A method for center computation on a set of non-equal length time series

Abstract

The application relates to the field of data processing, in particular to a center calculation method for a non-equal-length time sequence set. The method comprises the following steps: obtaining the non-equal-length time sequence set and determining the sequence lengths of all time sequences; calculating the average value of the sequence lengths of the time sequences to determine an initial clustering center sequence; determining an average sequence corresponding to the non-equal-length time sequence set according to the non-equal-length time sequence set and the initial clustering center sequence; calculating the Euclidean distance between the initial clustering center sequence and the average sequence to obtain a distance vector; judging the size between the distance vector and a preset iteration error; if the distance vector is not smaller than the iteration error, updating the average sequence into the initial clustering center sequence, and iteratively executing the relevant steps. The center calculation method for the non-equal-length time sequence set has the characteristics of high efficiency, simplicity and accuracy, and thus can solve the problems of the prior art of determining the clustering center of the non-equal-length sequence.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of data processing, in particular to a center calculation method for a set of non-equal length time series. BACKGROUND

[0002] The application field of cluster analysis is quite extensive, and cluster algorithms realize unsupervised classification by comparing the similarities between samples. The common way is to calculate the distance between samples and centers to find the similarities between data. Therefore, for most cluster algorithms, the selection of cluster centers determines the accuracy of cluster analysis.

[0003] According to the existing literature, cluster algorithms mainly include hierarchical clustering, model-based clustering, partition-based clustering, and density-based clustering. Current cluster algorithms can realize clustering of equal length sequences and clustering of non-equal length sequences. For equal length sequences, a direct clustering method can be used. In the clustering process, the cluster center is first selected, and the selection method of the cluster center is found to have good performance. Then, a distance function is used as an evaluation index to realize clustering.

[0004] The clustering of non-equal length sequences usually uses an indirect clustering method. First, the non-equal length sequences are mapped to a feature variable space, which realizes the conversion of non-equal length sequences to equal length sequences. Then, existing equal length sequence clustering algorithms are used to realize cluster analysis. This space transformation processing method avoids the problem of finding the center of non-equal length sequences, but increases the computational complexity and computation time due to the space transformation, and also has high requirements for the selection of feature variables. Different applications depend on the use of different feature variable spaces to express specific similarities. For example, the similarity in financial data analysis and market prediction is different from the similarity in weather forecasting or medicine, which is reflected in the selection of feature variable spaces used to express the similarity. In order to overcome this problem, direct clustering for non-equal length sequences is needed.

[0005] Recent research results show that the cluster center of equal length sequences is usually determined based on a certain distance iteration, such as Mahalanobis distance, Euclidean distance, and Manhattan distance. The cluster center of equal length sequences is determined by comparing the point-by-point distance to determine the center of the class. The DTW distance is usually used to calculate the distance of non-equal length time series. The DTW distance is effective as an index for comparing the total distance of non-equal length sequences. However, the DTW distance is not a point-by-point distance, and therefore cannot obtain each element of the cluster center sequence. Therefore, determining the cluster center of non-equal length sequences is a key problem in direct clustering of non-equal length sequences. SUMMARY

[0006] The present application provides a center calculation method for a set of non-equal length time series, which can solve the problem of the prior art of determining the cluster center of non-equal length sequences.

[0007] The technical solution of this application is a method for central calculation of sets of non-equal-length sequences, including:

[0008] S1: Obtain a set of non-equal-length time series that includes at least two time series of unequal length, and determine the sequence length of all time series in the set of non-equal-length time series;

[0009] S2: Calculate the average sequence length of all time series in the set of non-equal time series, and determine at least one initial cluster center sequence based on the average sequence length.

[0010] S3: Based on the set of non-equal time series and the initial cluster center sequence, determine the average sequence corresponding to the set of non-equal time series.

[0011] S4: Calculate the Euclidean distance between the initial cluster center sequence and the average sequence to obtain the distance vector;

[0012] S5: Determine the magnitude of the distance vector and the preset iteration error. If the distance vector is less than the preset iteration error, output the corresponding initial cluster center sequence as the set center. If the distance vector is not less than the preset iteration error, update the initial cluster center sequence with the average sequence. Iterate through steps S3 to S5 until the distance vector is less than the preset iteration error.

