KR102433568B1 - Fast Constrained Dynamic Time Warping Method for Similarity Measure of Time Series Data, Computer readable recording media, Computing device - Google Patents

Abstract

In the high-speed constrained dynamic time warping method according to an embodiment of the present invention, the resolution of the preset window area is converted into multi-resolution each having a data length of 1/2 and a data length of 1/4 through a first coarsening process. forming; Selective warping of a window area having a resolution including the 1/2 data length after alignment is performed by limiting a window area of lower resolution among multi-resolutions having the 1/2 data length to the limited window area of the SC-DTW tracing the route; The first segment and the second segment, respectively, are selected from the window area for performing the alignment operation within the limited window area of the SC-DTW according to the estimated selective warping path and the setting parameter r in the window area having a resolution including the 1/2 data length. forming with; aligning the first segment and the second segment within the limited window area; estimating a selective warping path within the aligned first and second segments; and calculating a selective warping path and a DTW distance of a resolution of the preset window area by using a selective warping path of resolution having an estimated data length of 1/2.

Description

A high-speed constrained dynamic time warping method for measuring the similarity of time series data, a recording medium that can read a program executing the same, and an arithmetic device including the same media, computing device}

The present invention relates to a high-speed constrained dynamic time warping method for measuring the similarity of time series data, a recording medium capable of reading a program executing the same, and an arithmetic device including the same.

Time series data mining includes many fields such as clustering, classification, fault detection, pattern recognition, and prediction.

Among them, measuring the similarity between two time series data is the most frequent and important task. In order to accurately measure the similarity between time series data, it is necessary to align the two data on the time axis. Dynamic time warping (hereinafter, DTW) warps two data on the time axis, finds the most optimal alignment among all possible alignments, and measures the similarity.

Accordingly, DTW has many fields such as gesture, image, speech recognition, intrusion detection, financial analysis, biometrics and medical diagnosis, etc. is being used in However, DTW considering the number of all sortable cases has a problem that requires a high amount of computation according to the length of two input data for which similarity is to be measured.

In order to overcome the limitations of DTW in terms of high computational complexity, various algorithms have been proposed. An indexing technique that reduces the number of times the DTW algorithm is used, and a constraint and data abstraction technique that reduces the DTW computational complexity. etc.

Here, the indexing technique uses a lower bounding function having a lower complexity than DTW to remove in advance the comparison data sequences that are not likely to be similar between the data sequences to be compared and the input data sequences. Thereafter, it is a technique of improving the high operation time by performing DTW operation by limiting only the remaining comparison data sequences.

The constraint method, which introduces a constraint to perform sorting operations only within a limited specific range, is the Sakoe-Chiba DTW (SC-DTW), which performs equivalent sorting on all data points, and the latest data point on the time axis. Incremental DTW (I-DTW), which does more sorting on (points).

This constraint technique can reduce the amount of computation by reducing the number of alignments to be considered, and pathological alignment problems ( By suppressing the pathological alignment problem, higher accuracy can be expected compared to the standard DTW that considers all alignments.

However, these constraint techniques always perform alignment operations in a fixed range without considering the optimal alignment position that may be formed differently depending on the relative relationship between the two input data for which the similarity is to be measured. If the length of the data is long because the amount of computation is still quadratic, depending on the length, a high amount of computation is required.

The data abstraction technique is a technique to improve the high amount of computation by using a data representation that reduces the dimensions to consider of two input data, such as piecewise aggregate DTW (P-DTW), blocked DTW (B-DTW), and fast DTW. There is this.

P-DTW is a technique to create a new data expression by dividing each point of the two data for which similarity is to be measured at a certain ratio and then taking the average of each group to create a new data expression. However, there is a limit in that points with important characteristics can be missed in the process of taking the average.

B-DTW using a technique to efficiently reduce points with consecutive values of data can improve the amount of computation by reducing the dimension of the data to be computed, but it has an inaccurate similarity measurement value as much as the dimension of the reduced data.

The Fast DTW technique hierarchically reduces the resolution of two data to measure the similarity to form multi-resolution, tracks the optimal alignment position from the lowest layer, and then calculates the approximate optimal alignment of the layer immediately above. It is a technique that uses the method used to estimate the location. The fast DTW technique, which incrementally estimates the optimal alignment position of the original resolution in a way that only considers the alignment around the estimated optimal alignment position, efficiently calculates the optimal alignment position that is formed differently depending on the relative relationship between the two input data. calculation time can be improved by estimating .

The fast DTW algorithm representing a linear amount of computation can track the optimal alignment position more accurately as the value of the design parameter is larger, but this leads to an increase in the amount of computation. Accordingly, fast DTW can expect a decrease in the amount of computation only when the increase in the amount of computation by the length of the two data for which the similarity is to be measured is greater than the increase in the amount of computation by the design parameter of the fast DTW, and pathological alignment problems ( The fast DTW algorithm with pathological alignment problem shows a relatively low classification accuracy when compared to the constraint technique.

Accordingly, the present invention proposes a fast constrained DTW method in which the optimal alignment position estimation method of the fast DTW algorithm is applied within the constraints of the constraint method.

The fast constrained DTW method of the present invention can support classification accuracy similar to that of the constrained method, and is always combined with fast DTW and constrained methods regardless of the design parameters of the fast DTW method and the length of two input data. It is characterized in that it is relatively low or similar and requires a linear operation time.

