Dynamic time warping distance method and system based on key structure point alignment

Abstract

In the disclosed embodiment, a dynamic time warping distance method and system based on key structure point alignment is provided, which belongs to the field of data processing technology, and specifically includes: determining the key point sequence composed of the key structure points of each time series; constructing its regular distance matrix according to the key point sequence and performing dynamic time warping distance calculation, and obtaining the alignment relationship between the two time series according to the optimal state transfer path in dynamic programming; projecting the alignment relationship into the distance accumulation matrix in the dynamic time warping distance calculation, finding the matrix position corresponding to the key point alignment in the distance accumulation matrix, connecting all matrix positions and expanding the range, and obtaining the constraint range of the distance calculation; under the constraint range, calculating the cumulative distance according to the calculation method of the cumulative distance. Through the scheme disclosed in the present invention, the optimal constraint range is achieved, the calculation amount of the distance accumulation matrix is ​​reduced, the approximate regular distance is obtained by rapid calculation, and the calculation efficiency and accuracy are improved.

Description

Technical Field

[0001] The disclosed embodiments relate to the field of data processing technology, and in particular to a dynamic time warping distance method and system based on key structure point alignment. Background Art

[0002] At present, time series is a concept derived from data mining. It generally refers to an ordered set of values ​​of the same statistical indicator arranged in chronological order. Time series analysis has achieved important applications in finance, medicine, meteorology, geology and other fields. The similarity measurement of time series is an important basis for time series analysis. By comparing and determining the similarities and differences between two groups of time series, the classification and clustering of time series can be further realized. Distance measurement is usually used to describe the similarity between time series. The smaller the distance between two time series, the more similar the series are.

[0003] However, the traditional calculation method has a large computational overhead for the cumulative distance matrix. As the data size increases, the calculation time and energy consumption will increase significantly, making it difficult to apply to time series analysis of big data.

[0004] It can be seen that there is an urgent need for a dynamic time warping distance method based on key structure point alignment with high computational efficiency and accuracy. Summary of the invention

[0005] In view of this, the embodiments of the present disclosure provide a dynamic time warping distance method and system based on key structure point alignment, which at least partially solves the problems of poor computational efficiency and accuracy in the prior art.

[0006] In a first aspect, an embodiment of the present disclosure provides a dynamic time warping distance method based on key structure point alignment, including:

[0007] For two time series, respectively traverse the curve images of the two time series, and determine the key point sequence composed of the key structural points of each time series according to the distribution of extreme value points;

[0008] According to the key point sequence, construct its regularized distance matrix and perform dynamic time regularized distance calculation, and obtain the alignment relationship between the two time series according to the optimal state transfer path in dynamic programming;

[0009] Projecting the alignment relationship into the distance accumulation matrix in the dynamic time warping distance calculation, finding the matrix position corresponding to the key point alignment in the distance accumulation matrix, connecting all the matrix positions and performing range expansion to obtain the constraint range of the distance calculation;

[0010] Under the constraint range, the cumulative distance is calculated according to the cumulative distance calculation method.

[0011] According to a specific implementation of the embodiment of the present disclosure, for two time series, the step of traversing the two time series curve images respectively and determining the key point sequence composed of the key structural points of each time series according to the extreme point distribution includes:

[0012] The key structural points of the time series are determined by the distribution of turning points in the curve image, and secondary screening is performed based on the distance threshold between all the key structural points to exclude densely appearing key structural points, so as to obtain a key point sequence for each time series.

[0013] According to a specific implementation of an embodiment of the present disclosure, the step of constructing a regular distance matrix of the key point sequence and performing dynamic time regular distance calculation, and obtaining an alignment relationship between the two time series according to the optimal state transition path in dynamic programming includes:

[0014] Constructing the regular distance matrix according to the key point sequence;

[0015] Performing dynamic time warping distance calculation to warp the path according to the warping distance matrix;

[0016] Each tuple in the regularized path is used as an alignment relationship between the two time series.