[0013] Optionally, step S2 includes:

[0014] S21: Based on the set of non-equal time sequence S′={s i ′}={s1′,s2′,…,s p All time series s in '} i Given the sequence length of ', calculate the length of all time series s. i The average length m of the sequence of ′ a ;

[0015] Calculate the average length m of the sequence a The formula is shown below:

[0016]

[0017] In the formula, p represents the number of time series in the set of non-equal time series;

[0018] m i s i The sequence length of ', 1≤i≤p;

[0019] S22: Calculate the sequence length m of each time series. i The average length m of the sequencea The sequence difference Δm between them;

[0020] The formula for calculating the sequence difference Δm is shown below:

[0021] Δm=min(|m a -m i |);

[0022] S23: Determine several time series s corresponding to the smallest sequence difference Δm. i And in the corresponding several time series s i Select a time series s from ' i ′ as an initial cluster center sequence s ma ′;

[0023] m q Represents the initial cluster center sequence s ma The sequence length of ′, 1≤m q ≤p.

[0024] Optionally, step S3 includes:

[0025] S31: Calculate all time series s respectively. i ′ and the initial cluster center sequence s ma The distance matrix E between ′ i ;

[0026] S32: Based on the standard of minimum path planning, in the distance matrix E i Determine the corresponding time series s i 'Planning Path' n represents the number of grid points traversed by the planned path;

[0027] S33: According to the planned path Determine the initial cluster center sequence s ma ′ Corresponds to the time series set {s i For each time series in '}, find similar sequences and accordingly determine the set of similar sequences l = {l} including all similar sequences. i}={l1, l2, …, l p}(1≤i≤p); l i Represents the initial cluster center sequence s ma ′ Corresponding to time series s i Similar sequences of ′

[0028] S34: Based on similar sequences l i Calculate the average sequence value of all similar sequences in the set of similar sequences. The formula for calculating the average sequence l′ is as follows:

[0029]

[0030] Optionally, step S4 includes:

[0031] S41: Calculate the initial cluster center sequence s ma The Euclidean distance between l' and the average sequence l' is used to obtain the distance vector D;

[0032] The formula for calculating the distance vector D is as follows:

[0033]

[0034] And, step S5 includes:

[0035] S51: Determine the relationship between the distance vector D and the preset iteration error ε. If the distance vector D is less than the preset iteration error ε, output the initial cluster center sequence s. ma ′ is the cluster center;

[0036] S52: If the distance vector D is not less than the preset iteration error ε, update the initial cluster center sequence s with the average sequence l′. ma ′, iteratively execute steps S3 to S5 until the distance vector D is less than the preset iteration error ε.

[0037] Optionally, step S2 includes:

[0038] S21: Based on the set of non-equal time sequence U={u i} = {u1, u2, ..., u h All time series u in} i Given the sequence length, calculate the length of all time series u. i The average length w of the sequence avg ;

[0039] Calculate the average length m of the sequence a The formula is shown below:

[0040]

[0041] In the formula, h represents the number of time series in the set of non-equal time series;

[0042] w i Indicate u i The sequence length, 1≤i≤h;

[0043] S22: Select the sequence with the closest length to w from the set of non-equal-length sequences U. avg k time series u iAs the initial cluster center sequence set

[0044] Represents the initial cluster center sequence. Represents the initial cluster center sequence The length.

[0045] Optionally, step S3 includes:

[0046] S31: Calculate the time series u respectively i With k initial cluster center sequences The dtw distance between them yields the matrix F. ； Matrix F is shown below:

[0047]

[0048] In the formula,

[0049] S32: Determine the set of average sequences based on matrix F.

[0050] Represents the average sequence. Represents the average series The length.

[0051] Optionally, step S4 includes:

[0052] S41: Calculate the sequence of k initial cluster centers respectively. with average sequence The Euclidean distance between them yields the set of distance vectors D′=[d′ j ]=[d′1,d′2,…,d′ k ],d′ j Represents the initial cluster center sequence with average sequence The distance vector between them;

[0053] Distance vector d j The calculation formula is as follows:

[0054]

[0055] And, step S5 includes:

[0056] S51: Determine the distance vector d′ j The magnitude of the distance vector d′ is related to the preset iteration error ε. j If the iteration error is less than the preset value ε, output the corresponding time series. As cluster center;

[0057] S52: if the distance vector d' is not less than the preset iteration error ε, updating the initial clustering center sequence into the average sequence j Steps S2-S5 are iteratively executed until the distance vector d' is less than the preset iteration error ε. j

[0058] Advantages:

[0059] The present application sets the initial clustering center sequence for the set center in advance, then sequentially determines the average sequence and the distance vector, audits the distance vector according to the iteration error set according to the requirement, updates the initial clustering center sequence into the average sequence, iteratively executes the related steps until the distance vector is less than the preset iteration error, and finally outputs the set center.