W.-S. Han, J. Lee, Y.-S. Moon, S.-W. Hwang, and H. Yu, "A New Approach for Processing Ranked Subsequence Matching Based on Ranked Union," In Proc. of Int'l Conf. on Management of Data, ACM SIGMOD, Athens, Greece, pp.457-468, Jun. 2011.

The present invention shows a reduction in computational complexity in the length section of all data by applying a technique that considers the characteristics between two data of the fast DTW technique within the alignments of the limited area of the constrained DTW technique, and the constrained DTW technique The purpose of the present invention is to provide a fast-constrained dynamic time-warping method, which is an efficient method that exhibits classification accuracy similar to .

Another object of the present invention is to provide a recording medium in which a program for executing each step of a constrained dynamic time warping method at high speed for measuring the similarity of time series data is recorded.

Another object of the present invention is to provide an arithmetic device having a recording medium recording a program for executing each step of the constrained dynamic time warping method at high speed for measuring the similarity of time series data.

A high-speed constrained dynamic time warping method for measuring the similarity of time series data according to an embodiment of the present invention for solving the above problems is time series data implemented as a computer readable code on a computer readable recording medium As a high-speed, constrained dynamic time warping method for measuring the similarity of forming each with In the computer, the optimal warping path that has the 1/4 data length and is tracked by performing an alignment operation by limiting the window region of the lowest resolution among the multi-resolution to the limited window region of the SC-DTW is a second process (projection) Based on the optimal warping path and setting parameter r found in the window region of resolution having the 1/4 data length through forming cells of the window region into first and second segments, respectively; and the first segment and the second segment region having a resolution of 1/2 data length formed by utilizing an optimal warping path of resolution having a 1/4 data length estimated through a third refinement in the computer. and calculating the optimal warping path and DTW distance within the calculated first and second segments after calculating the cells of .

A recording medium according to an embodiment of the present invention for solving the above problems may be a storage medium recording a program for executing each step of the constrained dynamic time warping method at high speed for measuring the similarity of time series data.

An arithmetic device according to an embodiment of the present invention for solving the above problems is characterized in that it comprises a recording medium in which a program for executing each step of the constrained dynamic time warping method at high speed for measuring the similarity of time series data is recorded. .

The present invention applies a method of estimating the position of an optimal warping path using the multi-resolution of fast DTW within a window region of a specific type of a constraint technique to apply the existing constraint (constraints) and fast DTW methods are lower or similar, have a linear amount of computation, and efficiently suppress the pathological alignment problem, so that the high-speed constraint exhibits classification accuracy similar to that of the constraint method. It is a fast constrained DTW method.

According to the fast constrained DTW method described above, an experiment using 19 UCR time series datasets and sine waves of one cycle having various data lengths by different sampling As a result, fast I-DTW proposed by applying the window of the most recent I-DTW algorithm among the constraint methods is the existing I-DTW and fast DTW in 19 datasets. Compared to , it has a reduction rate of about 52.2% and 22.3% of the computational amount, and a classification accuracy similar to that of I-DTW, and has a similar or lower linear computation time in all sine wave length sections It can be seen that the results of

1 is a flowchart illustrating a constrained dynamic time warping method for measuring similarity of time series data according to an embodiment of the present invention.
2 is a diagram illustrating a process of aligning two data sequences (arrows indicate aligned points), (a) is Euclidean distance, (b) DTW distance.
3 is a diagram illustrating a cost matrix.
4 is a diagram illustrating a cumulative cost matrix having a selective warping path.
5 is a diagram comparing the complexity of (a) Euclidean distance and (b) DTW distance.
6 is a diagram showing the cumulative cost matrix of constrained DTW ((a) SC-DTW, (b) I-DTW).
7 is a road showing the accumulated cost matrix of four different resolutions for the fast-DTW algorithm, (a) a lower resolution with 1/8 data length compared to the original, and (b) 1/1/2 data length compared to the original. A resolution of 4, (c) a resolution of 1/2 the data length compared to the original, (d) the original resolution.
8 is a diagram showing the accumulated cost matrix with two different resolutions for the worst case fast DTW algorithm.
9 is a road showing the cumulative cost matrix of three different resolutions for fast SC DTW, (a) low resolution with 1/4 data length compared to the original, and (b) 1/2 data length compared to the original. resolution, (c) the original resolution.
10 is a pseudo code of the fast SC-DTW algorithm.
11 is a diagram comparing classification accuracy according to radius between fast SC-DTW and fast DTW.
12 is a diagram comparing classification accuracy according to a radius between fast SC-DTW and SC-DTW.
13 is a diagram comparing classification accuracy according to radius between fast I-DTW and fast-DTW.
14 is a diagram comparing classification accuracy according to a radius between fast I-DTW and I-DTW.
15 is a diagram comparing calculated complexity for fast DTW, SC-DTW, fast SC-DTW, I-DTW, and fast I-DTW.
16 is a diagram illustrating elapsed times of standard DTW, fast DTW, SC-DTW, fast SC-DTW, fast I-DTW, and fast I-DTW in the first time series (small).
17 is a diagram illustrating elapsed times of standard DTW, fast DTW, SC-DTW, fast SC-DTW, fast I-DTW, and fast I-DTW in the second time series (large).

Hereinafter, embodiments of the present specification will be described with reference to the accompanying drawings. However, it is to be understood that the technology described herein is not limited to specific embodiments, and includes various modifications, equivalents, and/or alternatives of the embodiments of the present specification. . In connection with the description of the drawings, like reference numerals may be used for like components. In the present specification, expressions such as “have,” “may have,” “include,” or “may include” indicate the presence of a corresponding characteristic (eg, a numerical value, function, operation, or component such as a part). and does not exclude the presence of additional features.