[0017] According to a specific implementation of an embodiment of the present disclosure, the step of projecting the alignment relationship into a distance accumulation matrix in dynamic time warping distance calculation, finding a matrix position corresponding to key point alignment in the distance accumulation matrix, connecting all the matrix positions and performing range expansion to obtain a constraint range for distance calculation includes:

[0018] Establishing a distance accumulation matrix corresponding to the time series;

[0019] Projecting each of the tuples in the regularized path into the distance accumulation matrix, marking the matrix position corresponding to each of the tuples in the distance accumulation matrix and arranging them in time sequence, to obtain a point sequence of the distance accumulation matrix;

[0020] All points in the point sequence are connected and range expanded to obtain the constraint range.

[0021] According to a specific implementation of the embodiment of the present disclosure, the step of calculating the cumulative distance under the constraint range according to the cumulative distance calculation method includes:

[0022] The near-optimal distances of the matrix elements in the distance accumulation matrix are calculated under the constraint range to obtain the accumulated distance.

[0023] In a second aspect, an embodiment of the present disclosure provides a dynamic time warping distance system based on key structure point alignment, including:

[0024] An extraction module is used for respectively traversing the curve images of the two time series for two time series, and determining a key point sequence composed of key structural points of each time series according to the distribution of extreme value points;

[0025] An alignment module is used to construct a regular distance matrix according to the key point sequence and perform dynamic time regular distance calculation, and obtain an alignment relationship between the two time series according to the optimal state transfer path in dynamic programming;

[0026] A projection module is used to project the alignment relationship into the distance accumulation matrix in the dynamic time warping distance calculation, find the matrix position corresponding to the key point alignment in the distance accumulation matrix, connect all the matrix positions and perform range expansion to obtain the constraint range of the distance calculation;

[0027] The calculation module is used to calculate the cumulative distance according to the calculation method of the cumulative distance within the constraint range.

[0028] The dynamic time warping distance scheme based on key structure point alignment in the disclosed embodiment includes: for two time series, traversing the curve images of the two time series respectively, and determining the key point sequence composed of the key structure points of each time series according to the extreme point distribution; constructing its regularized distance matrix and performing dynamic time warping distance calculation according to the key point sequence, and obtaining the alignment relationship between the two time series according to the optimal state transfer path in dynamic programming; projecting the alignment relationship into the distance accumulation matrix in the dynamic time warping distance calculation, finding the matrix position corresponding to the key point alignment in the distance accumulation matrix, connecting all the matrix positions and expanding the range to obtain the constraint range of the distance calculation; under the constraint range, calculating the cumulative distance according to the cumulative distance calculation method.

[0029] The beneficial effects of the embodiments of the present disclosure are as follows: through the scheme of the present disclosure, the optimal constraint range is approached, the amount of calculation of the distance accumulation matrix is ​​greatly reduced, and the approximate regular distance can be quickly calculated, thereby improving the calculation efficiency and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0031] Figure 1 A flow chart of a dynamic time warping distance method based on key structure point alignment provided in an embodiment of the present disclosure;

[0032] Figure 2 A schematic diagram of a key point sequence extraction process provided by an embodiment of the present disclosure;

[0033] Figure 3 A schematic diagram of a constraint range calculation process provided by an embodiment of the present disclosure;

[0034] Figure 4 A comparison chart of the experimental cumulative time of a dynamic time warping distance method based on key structure point alignment and a classical algorithm provided in an embodiment of the present disclosure;

[0035] Figure 5 A structural schematic diagram of a dynamic time warping distance system based on key structural point alignment provided in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0036] The embodiments of the present disclosure are described in detail below with reference to the accompanying drawings.

[0037] The following describes the embodiments of the present disclosure through specific examples, and those skilled in the art can easily understand other advantages and effects of the present disclosure from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all of the embodiments. The present disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present disclosure. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present disclosure.

[0038] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein may be used to implement this device and / or practice this method.

[0039] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present disclosure. The drawings only show components related to the present disclosure rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0040] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects described may be practiced without these specific details.

[0041] The embodiment of the present disclosure provides a dynamic time warping distance method based on key structure point alignment, which can be applied to the time series distance warping process in data mining scenarios.