[0060] In conclusion, the center calculation method of the non-equal-length time sequence set based on the twisted path has the characteristics of high efficiency, simplicity and accuracy, is convenient to operate, can solve the problems of the prior art of determining the clustering center of the non-equal-length sequence, and has a very high recognition accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0061] In order to more clearly illustrate the technical solutions of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. Obviously, for those skilled in the art, other drawings can also be obtained from these drawings without any creative labor.

[0062] Figure 1 The figure is a flowchart of the center calculation method of the non-equal-length time sequence set in the embodiments of the present application. DETAILED DESCRIPTION

[0063] The embodiments will be described in detail below, and the examples are shown in the drawings. When the following description refers to the drawings, the same numbers in different drawings represent the same or similar elements unless otherwise indicated. The implementation described in the following embodiments does not represent all the implementation consistent with the present application. It is only an example of the system and method consistent with some aspects of the present application as described in the detailed description of the claims.

[0064] In the prior art, let the sequence set S = {s i}(1≤i≤p), where the sequence When n1 = n2 = … = n p , then s1, s2, …, s p The matrix formed by s1, s2, …, sp is as follows:

[0065] ​​​

[0066] The center of s = [s1, s2,..., sn] can be represented as p where n a = n1.

[0067] sa i = (1≤i≤n a ) can be calculated as follows:

[0068]

[0069] When there is any one n i , such that n i ≠ n j (1≤i≤p, 1≤j≤p, and i≠j), then s1, s2,..., sn p cannot form a matrix, so the center of s cannot be calculated.

[0070] To solve the above problem, the present application provides a center calculation method for a non-equal-length time sequence set, as shown in Figure 1 , which is a flowchart of the center calculation method for a non-equal-length time sequence set in the embodiments of the present application, comprising: Figure 1 S1: obtaining a non-equal-length time sequence set including at least two unequal-length time sequences to be calculated for the set center, and determining the sequence lengths of all time sequences in the non-equal-length time sequence set;

[0071] S2: calculating the average of the sequence lengths of all time sequences in the non-equal-length time sequence set, and determining at least one initial clustering center sequence according to the average of the sequence lengths;

[0072] S3: determining the average sequence corresponding to the non-equal-length time sequence set according to the non-equal-length time sequence set and the initial clustering center sequence;

[0073] S4: calculating the Euclidean distance between the initial clustering center sequence and the average sequence to obtain a distance vector;

[0074] S5: judging the size between the distance vector and a preset iteration error, if the distance vector is smaller than the preset iteration error, outputting the corresponding initial clustering center sequence as the set center, if the distance vector is not smaller than the preset iteration error, updating the initial clustering center sequence with the average sequence, and iteratively executing steps S3-S5 until the distance vector is smaller than the preset iteration error.

[0075] (I) Embodiment I

[0076]

[0077] ​​Example 1 is the CCA-TP iterative algorithm based on non-equal length sequence cluster centers of twisted paths.

[0078] In this embodiment of the application, step S1 includes:

[0079] Let the set of non-uniform length sequences S′={s i ′}, where the sequence

[0080] There exists any m i and m j , making m i ≠m j (1≤i≤p, 1≤j≤p, and i≠j).

[0081] To obtain the set {s1′, s2′, ..., s} p Approximate center of ′} First, we need to determine n. a .

[0082] In this embodiment, the average length of the sequence in the set is selected as m. a ,Right now

[0083]

[0084] In the formula, p represents the number of time series in the set of non-equal time series;

[0085] m i s i The sequence length of ′ is 1≤i≤p.

[0086] Next, we calculate sa′ using an iterative method, and let the iteration error be ε.

[0087] And, step S2 includes:

[0088] S21: Based on the set of non-equal time sequence S′={s i ′}={s1′,s2′,…,s p All time series s in '} i Given the sequence length of ', calculate the length of all time series s. i The average length m of the sequence of ′ a ;

[0089] Calculate the average length m of the sequence a The formula is shown below:

[0090]

[0091] In the formula, p represents the number of time series in the set of non-equal time series;

[0092] m i denotes the sequence length of s i ′, 1≤i≤p.

[0093] S22: calculate the sequence difference Δm between the sequence length m i and the average value m a of the sequence length respectively;

[0094] The formula for calculating the sequence difference Δm is as follows:

[0095] Δm = min(|m a -m i |);

[0096] S23: determine a number of time sequences s i ′ corresponding to the minimum sequence difference Δm and select one time sequence s i ′ from the corresponding number of time sequences s i ′ as an initial clustering center sequence s ma ′;

[0097] m q denotes the sequence length of the initial clustering center sequence s ma ′, 1≤m q ≤p.