In this specification, expressions such as “A or B,” “at least one of A and/and B,” or “one or more of A or/and B” may include all possible combinations of the items listed together. . For example, "A or B," "at least one of A and B," or "at least one of A or B" means (1) includes at least one A, (2) includes at least one B; Or (3) it may refer to all cases including both at least one A and at least one B.

As used herein, expressions such as "first," "second," "first," or "second," can modify various elements, regardless of order and/or importance, and refer to one element. It is used only to distinguish it from other components, and does not limit the components. For example, the first user equipment and the second user equipment may represent different user equipment regardless of order or importance. For example, without departing from the scope of the rights described in this specification, a first component may be referred to as a second component, and similarly, the second component may also be renamed as a first component.

A component (eg, a first component) is "coupled with/to (operatively or communicatively)" to another component (eg, a second component) When referring to "connected to", it will be understood that the certain element may be directly connected to the other element or may be connected through another element (eg, a third element). On the other hand, when it is said that a component (eg, a first component) is "directly connected" or "directly connected" to another component (eg, a second component), the component and the It may be understood that other components (eg, a third component) do not exist between other components.

As used herein, the expression "configured to (or configured to)" depends on the context, for example, "suitable for," "having the capacity to ," "designed to," "adapted to," "made to," or "capable of." The term “configured (or configured to)” may not necessarily mean only “specifically designed to” in hardware. Instead, in some circumstances, the expression “a device configured to” may mean that the device is “capable of” with other devices or parts.

For example, the phrase “a processor configured (or configured to perform) A, B, and C” refers to a dedicated processor (eg, an embedded processor) for performing the operations, or by executing one or more software programs stored in a memory device. , may mean a generic-purpose processor (eg, a CPU or an application processor) capable of performing corresponding operations.

The terms used herein are used only to describe specific embodiments, and may not be intended to limit the scope of other embodiments. The singular expression may include the plural expression unless the context clearly dictates otherwise. Terms used herein, including technical or scientific terms, may have the same meanings as commonly understood by one of ordinary skill in the art described herein. Among the terms used in this specification, terms defined in a general dictionary may be interpreted with the same or similar meaning as the meaning in the context of the related art, and unless explicitly defined in the present specification, have ideal or excessively formal meanings. is not interpreted as In some cases, even the terms defined in this specification cannot be construed to exclude the embodiments of the present specification.

Hereinafter, a method and apparatus for fast and constrained dynamic time warping for measuring the similarity of time series data according to an embodiment of the present invention will be described in more detail based on the accompanying drawings.

First, before describing the present invention, dynamic time warping (hereinafter, DTW) will be briefly described.

The DTW calculates the DTW distance by matching two data on the time axis through a non-linear alignment process as shown in FIG. 2B.

This means that in measuring the similarity between data having time-dependent characteristics, the DTW distance measurement method has better performance than the Euclidean distance measurement method as shown in FIG. 2(a). to be able to represent

In order to match the sequences of two data as perfectly as possible, it is necessary to perform the optimal alignment among all possible alignments.

In order to find such an optimal alignment, it is necessary to first calculate the distance between two different points of the two data points. And by accumulating these differences while satisfying the conditions for finding the optimal alignment, the optimum alignment operation can be performed. The distances between two different points between these two data points and their accumulation are expressed by a cost matrix and an accumulated cost matrix, respectively.

는 다음과 같다.Cost matrix for DTW distance of two data x and y

is as follows

Here, d ₁ and d ₂ represent data lengths, and the cost matrix of FIG. 3 is used to calculate an accumulated cost matrix.

The optimal warping path p , which is a set of indices that directly affected the optimal alignment in the process of calculating the accumulated cost matrix, is defined as follows.

Here, L means the length of the optional warping path.

An optimal warping path p of the accumulated cost matrix satisfies a boundary condition, a monotonicity condition, and a step size condition, and is calculated as shown in FIG. 4 do.

1) Boundary condition

The starting and ending points of the optimal warping path are defined as follows:

2) Monotonicity condition

The index value of the optimal warping path must be greater than or equal to the previous index value.

3) Step size condition

The difference between neighboring values of the optimal warping path has a step size and can be expressed as follows.

연산 공식은 다음과 같이 표현할 수 있다.Accumulated cost matrix

The arithmetic formula can be expressed as follows.

After generating the accumulated cost matrix, the optimal warping path is a backtracking method that follows a small value from A(d ₁ ,d ₂ ) to A(1,1) as shown in FIG. 4 . can be calculated through

The set of index values of the optimal warping path coincides with the aligned arrows of FIG. 2, and through this process, the DTW can measure the similarity between the two time series data. The DTW distance value indicating the similarity measurement result is as follows.

Hereinafter, a constrained DTW algorithm will be described.

The red part of FIG. 5 represents the amount of calculation of the Euclidean distance (ED) and the standard DTW (standard DTW).

ED requires O(n) operations when the length of two data for measuring similarity is n, whereas DTW requires o(n ² ) operations.

That is, if the length of the two data sequences increases, Euclidean linearly increases the amount of computation, and DTW increases quadratic.

However, in calculating the DTW, it is not necessary to trace the optimal warping path that takes into account the number of cases for all alignments.