[0042] See also Figure 1 , is a flow chart of a dynamic time warping distance method based on key structure point alignment provided by an embodiment of the present disclosure. Figure 1 As shown, the method mainly comprises the following steps:

[0043] S101, for two time series, respectively traverse the curve images of the two time series, and determine a key point sequence consisting of key structural points of each time series according to the distribution of extreme value points;

[0044] Optionally, in step S101, for two time series, traversing the two time series curve images respectively, and determining a key point sequence consisting of key structural points of each time series according to the distribution of extreme points, includes:

[0045] The key structural points of the time series are determined by the distribution of turning points in the curve image, and secondary screening is performed based on the distance threshold between all the key structural points to exclude densely appearing key structural points, so as to obtain a key point sequence for each time series.

[0046] When implementing it, Figure 2 As shown, for two time series: X{x1, x2, x3, … m} and Y{y1, y2, y3, ... y n}, traverse the two sequences respectively and perform two screenings to obtain their respective key point sequences:

[0047] The first screening is to screen the points in the target sequence whose product of the left and right slopes is less than 0, and to find the difference of the arc tangent function of the left and right slopes, and to screen the points whose difference is greater than the threshold.

[0048] The second screening is to traverse the results of the first screening based on the distance threshold, and remove the points whose distance to the previous point is less than the threshold. The points obtained from the two screenings are arranged in the original time sequence to obtain the key point sequence of the time series.

[0049] S102, constructing a regularized distance matrix according to the key point sequence and performing dynamic time regularized distance calculation, and obtaining an alignment relationship between the two time series according to an optimal state transfer path in dynamic programming;

[0050] Optionally, in step S102, according to the key point sequence, constructing its regularized distance matrix and performing dynamic time regularized distance calculation, and obtaining the alignment relationship between the two time series according to the optimal state transition path in dynamic programming, including:

[0051] Constructing the regular distance matrix according to the key point sequence;

[0052] Performing dynamic time warping distance calculation to warp the path according to the warping distance matrix;

[0053] Each tuple in the regularized path is used as an alignment relationship between the two time series.

[0054] In the specific implementation, two key point sequences X' and Y' of the two sequences are obtained through two screenings. For the key point sequence,

[0055] X'{(k1,x k1 ),(k2,x k2 ),(k3,x k3 ), ... (k p ,x kp )} and Y'{(l1,y l1 ), (l2,y l2 ),……(l j ,y lj )……(l q ,y lq )}, construct its regular distance matrix K, and calculate each element in the matrix as follows:

[0056]

[0057] K[11[11=d(1,1)

[0058]

[0059] This step is very similar to the calculation of the DTW algorithm, the difference is that the elements of the matrix K are less than the matrix D in the original time series DTW distance algorithm. In addition, in the process of calculating the elements of the K matrix, it is not necessary to obtain the cumulative distance value K[p][q], but to obtain the change path of (i, j) that makes K[i][j] take the minimum value during the calculation of each K[i][j], that is, the cumulative path of d(i, j). We call this path a regularized path, path = {(1, 1), ... (i, j), ... (m, n)}, where each (i, j) tuple is called an alignment relationship. By calculating the dynamic regularized distance of the key point sequence, the alignment relationship between the key point sequences is obtained.

[0060] S103, projecting the alignment relationship into the distance accumulation matrix in the dynamic time warping distance calculation, finding the matrix position corresponding to the key point alignment in the distance accumulation matrix, connecting all the matrix positions and performing range expansion to obtain the constraint range of the distance calculation;

[0061] On the basis of the above embodiment, as described in step S103, the alignment relationship is projected into the distance accumulation matrix in the dynamic time warping distance calculation, the matrix position corresponding to the key point alignment in the distance accumulation matrix is ​​found, all the matrix positions are connected and the range is expanded to obtain the constraint range of the distance calculation, including:

[0062] Establishing a distance accumulation matrix corresponding to the time series;

[0063] Projecting each of the tuples in the regularized path into the distance accumulation matrix, marking the matrix position corresponding to each of the tuples in the distance accumulation matrix and arranging them in time sequence, to obtain a point sequence of the distance accumulation matrix;

[0064] All points in the point sequence are connected and range expanded to obtain the constraint range.