[0098] Specifically, find a sequence s p ′ in {s1′, s2′, …, s a ′} whose length is closest to m ma ′.

[0099] The length of the sequence is m q (1≤m q ≤p), that is, it satisfies Δm = min(|m a -m i |) (1≤i≤p).

[0100] If there are multiple sequences that satisfy the condition of minimum Δm, randomly select one sequence as s ma ′.

[0101] And, step S3 includes:

[0102] S31: calculate the distance matrix E i between the time sequence s ma ′ and the initial clustering center sequence s i ′ respectively;

[0103] S32: based on the minimum value path planning standard, determine the minimum distance value in the distance matrix Ei Determine the corresponding time series s i 'Planning Path' n represents the number of grid points traversed by the planned path;

[0104] S33: According to the planned path Determine the initial cluster center sequence s ma ′ Corresponds to the time series set {s i For each time series in '}, find similar sequences and accordingly determine the set of similar sequences l = {l} including all similar sequences. i}={l1, l2, …, l p}(1≤i≤p); l i Represents the initial cluster center sequence s ma ′ Corresponding to time series s i Similar sequences of ′

[0105] S34: Based on similar sequences l i Calculate the average sequence value of all similar sequences in the set of similar sequences. The formula for calculating the average sequence l′ is as follows:

[0106]

[0107] Specifically, the similarity sequences of the initial cluster center sequence to all time series in the set are calculated sequentially, and the set of similar sequences including all similar sequences is determined accordingly. The average sequence is obtained by averaging all similar sequences in the set of similar sequences.

[0108] And, step S4 includes:

[0109] S41: Calculate the initial cluster center sequence s ma The Euclidean distance between l' and the average sequence l' is used to obtain the distance vector D;

[0110] The formula for calculating the distance vector D is as follows:

[0111]

[0112] And, step S5 includes:

[0113] S51: Determine the relationship between the distance vector D and the preset iteration error ε. If the distance vector D is less than the preset iteration error ε, output the initial cluster center sequence s. ma ′ is the cluster center;

[0114] S52: If the distance vector D is not less than the preset iteration error ε, update the initial cluster center sequence s with the average sequence l′. maThe steps S3-S5 are iteratively performed until the distance vector D is less than a preset iteration error ε.

[0115] (II) Embodiment II

[0116] Embodiment II is a CCA-TP-CLUS clustering algorithm based on non-equal length sequence clustering centers of twisted path.

[0117] In the embodiments of the present application, the step S1 comprises:

[0118] A non-equal length sequence set U={u i} is set, wherein the sequence

[0119] There exist any one w i and w j , such that w i ≠w j (1≤i≤h, 1≤j≤h, and i≠j).

[0120] The purpose of the embodiments of the present application is to obtain a set {v1, v2, …, vh} composed of k clustering center sequences of the set {u1, u2, …, uh}, i.e., V={v h}, wherein k j wherein At the same time, the category to which u i belongs is determined.

[0121] And the step S2 comprises:

[0122] S21: According to the sequence length of all time sequences u i}={u1, u2, …, uh} in the non-equal length time sequence set U={u h}, the average value w i of the sequence length of all time sequences u i is calculated. avg

[0123] The formula for calculating the average value m a of the sequence length is as follows:

[0124] In the formula, h represents the number of time sequences in the non-equal length time sequence set;

[0125] w i represents the sequence length of u i , 1≤i≤h;

[0126] S22: In the non-equal length time sequence set U, the time sequence with the sequence length closest to w avg ​​​k time series u i as initial clustering center sequences

[0127] representing initial clustering center sequences, representing initial clustering center sequences lengths.

[0128] Specifically, calculate the average value of the lengths of all sequences u h i lengths, i.e.

[0129]

[0130] Select k sequences with lengths closest to w h from {u1, u2, …, u avg , respectively, as

[0131] where the lengths of the sequences are and take u a1 , u a2 , …, u ak as initial clustering centers.

[0132] Further, step S3 comprises:

[0133] S31: calculate the dtw distance between each time series u i and k initial clustering center sequences , respectively, to obtain a matrix F; the matrix F is as follows:

[0134]

[0135] wherein,

[0136] Specifically, find the minimum value of each row in the matrix F, and each minimum value in the column coordinate in F is the category to which the corresponding row coordinate sequence belongs.

[0137] S32: determine an average sequence set

[0138] representing average sequences, representing average sequences lengths.

[0139] Further, step S4 comprises:

[0140] S41: calculate the dtw distance between each initial clustering center sequence and each average sequence ​Euclidean distance between the initial clustering center sequence j ]=[d′1,d′2,…,d′ k ],d′ j represents the distance vector between the initial clustering center sequence and the average sequence .