The accumulated cost matrix for the most representative SC-DTW among the constraint techniques and the recently announced I-DTW is shown in FIG. 6 .

Here, the red part in FIG. 6 indicates the matching indexes on the time axis between the two data for which the similarity is to be measured, and the blue part formed based on this indicates only the alignments in a specific area, not all alignments. represents a window region for the purpose, which lowers the computational amount and effectively suppresses pathological alignment problems that may lower the classification accuracy due to excessive alignments far away on the time axis.

에의해 결정된다.SC-DTW always forms a window of the same length in the horizontal axis and the vertical axis based on the part where the indices of the two data coincide. In this case, the length of the window is a window percentage value r',

is determined by

The length l of the window can be calculated by the following equation (10).

d ₁ and d ₂ mean the lengths of each of the two data sequences.

In (a) of FIG. 6 , when r' = 0.1, which is the most commonly used window percentage value, the amount of computation can be reduced by about 80% compared to a standard DTW (standard DTW).

The I-DTW uses the data characteristic that the later part of the data is more important historically than the first part, and as shown in FIG. This is a method of gradually increasing the length of the window as the (index) value increases.

는 하기의 식(11)을 통해 연산될 수 있다.Window length of I DTW

can be calculated through the following equation (11).

n _i and m _i mean the lengths of each of the two data for the corresponding index _i .

SC-DTW and I-DTW require N(2N·r′+1) and N(N·r′+1) operations, respectively, when the length of the two data is N, so the existing standard (standard) It can be expected to reduce the amount of computation compared to DTW.

However, the constraint method has a fixed window that does not consider the relationship between the two data for which the similarity is to be measured, and still has a quadratic amount of computation. need.

Hereinafter, the Fast DTW algorithm will be briefly described. Fast DTW, which is the most representative algorithm among data abstraction techniques that improves the high computational amount by using the data representation with reduced dimensions of two input data, utilizes multi-resolution as shown in Figure 7. This is a technique for reducing the amount of computation by considering only the alignments of the peripheral regions of the approximate optimal warping path estimated from the resolution of . This fast DTW can implement the algorithm in the following order.

1) First treatment process (Coarsening)

A hierarchical multi-resolution is made by reducing data points by repeating the method of tying each adjacent point of two time series data two and taking the average.

2) Second process (Projection)

The position of the optimal warping path is found from the lowest resolution, and this is used to estimate the approximate position of the optimal warping path of the resolution immediately above.

3) Third Refinement

Considering the approximate location of the optimal warping path estimated from the resolution immediately below and the perimeter of the optimal warping path estimated by the radius set from the design parameter. Tracks the location of the optimal warping path of the current resolution.

7 shows an implementation process of the fast DTW algorithm.

A total of four multi-resolution ( multi-resolution).

When the position of the optimal warping path considering all alignments in FIG. 7(a), which is the resolution having the lowest 1/8 data length, is traced, it is the same as the red line in FIG. 7(a).

The position of the selective warping path of the resolution having a data length of 1/8 found in this way is used to estimate the approximate location of the selective warping path in FIG. .

At a resolution with a data length of 1/4, the region additionally reflecting the location of the estimated selective warping path and its surroundings is formed by dark gray boxes and light gray boxes, respectively. Afterwards, the location of the optional warping path is traced again.

At this time, the additional reflection of the surrounding area of the estimated selective warping path is determined by the setting parameter 'r(radius)', and r=1 is used in FIG. 7 .

This is repeated until the selective warping path and DTW distance of FIG. 7(d), which are the original resolution, are calculated through (c) of FIG.

The calculation result of DTW becomes the DTW distance and optional warping path.

Comparing the computational amount of Fast DTW with standard DTW under the assumption that only the DTW distance excluding the optional warping path is computed, fast DTW calculates the accumulated cost matrix from the lowest resolution to the original resolution 16, 44, 97 and A total of 369 cells of 212 were computed, and a total of 2x (16+8+4 ) = 56 was performed.

Finally, in order to trace the selective warping path indicated by the red line, from the lowest resolution to the original resolution, 5, 11, 24, and 49 operations were performed as much as the length of the selective warping path, respectively, assuming that only the DTW distance is calculated. Except for the last number of operations, 5+11+24=40 calculations were performed, and a total of 369+56+40=465 calculations were performed. And, assuming that the standard DTW calculates only the DTW distance, the operation of 32x32=1,024 is performed. That is, a reduction in the amount of computation by about 45.41% can be expected.

Fast DTW requires computation in a total of three parts: cumulative cost matrix computation, multi-resolution formation, and selective warping path tracking.

For simplicity of calculation, hereinafter, it will be assumed that the lengths of both time series data are N, and all analyzes will be evaluated assuming the worst-case.

As shown in the red line in FIG. 8 (a), when a selective warping path is formed in a portion where the indices of two data coincide, an area to be aligned as shown in FIG. 8 (b) is formed, in this case It becomes the worst case in which cells in the region with the largest number of are computed.

The dark gray box in Fig. 8(b), estimated by the selective warping path estimated in Fig. 8(a), includes three cells in one line, and multiplies the length N of the data to have a total of 3N cells. form them In addition, the light gray box in Fig. 8 (b) indicating the peripheral region of the estimated selective warping path is when the setting parameter r (radius) is '1', and a total of 4Nr including 4r cells in one line form the cell of Accordingly, the total number of cells at the original resolution becomes the following equation (12).