[0065] When implementing it, Figure 3 As shown. Construct the distance accumulation matrix D of the time series, project the regular path path of the key point obtained in step S102 into the distance accumulation matrix, mark the matrix position corresponding to each (i, j) tuple, and arrange them in chronological order to obtain a point sequence in the regular distance matrix of the time series.

[0066] The distance accumulation matrix D is regarded as a grid. Through the straight line path algorithm of the grid, each point in the path path can be connected. The connected grid straight lines are represented in the matrix as a path path S passing through each matrix element. Extending r matrix elements from the matrix path path S to all sides, a matrix element collection S widened from the path path S is obtained, and this matrix element collection S is used as the constraint range for regular distance calculation.

[0067] S104, calculating the cumulative distance according to the cumulative distance calculation method within the constraint range.

[0068] Furthermore, in step S104, the cumulative distance is calculated according to the cumulative distance calculation method within the constraint range, including:

[0069] The near-optimal distances of the matrix elements in the distance accumulation matrix are calculated under the constraint range to obtain the accumulated distance.

[0070] In specific implementation, the near-optimal distance of the matrix elements in the distance accumulation matrix is ​​calculated under the constraint range to obtain the cumulative distance. For example, the elements of the distance accumulation matrix D can be calculated under the constraint range S according to the following formula:

[0071] d(i, j) = (x i -y j ) 2

[0072] D[1][1]=d(1,1)

[0073]

[0074] In the above calculation, only the matrix elements of [i][j]∈S are calculated, or written as (i, j)∈S. The final calculated value D[m][n] is the cumulative distance value required by this algorithm.

[0075] The dynamic time warping distance method based on key structure point alignment provided in this embodiment greatly reduces the amount of calculation of the distance accumulation matrix through the near-optimal constraint range, realizes rapid calculation of the approximate warping distance, and improves the calculation efficiency and accuracy.

[0076] The present invention will be described below in conjunction with two embodiments.

[0077] Embodiment 1:

[0078] For the time series A and B in the embodiment, they are first input into the key point extraction module of step (s01) to normalize the time axis position and value range of the time series. The purpose of this step is to prevent the length and value of the time series from interfering with the determination of key structural points. Each sequence element is traversed separately, and the sequence elements that meet the following formula are selected as the key structural points of the sequence:

[0079] {x i |(x i -x i-1 )(x i+1 -x i )<0}

[0080] {x i ||arctan(x i -x i-1 )-arctan(x i+1 -x i )|>γ}

[0081] Next, we need to remove some sequence points that are too close on the sequence image to prevent the structure points from being too dense. We traverse the key structure points that have passed the first screening, according to the formula:

[0082]

[0083] When a structure point xki is connected to its previous structure point x kh When the above inequality is satisfied, this structural point is removed from the key structural point set. Then the points that pass the second screening are arranged in the original time sequence, and the corresponding time axis coordinates and values ​​are combined into a two-tuple sequence. For the time series of this embodiment, the key point sequences of the original time series A and B are A'{(1,4), (3,4), (10,14), (16,0), (20,7), (22,3), (30,1)}, B'{(1,2), (17,4), (21,11), (24,3), (26,5), (30,0)}. The process diagram of this embodiment is shown in the legend. Figure 2 shown.

[0084] Furthermore, the key point sequence will be input into the alignment relationship module of step (s02). According to the obtained key point sequence, the regular distance matrix of the key point sequence is constructed as follows:

[0085]

[0086] K[1][1]=d(1,1)

[0087]

[0088] While calculating the regular distance matrix, the alignment path between the key point sequences is obtained, that is, the distance accumulation path. The alignment path is then input into the alignment relationship projection module that implements (s03). First, the regular distance matrix of the original sequences A and B is constructed, but the elements in the matrix are not calculated immediately.

