Formula (5)
The partial sequence _X stored in the time warping matrix _[i s: i _e] and the start position _{i s} of the partial sequence _Y: p indicating the start position _{j s} of _{[j s j e] (i} , j) Is calculated by the following equation (7),
p (i, j) = {p (i, j-1) (if s _best = s (i, j-1)),
p (i-1, j) (if s _best = s (i-1, j)),
p (i-1, j-1) (if s _best = s (i-1, j-1)),
(I, j) (if s _best = 0)} (7)
The similar partial sequence detection method according to claim 1, wherein the start position i _s , j _s is calculated by the following equation (8).
(I _s , j _s ) = p (i _e , j _e ) (8)
However, i = 1,2, ..., shown n, j = 1,2, ..., m, the distance between the ‖x _i -y _j ‖ the _{x i} and _{y j.} The processor is
Using the similarity score stored in the time warping matrix of the storage unit to detect and output a pair of similar partial sequences,
The average value s ′ of the similarity score is calculated by the following equation (6),
s ′ = s (i, j) / W (6)
When the average value s ′ of the calculated similarity score is equal to or greater than a predetermined threshold ε, and the lengths of the two partial sequences used for calculating the similarity score are both equal to or greater than the predetermined length ζ The similar partial sequence detection method according to claim 2, wherein the two partial sequences are detected and output as a pair of similar partial sequences.
Here, W indicates the length of the time warping path between the partial sequence X [i _s : i _e ] and the partial sequence Y [j _s : j _e ]. The processor is
When the average value s ′ of the calculated similarity score is equal to or greater than a predetermined threshold ε, and the lengths of the two partial sequences used for the calculation are both equal to or greater than a predetermined length ζ,
The two partial sequences are stored in the storage unit as similar partial sequence pair candidates,
Among the similar partial sequence pair candidates stored in the storage unit, when there is an overlap in at least a part of the time warping path, the time is selected from the overlapping similar partial sequence pair candidates. The similar partial sequence pair candidate with the longest warping path is selected, and the two partial sequences that are the selected similar partial sequence pair candidates are output as pairs of similar partial sequences. Similar partial sequence detection method.   A similar partial sequence detection program for causing a computer to execute the similar partial sequence detection method according to any one of claims 1 to 4. A similar partial sequence detection device for detecting a pair of similar partial sequences from two data streams using a time warping matrix indicating a similarity score between the two partial sequences,
A storage unit for storing the time warping matrix;
When one element of data of one of the two data streams is received, the degree of similarity between the partial sequence in the data stream including the element and the partial sequence in the other data stream Calculate the score,
The calculated similarity score and the start position and end position of the two partial sequences used for calculating the similarity score are stored in the time warping matrix of the storage unit in association with each other,
A processing unit that detects and outputs a pair of similar partial sequences using the similarity score stored in the time warping matrix of the storage unit;
A similar partial sequence detection device comprising: The processor is
When calculating the similarity score between the partial sequences of the two data streams,
The similarity score S (X [i _s : i _e ], Y [j _s : j _e ]) between two partial sequences X [i _s : i _e ] and Y [j _s : j _e ] is expressed as Calculated by equations (1) to (5),
S (X [i _s : i _e ], Y [j _s : j _e ]) = s (i _e , j _e ) (1)
s (i, j) = max {0, 2ε−‖x _i −y _j ‖ + s _best } Expression (2)
s _best = max {s (i, j-1), s (i-1, j), s (i-1, j-1)}
... Formula (3)
s (i, 0) = 0 Formula (4)
s (0, j) = 0 Formula (5)
The partial sequence _X stored in the time warping matrix _[i s: i _e] and the start position _{i s} of the partial sequence _Y: p indicating the start position _{j s} of _{[j s j e] (i} , j) Is calculated by the following equation (7),
p (i, j) = {p (i, j-1) (if s _best = s (i, j-1)),
p (i-1, j) (if s _best = s (i-1, j)),
p (i-1, j-1) (if s _best = s (i-1, j-1)),
(I, j) (if s _best = 0)} (7)
The similar partial sequence detection apparatus according to claim 6, wherein the start position i _s , j _s is calculated by the following equation (8).
(I _s , j _s ) = p (i _e , j _e ) (8)
However, i = 1,2, ..., shown n, j = 1,2, ..., m, the distance between the ‖x _i -y _j ‖ the _{x i} and _{y j.} The processor is
Using the similarity score stored in the time warping matrix of the storage unit to detect and output a pair of similar partial sequences,
The average value s ′ of the similarity score is calculated by the following equation (6),
s ′ = s (i, j) / W (6)
When the average value s ′ of the calculated similarity score is equal to or greater than a predetermined threshold ε, and the lengths of the two partial sequences used for calculating the similarity score are both equal to or greater than the predetermined length ζ The similar partial sequence detection apparatus according to claim 7, wherein the two partial sequences are detected and output as a pair of similar partial sequences.
Here, W indicates the length of the time warping path between the partial sequence X [i _s : i _e ] and the partial sequence Y [j _s : j _e ]. The processor is
When the average value s ′ of the calculated similarity score is equal to or greater than a predetermined threshold ε, and the lengths of the two partial sequences used for the calculation are both equal to or greater than a predetermined length ζ,
The two partial sequences are stored in the storage unit as similar partial sequence pair candidates,
Among the similar partial sequence pair candidates stored in the storage unit, when there is an overlap in at least a part of the time warping path, the time is selected from the overlapping similar partial sequence pair candidates. 9. The similar partial sequence pair candidate with the longest warping path is selected, and the two partial sequences that are the selected similar partial sequence pair candidates are output as a pair of similar partial sequences. Similar partial sequence detection device.

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