The length of data for all multi-resolutions is the following Equation (13).

Equation (14) is obtained by summing the number of cells to be calculated in the cumulative cost matrix for all multi-resolutions.

If Equation (14) is rearranged according to the infinite geometrical series, Equation (15) is the same.

In order to form data having a length of N/2, which is a resolution just below the original resolution, each of the two input data requires an amount of operation of N/2. Accordingly, Equation (16) is obtained when calculating the amount of calculations required to form all multi-resolutions.

Finally, the amount of computation required to track the optimal warping path requires as much as 2N of the sum of the lengths of the two data in the worst case.

Equation (17) is given when calculating the amount of computation required to track the optimal warping path of all multi-resolutions.

Assuming the worst case, the sum of equations (15), (16) and (17) represents the time complexity of fast DTW.

As a result of calculating the theoretical time complexity of fast DTW assuming the worst case, it can be confirmed that the amount of computation is linear according to the length of the data N, which is the ^quadratic ( When compared with the standard DTW and the limited method with quadratic), if the length of the data is sufficiently large compared to the 8r+14 part, it means that a significant reduction in the amount of computation can be expected.

However, when the length of the data is small compared to the 8r+14 part, it is difficult to expect a reduction in the amount of computation, and it has a pathological alignment problem. Compared with the constraint method, the classification accuracy is relatively low. indicates

A constraint technique that reduces the amount of computation by performing alignment operations only within a limited specific window region, and increases classification accuracy by suppressing a pathological alignment problem, does not consider the relationship between two input data, It has a limit with a quadratic amount of computation.

On the other hand, the fast DTW algorithm uses multi-resolution to estimate the optimal warping path that is formed differently depending on the relationship between the two data for which the similarity is to be measured, indicating a linear amount of computation. , when the increase in the amount of computation by the length of the two input data is greater than the increase in the amount of computation by the setting parameter r, a reduction in the amount of computation can be expected. The classification accuracy is low.

Hereinafter, the optimal warping path estimation method of the fast DTW algorithm is applied within the limited window area of the constraint method to further reduce the amount of computation and constrain it to high speed representing a linear computation time. To propose a dynamic time warping (fast constrained DTW, hereinafter fcDTW) method.

Referring to FIG. 1 , the high-speed constraint dynamic time warping method ( S700 ) for measuring the similarity of time series data according to an embodiment of the present invention uses a first coarsening process to reduce the resolution of a preset window area to 1/ Forming each of the multi resolutions having 2 data lengths and 1/4 data lengths (S710), and having the 1/4 data length and limiting the window area of the lowest resolution among the multi resolutions to the limited window area of the SC-DTW and the optimal warping path tracked by performing an alignment operation in the SC-DTW based on the optimal warping path found in the window region of the resolution having the 1/4 data length through the second projection and the setting parameter r. Estimating through the step of forming (S720) the first segment and the second segment, respectively, and the third processing process (refinement) of cells in the window area for which the alignment operation of the resolution having a data length of 1/2 is performed within the limited window area of After calculating the cells of the first segment and the second segment region of the resolution having the 1/2 data length formed by using the optimal warping path of the resolution having the 1/4 data length, the calculated first segment and the second segment are calculated. and calculating an optimal warping path and a DTW distance within 2 segments ( S730 ).

Here, the first processing (coarsening) may be a process of reducing the data points by repeating a method of tying each adjacent point of the two time series data two by two and taking the average to make the data points into a hierarchical multi-resolution.

The second process (projection) may be a process of finding the location of the selective warping path from the lowest resolution and estimating the approximate location of the next lower resolution selective warping path.

The third process (Refinement) estimates the location of the selective warping path of the current resolution considering the approximate location of the selective warping path estimated from the resolution immediately below and the periphery of the selective warping path estimated by the radius set from the design parameters. It may be a process

Meanwhile, the setting parameter may be an additional reflection radius value of a peripheral area of the estimated selective warping path.

In addition, the first segment and the second segment are displayed as cells of the window area with different resolutions. That is, in S700 according to an embodiment of the present invention, the first processing (coarsening), the second processing (projection) and the third processing (projection) of the fast DTW within the window region of the applied constrained DTW ( It is implemented through refinement). First, the implementation process of fast SC-DTW to which the most representative SC-DTW algorithm among constraint techniques is applied is as follows.

In FIG. 9, the window percentage value r' of the SC-DTW was 0.2, and the setting parameter r indicating the additional reflection range of the area around the estimated optimal warping path is 1. was used.

In the original resolution of FIG. 9(c), through a first coarsening, a multi-resolution of resolution having data lengths of 1/2(b) and 1/4(a) resolution) is formed.

In the lower resolution of FIG. 9 (a), after alignment is performed by limiting the limited window area of the SC-DTW, an optimal warping path is traced, and it is directly above It is used to estimate an approximate optimal warping path of resolution having a data length of 1/2 that is resolution.

In the resolution having a data length of 1/2 of FIG. 9 ( b ), a limited window area of the SC-DTW to match the estimated optimal warping path and the setting parameter r The regions where the alignment operation is performed are formed like dark gray boxes and light gray boxes, respectively, and after performing the alignment operations in these regions, the optimal warping path is traced.

Finally, the selective warping path and DTW distance of the original resolution are calculated using the selective warping path of the resolution having the estimated 1/2 data length in FIG. 9(c).