[0089] Find the position where the alignment relationship is projected into the regular distance matrix of the original sequence as the initial set S{(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 5), (7, 6)} of the constraint range, and connect these matrix element positions through a straight line path algorithm. Then, for each connected path, expand r ranges around. In this embodiment, r is taken as 1, so for each (i, j) in S, (i, j+1), (i, j-1), (i+1, j-1), (i+1, j), (i+1, j+1), (i-1, j-1), (i-1, j), (i-1, j+1) are added to the set of constraint ranges, and the set is output as the calculated constraint range. The process of this embodiment can be shown in the accompanying figure Figure 3 shown.

[0090] The module for calculating the dynamic time warping distance under the constraint range is implemented by combining the constraint range with the input of the warping distance matrix to be calculated (s04), and each matrix element is calculated or skipped as follows:

[0091] d(i,j)=(A i -B j ) 2

[0092] D[1][1]=d(1,1)

[0093]

[0094] The obtained D[m][n] is the approximate dynamic time warping distance value obtained by the algorithm. In this embodiment, the approximate dynamic time warping distance between A and B is 83.98, which is 83.59 calculated according to the classical dynamic time warping distance. The error is 0.39, and the error rate is only 0.4%.

[0095] Embodiment 2:

[0096] By calculating the distance value of the time series through this algorithm, and comparing it with the classic dynamic time warping distance algorithm, this embodiment provides a classification experiment using the 1-nn method to verify its performance. The data used in the classification experiment comes from the UCR public data set. Each data in the data set consists of a time series and a corresponding label value, and is divided into a training set and a validation set. In this embodiment, the test set samples of several data sets in UCR are used as input, and the training set is used as the original data of the 1-nn classifier. The input samples are compared with the predicted label values ​​of the 1-nn classifier and their own true label values ​​to obtain the classification accuracy of the algorithm, and the time taken to complete each data set is recorded at the same time. In this embodiment, the classic dynamic time warping distance algorithm (DTW) is used as a control algorithm to verify the classification accuracy and calculation speed of the algorithm. The following table shows the comparison results of the classification error rate. The lower the algorithm error rate, the higher the accuracy:

[0097]

[0098]

[0099] Table 1

[0100] As can be seen from Table 1, the classification error rate of the proposed algorithm in the classification test of 24 data sets is very close to that of the classic DTW, which proves that the proposed algorithm has the same classification accuracy as the DTW algorithm.

[0101] In addition, the cumulative time taken by this algorithm and the classic dynamic time warping distance algorithm to pass the classification test of 24 data sets can reflect the performance of the two algorithms in terms of computing speed. Figure 4 As shown in the figure, the cumulative time of the algorithm in this paper is significantly smaller than that of the dynamic time warping distance algorithm as the number of completed data sets increases. This shows that the algorithm in this paper has a great speed improvement compared with the dynamic time warping distance algorithm and greatly reduces the consumption of computing resources.

[0102] Corresponding to the above method embodiment, see Figure 5 The embodiment of the present disclosure further provides a dynamic time warping distance system 50 based on key structure point alignment, including:

[0103] An extraction module 501 is used for respectively traversing the curve images of the two time series for two time series, and determining a key point sequence composed of key structural points of each time series according to the distribution of extreme value points;

[0104] An alignment module 502 is used to construct a regular distance matrix according to the key point sequence and perform dynamic time regular distance calculation, and obtain an alignment relationship between the two time series according to the optimal state transfer path in dynamic programming;

[0105] A projection module 503 is used to project the alignment relationship into the distance accumulation matrix in the dynamic time warping distance calculation, find the matrix position corresponding to the key point alignment in the distance accumulation matrix, connect all the matrix positions and perform range expansion to obtain the constraint range of the distance calculation;

[0106] The calculation module 504 is used to calculate the cumulative distance according to the calculation method of the cumulative distance under the constraint range.

[0107] Figure 5 The system shown can correspondingly execute the contents of the above method embodiment. For the parts not described in detail in this embodiment, refer to the contents recorded in the above method embodiment and will not be repeated here.

[0108] The units involved in the embodiments described in the present disclosure may be implemented by software or by hardware.

[0109] It should be understood that various parts of the present disclosure may be implemented in hardware, software, firmware, or a combination thereof.

[0110] The above is only a specific implementation of the present disclosure, but the protection scope of the present disclosure is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present disclosure should be included in the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be based on the protection scope of the claims.

Claims

1. A dynamic time warping distance method based on key structure point alignment, characterized in that: include: For two time series, respectively traverse the curve images of the two time series, and determine the key point sequence composed of the key structural points of each time series according to the distribution of extreme value points; According to the key point sequence, construct its regularized distance matrix and perform dynamic time regularized distance calculation, and obtain the alignment relationship between the two time series according to the optimal state transfer path in dynamic programming; The step of constructing a regularized distance matrix according to the key point sequence and performing dynamic time regularized distance calculation, and obtaining an alignment relationship between the two time series according to the optimal state transfer path in dynamic programming, comprises: Constructing the regular distance matrix according to the key point sequence; Performing dynamic time warping distance calculation to warp the path according to the warping distance matrix; Taking each tuple in the regularized path as an alignment relationship between two time series; Projecting the alignment relationship into the distance accumulation matrix in the dynamic time warping distance calculation, finding the matrix position corresponding to the key point alignment in the distance accumulation matrix, connecting all the matrix positions and performing range expansion to obtain the constraint range of the distance calculation; The step of projecting the alignment relationship into the distance accumulation matrix in the dynamic time warping distance calculation, finding the matrix position corresponding to the key point alignment in the distance accumulation matrix, connecting all the matrix positions and performing range expansion to obtain the constraint range of the distance calculation includes: Establishing a distance accumulation matrix corresponding to the time series; Projecting each of the tuples in the regularized path into the distance accumulation matrix, marking the matrix position corresponding to each of the tuples in the distance accumulation matrix and arranging them in time sequence, to obtain a point sequence of the distance accumulation matrix; Connect all points in the point sequence and expand the range to obtain the constraint range; Under the constraint range, the cumulative distance is calculated according to the cumulative distance calculation method.

2. The method according to claim 1, characterized in that The step of traversing the two time series curve images respectively and determining the key point sequence composed of the key structural points of each time series according to the distribution of extreme points comprises: The key structural points of the time series are determined by the distribution of turning points in the curve image, and secondary screening is performed based on the distance threshold between all the key structural points to exclude densely appearing key structural points, so as to obtain a key point sequence for each time series.

3. The method according to claim 1, characterized in that The step of calculating the cumulative distance according to the calculation method of the cumulative distance within the constraint range includes: The near-optimal distances of the matrix elements in the distance accumulation matrix are calculated under the constraint range to obtain the accumulated distance.

4. A dynamic time warping distance system based on key structure point alignment, characterized in that: include: An extraction module is used for respectively traversing the curve images of the two time series for two time series, and determining a key point sequence composed of key structural points of each time series according to the distribution of extreme value points; An alignment module, used to construct a regular distance matrix according to the key point sequence and perform dynamic time regular distance calculation, and obtain an alignment relationship between the two time series according to the optimal state transfer path in dynamic programming; The alignment module is also used to: Constructing the regular distance matrix according to the key point sequence; Performing dynamic time warping distance calculation to warp the path according to the warping distance matrix; Taking each tuple in the regularized path as an alignment relationship between two time series; A projection module is used to project the alignment relationship into the distance accumulation matrix in the dynamic time warping distance calculation, find the matrix position corresponding to the key point alignment in the distance accumulation matrix, connect all the matrix positions and perform range expansion to obtain the constraint range of the distance calculation; The projection module is also used to: Establishing a distance accumulation matrix corresponding to the time series; Projecting each of the tuples in the regularized path into the distance accumulation matrix, marking the matrix position corresponding to each of the tuples in the distance accumulation matrix and arranging them in time sequence, to obtain a point sequence of the distance accumulation matrix; Connect all points in the point sequence and expand the range to obtain the constraint range; The calculation module is used to calculate the cumulative distance according to the calculation method of the cumulative distance within the constraint range.

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