Comparing the amount of computation between the proposed fast SC-DTW and the existing SC-DTW under the assumption that only the DTW distance is calculated, the fast SC-DTW has the lowest resolution (a) to the original resolution of FIG. 9 A total of 430 cells of 44, 122, and 264 were calculated for the cumulative cost matrix up to (c) of Fig. 9 (b), ( a) A total of 2x(20+10)=60 operations were performed to form multi-resolutions each having a data length of 20 and 10 points.

Finally, the lengths of the selective warping paths indicated by the red lines in Figs. 9 (a) and (b) are 13 and 26, respectively, and calculations are performed for a total of 39 selective warping paths, so that a total of 430+60+39= It becomes 529.

The total number of cells in the SC-DTW window area of FIG. 8(c) is 608.

That is, compared to SC-DTW, fast SC-DTW can expect a reduction in the amount of computation by about (608-529)/608x100=12.99% in the situation of FIG. 9 .

Compared to fast DTW that tracks the optimal warping path in all sortable regions, the proposed fast SC-DTW that tracks the selective warping path within the window region of SC-DTW as shown in FIG. 9 is the selective warping path. If is located near the coincident part on the time axis of the two input data, it has a similar amount of computation to that of fast DTW. Since a path is formed, it has a lower computational amount due to a shorter warping path than the fast DTW.

In addition, the existing fast DTW can cause pathological alignment problems when a selective warping path is formed at a distant location on the time axis, thereby reducing the overall classification accuracy.

In contrast, the proposed fast SC-DTW can increase the overall classification accuracy by forming a selective warping path within the window region of the SC-DTW that effectively suppresses the pathological alignment problem.

FIG. 10 shows the pseudo code of the fast constrained dynamic time warping method (Fast SC-DTW) for measuring the similarity of time series data proposed in the present invention.

Lines 7-36 correspond to the first coarsening, and lines 8-30 are the total amount of computation required for the lower resolution among the multi-resolutions generated so far, and when forming the additional resolution, it is necessary from the additional resolution to the current low resolution. It corresponds to the process of determining whether to additionally generate multi-resolution by comparing the total amount of computation.

Lines 32-34 create additional multi-resolution by tying each point adjacent to the current lower resolution two by two and averaging them.

In lines 38-47, the second projection and the third refinement are repeated based on the determined multi-resolution, and in lines 42 and 45, the low resolution and estimated selective warping that consider alignment in all regions, respectively. Calculate the optional warping path and DTW distance for resolutions other than the lower resolution, which takes into account alignment to the path and its surrounding area.

The pseudo code of the fast constrained DTW of the present application to which another constrained technique is applied can be implemented by correcting lines 9, 12, 19, 42, and 45 in the pseudo code of the fast SC-DTW of FIG. 10 to suit the applied constrained DTW.

Hereinafter, the classification accuracy and time of the fast constrained DTW algorithm proposed herein using various time series datasets provided by UCR and sine wave data of one cycle with different sampling The time complexity is compared with the existing constraint method and fast DTW.

See Table 1 below, and a total of 19 time series data sets presented in Table 1 were used for the experiment.

Each dataset consists of 2 to 50 class numbers, 24 to 1,000 train sizes, 28 to 6,174 test sizes, and 60 to 637 lengths for medical, robotic, handwriting recognition. (handwriting recognition) and the like. The order of the 19 data sets was arranged according to the length for the analysis of the experimental results.

Table 1. Table showing information on UCR time series datasets.

Classification of time series data sets was carried out using the nearest neighbor method, which is mainly used in similarity measurement including the DTW algorithm.

Each test dataset and training dataset of the 19 time series datasets are used as query sequences and sub-sequences.

When a query sequence is input, the similarity of all subsequences is measured using the algorithms used in the experiment, and the class information of the subsequence having the smallest similarity measurement value among them is output as the classification result of each algorithm.

Classification of time series data sets was carried out using the nearest neighbor method, which is mainly used in similarity measurement including the DTW algorithm.

Each test dataset and training dataset of the 19 time series datasets are used as query sequences and sub-sequences.

When a query sequence is input, the similarity of all subsequences is measured using the algorithms used in the experiment, and the class information of the subsequence having the smallest similarity measurement value among them is output as the classification result of each algorithm.

Additionally, the Euclidean distance (ED), which is the most traditional method for measuring similarity, was also implemented to compare classification performance.

Table 2 shows the classification accuracies for 19 data sets of the 7 algorithms implemented for the experiment, and Avg means the average of the classification accuracies for all data sets.

All implemented DTW algorithms that measure similarity through the sorting process between two input data show higher classification accuracy compared to the traditional ED method, and I-DTW and SC-, two constrained DTW techniques that effectively suppress the pathological alignment algorithm. It can be seen from Table 2 (a) that DTW shows a higher overall classification accuracy than standard DTW.

Table 2. Classification accuracy according to radius

The average classification accuracy of fast DTW, fast SC-DTW, and fast I-DTW in Table 2 (b), (c) and (d) increased with the increase in the set parameter radius, the standard DTW, SC-DTW and It can be confirmed that it is similar to the average classification accuracy of I-DTW.

11 and 12 show the results of comparing the classification accuracy of the proposed fast SC-DTW, the conventional fast DTW, and the SC-DTW for the analysis of the experimental results, respectively.

Similarly, compared with fast DTW and I-DTW, the proposed fast I-DTW is shown in FIGS. 13 and 14 .

The red dots in FIG. 11 indicate the classification accuracy of the two algorithms arranged on the horizontal and vertical axes for 19 data sets, and two regions are formed based on the blue line indicating the part where the horizontal and vertical axes coincide, If there are many points in a specific area, it means that the algorithm in that area showed a higher overall classification accuracy for 19 data sets compared to the algorithm in other areas.

11, which compares the classification accuracy of fast SC-DTW and fast DTW, there are more red dots located in the proposed fast SC-DTW region than the fast DTW region at all radii, which is proposed for 19 data sets. This means that the fast SC-DTW showed a higher overall classification accuracy.

FIG. 12 compares the classification accuracy of fast SC-DTW and SC-DTW. In cases where the radius is 0, 1, and 2, there is a difference in overall classification accuracy between the two algorithms, but when the radius is 3 or more, red dots are Most of them are located on the blue line, which is the midpoint between the two regions, which means that the classification accuracy of the two algorithms is overall similar for the 19 data sets.

From the experimental results, it can be confirmed that fast SC-DTW operating within the window region of SC-DTW effectively suppresses pathological alignment problems like SC-DTW.

In addition, referring to FIGS. 13 and 14, fast I-DTW also shows higher accuracy at all radii compared to fast DTW, and when the radius is 3 or more, it shows an overall classification accuracy similar to that of I-DTW. can confirm.

Table 3. Number of cells retrieved by radius

Table 4. Ratio of Number of Search Cells to Standard DTW by Radius

(a) of Table 3 is ED, DTW, SC-DTW and I-DTW, (c), (d), and (e) are Table 1 for fast DTW, fast SC-DTW, and fast I-DTW algorithms, respectively. It represents the total number of cells calculated to process all test data of each of the 19 datasets of .

을 나타낸다.The total number of cells computed includes optional warping path tracking and operations to shrink resolution. For the analysis of the experimental results, the total number of cells calculated in processing all the test datasets of each algorithm as shown in Equation (19) below is compared with the standard DTW and the results expressed as a ratio (R _NSC ) are shown in Table 4, Avg is the average for 19 data sets

second indicates.

In Equation (19) below, NSC _{standard DTW} means the total number of cells calculated in the standard DTW, and NSC _otherDTW means the total number of cells calculated in other implemented DTW algorithms.

The fast SC-DTW and fast I-DTW proposed in the classification accuracy confirmed earlier showed the classification accuracy that almost converges with the SC-DTW and I-DTW when the set parameter radius is 3 or more.

을 갖는 fast DTW 및 SC-DTW를 하기의 수식(20)을 활용하여 비교하면, 약 30.1% 및 40.3%의 연산량 감소율을 나타냄을 확인할 수 있다.In Table 4, when the radius is 3, the proposed fast SC-DTW with an average R _NSC of 11.4%fmf was 16.3% and 19.1%, respectively.

Comparing the fast DTW and SC-DTW with , using Equation (20) below, it can be seen that the calculation amount reduction rate is about 30.1% and 40.3%.

을 갖는 fast I-DTW는 약 52.2% 및 22.9%의 연산량 감소율을 나타냄을 확인할 수 있다.In addition, 7.8% of DTW and I-DTW showed R _NSC of 16.3% and 10.1%.

It can be seen that the fast I-DTW with

을 radius에 따라 비교하며 또한, 제안된 fast I-DTW와 기존의 fast DTW 및 I-DTW에 대한

역시 함께 비교한다. 14 shows the existing fast DTW and SC-DTW for 19 data sets and the proposed fast SC-DTW.

are compared according to the radius, and also for the proposed fast I-DTW and the existing fast DTW and I-DTW

Also compare them together.

을 도시한다. 실험에서 사용된 데이터셋들의 길이가 클수록, 반경(radius)이 작을수록 낮은

을 기대할 수 있는 fast DTW는 도 14에서 length가 짧은 데이터 셋들 보다 length가 긴 데이터 셋들이 더 낮은

을 나타내며, 범위(radius)이 작을수록 모든 데이터 셋들의

이 전반적으로 낮게 형성됨을 확인할 수 있다.Regardless of the setting parameter radius, SC-DTW is always constant for all radii.

shows The larger the length of the datasets used in the experiment and the smaller the radius, the lower the

The fast DTW that can be expected is lower in the long-length data sets than the short-length data sets in FIG.

, and the smaller the radius, the more

It can be seen that the overall formation is low.

이 반경(radius)에 더 민감하게 반응함을 확인할 수 있고, 19개의 데이터 셋들 중 가장 길이가 짧은 도 15 (k)의 첫 번째 데이터셋은 100%의

을 나타내고 있으며, 이는 연산량이 감소하지 않음을 의미한다. In addition, referring to FIG. 14 , the data sets of which the length of the data are not long are

It can be seen that it responds more sensitively to this radius, and the first dataset in FIG. 15 (k), which has the shortest length among the 19 datasets, is 100%

, which means that the amount of computation does not decrease.

That is, when the radius is 10, the amount of computation of the first data having a length of 60, the Synthetic Control, is the same as that of the existing standard DTW, which has a radius of 10, When the length of data is less than or equal to 60 and when the length of data is 60 and the radius is greater than or equal to 10, it means that the fast DTW algorithm cannot expect a reduction in the amount of computation.

On the other hand, in FIG. 15 , fast SC-DTW always shows equal to or lower than fast DTW and SC-DTW for all radii and data sets.

이 낮은 경우, fast DTW와 유사하거나 낮은

을 나타내며, fast DTW의

이 SC-DTW 보다 큰 경우, SC-DTW와 유사하거나 낮은

을 나타냄을 도 15를 통해 확인할 수 있다. 유사하게, fast I-DTW의

역시 fast DTW 및 I-DTW 와 비교해 항상 유사하거나 낮음을 확인할 수 있다.The proposed fast SC-DTW, which performs fast DTW algorithm within the window of SC-DTW, is faster than SC-DTW.

If this is low, it is similar to or lower than fast DTW.

represents the fast DTW

If greater than this SC-DTW, it is similar to or lower than the SC-DTW

It can be seen through FIG. 15 that . Similarly, fast I-DTW's

Again, compared to fast DTW and I-DTW, it can be confirmed that it is always similar or lower.

Hereinafter, experimental results for fast constraints DTW, which is an efficient algorithm for reducing the computational complexity of dynamic time warping (DTW) for measuring the similarity of time series data proposed in the present invention, are presented below. present.

In the DTW technique, in order to respond to a time-dependent characteristic, data is aligned on the time axis, and similarity is measured by finding the most optimal alignment among all possible alignments.

Accordingly, it exhibits superior classification performance compared to other algorithms, but has limitations in application due to high computational complexity. The DTW algorithms based on the constraint method proposed to solve the problem of high computational complexity reduce the amount of computation by introducing a constraint that performs sorting only in a limited range, but do not consider the relationship between the input data and the length of the data ( length) is long, the amount of computation is still high.

On the other hand, fast DTW based on the data abstraction technique shows a lower classification accuracy than the constraint technique, but utilizes a technique for estimating the optimal alignment position formed differently depending on the relationship between the two data, and the data The longer the length of is, the more the amount of computation can be reduced.

Therefore, in the present invention, the relationship between the two data is considered by estimating the optimal alignment position of the fast DTW algorithm within the constraints of the existing constraint-based algorithms, and fast constrained DTW, which shows a low amount of computation in the length section of all data, is used. suggested.

As a result of experiments using 19 time series data provided by UCR, the proposed fast constrained dynamic time warping algorithm (fast constrained DTW) of the present application has about 52.2% and 22.3% of the computational amount compared to the existing fast DTW and constraint methods. It showed a reduction rate, and the classification accuracy was similar to that of the constraint method.

The high-speed constrained dynamic time warping method for measuring the similarity of time series data proposed in the present invention can be implemented as computer-readable codes on a computer-readable recording medium. The computer-readable recording medium includes all types of recording devices in which data that can be read by a computer system is stored. Examples of the computer-readable recording medium include ROM, RAM, CD-ROM, magnetic tape, and optical data storage device. In addition, the computer-readable recording medium is distributed in a computer system connected through a network, so that the computer-readable code can be stored and executed in a distributed manner. And functional programs, codes and code segments for implementing the present invention can be easily inferred by programmers in the art to which the present invention pertains.

In the above, the present invention has been described in detail with reference to the embodiments, but those of ordinary skill in the art to which the present invention pertains may make various substitutions, additions and modifications within the scope not departing from the technical spirit described above. Of course, it should be understood that such modified embodiments also fall within the protection scope of the present invention as defined by the appended claims below.

S700: High-speed, constrained dynamic time-warping method for similarity measurement of time series data

Claims (8)

In the high-speed constrained dynamic time warping method for measuring the similarity of time-series data implemented as the computer-readable code on a computer-readable recording medium,
forming, in the computer, a resolution of a preset window area into multi-resolution each having a 1/2 data length and a 1/4 data length by using a first coarsening;
In the computer, the optimal warping path that has the 1/4 data length and is tracked by performing an alignment operation by limiting the window region of the lowest resolution among the multi-resolution to the limited window region of the SC-DTW is performed in a second process (projection) Based on the optimal warping path and setting parameter r found in the window region of resolution having the 1/4 data length through forming cells of the window region into first and second segments, respectively; and
The first segment and the second segment region of the resolution having a data length of 1/2 formed by utilizing an optimal warping path of the resolution having a 1/4 data length estimated through a third refinement in the computer. A fast-constrained dynamic time warping method for measuring similarity of time series data, comprising calculating an optimal warping path and a DTW distance within the calculated first and second segments after calculating cells.
According to claim 1,
The first process (coarsening) is
High-speed constraint for similarity measurement of time series data, characterized in that it is a process of reducing data points by repeating a method of tying each adjacent point of two time series data two by two and taking the average to make hierarchical multi-resolution dynamic time warping method.
3. The method of claim 2,
The second process (Projection) is
A fast and constrained dynamic time warping method for measuring similarity of time series data, characterized in that it is a process of finding the position of the selective warping path from the lowest resolution and estimating the position of the next lower resolution selective warping path.
delete 4. The method of claim 3,
The setting parameters are
A high-speed constraint dynamic time warping method for measuring the similarity of time series data, characterized in that it is an additional reflection radius value of a peripheral region of the estimated selective warping path.
According to claim 1,
The fast and constrained dynamic time warping method for measuring the similarity of time series data, characterized in that the first segment and the second segment are displayed as cells of the window area with different resolutions.
A recording medium recording a program for executing each step of the constrained dynamic time warping method at high speed for measuring the similarity of time series data according to any one of claims 1 to 3, 5, and 6.
A computing device comprising a recording medium recording a program for executing each step of the constrained dynamic time warping method at high speed for measuring the similarity of time series data according to any one of claims 1 to 3, 5, and 6.

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