[0141] The distance vector d′ j is calculated as follows:

[0142]

[0143] And, step S5 includes:

[0144] S51: judging the size of the distance vector d′ j and the preset iteration error ε, if the distance vector d′ j is smaller than the preset iteration error ε, outputting the corresponding time sequence as the clustering center;

[0145] S52: if the distance vector d′ j is not smaller than the preset iteration error ε, updating the corresponding initial clustering center sequence into the average sequence . Steps S2-S5 are iteratively executed until the corresponding distance vector d′ j is smaller than the preset iteration error ε.

[0146] Specifically, the final result is to output the k clustering center sequences {v1, v2, …, v k}, and then run step S3 to obtain the category to which each u i belongs.

[0147] (Three) Experimental evaluation

[0148] In order to verify the effectiveness of the CCA-TP-CLUS algorithm for clustering non-equal length sequence sets, the algorithm is applied to random trajectory recognition.

[0149] Through multiple experiments, the effectiveness and superiority of the CCA-TP clustering algorithm are verified, and it is compared with other methods.

[0150] Based on the prior art, the sequences of different lengths can be converted to the same length by feature extraction, and then SOM neural network clustering is used, and finally BP neural network is used for classification and recognition of test sequences. In addition, based on the prior art, the same length sequences after feature extraction can be clustered by using the kmeans algorithm, and then classified and recognized by distance comparison.

[0151] The embodiments of the present application respectively compare the three algorithms of feature extraction+SOM neural network+BP neural network, feature extraction+kmeans and CCA-TP on multiple groups of data.

[0152] Specifically, first, a basic trajectory recognition experiment is designed. In the experiment, 5 testers are invited to participate in data collection, each tester respectively performs 20 times on 4 types of basic trajectories, and a total of 200 basic trajectories are obtained. The algorithm calculation time statistics table is shown in Table 1, and the algorithm recognition accuracy table is shown in Table 2.

[0153] Table 1 Comparison of time used by three methods

[0154]

[0155] Table 2 Recognition accuracy of three methods for basic trajectories and random trajectories

[0156]

[0157] From Table 1 and Table 2, compared with the two methods of FE+SOM+BPNN and FE+KMEANS, CCA-TP has obvious advantages in time complexity, the average running time in the experiment is 0.8725 seconds, which is better than the other two methods; at the same time, in the accuracy comparison, CCA-TP also achieves the best effect, the recognition accuracy for basic trajectories and random trajectories reaches 98.5% and 97.6%, and the average recognition accuracy is 98.05%.

[0158] The above embodiments of the present application are described in detail, but the content is only the preferred embodiments of the present application, and cannot be considered as limiting the scope of the present application. Any equivalent changes and improvements made within the scope of the present application should still belong to the patent coverage of the present application.

Claims

1. A method for center computation on a set of non-equal length time series, the method is applied to random trajectory recognition, characterized in that, Comprising: S1: obtaining a non-equal-length time series set including at least two unequal-length time series to be calculated for a set center, and determining the sequence length of all time series in the non-equal-length time series set; S2: calculating the average value of the sequence length of all time series in the non-equal-length time series set, and determining at least one initial clustering center sequence according to the average value of the sequence length; S3: determining the average sequence corresponding to the non-equal-length time series set according to the non-equal-length time series set and the initial clustering center sequence; S4: calculating the Euclidean distance between the initial clustering center sequence and the average sequence to obtain a distance vector; S5: judging the size between the distance vector and a preset iteration error, if the distance vector is smaller than the preset iteration error, outputting the corresponding initial clustering center sequence as the set center, if the distance vector is not smaller than the preset iteration error, updating the average sequence into the initial clustering center sequence, and iteratively executing steps S3-S5 until the distance vector is smaller than the preset iteration error.

2. The method for center calculation on a set of non-equal-length time series according to claim 1, wherein the step S2 comprises: S21: Calculate the average of the sequence lengths of all time series in the non-equally long time series set S22: Calculate the average of the sequence lengths of all time series in the non-equally long time series set S23: Calculate the average of the sequence lengths of all time series in the non-equally long time series set ； wherein denotes the number of time series in the set of non-equi-length time series; denotes the sequence length of ; S22: Calculate the sequence length of the time series respectively The sequence difference between the average value of the sequence length ; Calculate the sequence difference The formula is as follows: ;​ S23: determining the smallest sequence difference value corresponding time series and corresponding time series as an initial cluster center sequence ; , denotes a sequence of initial cluster centers a sequence length of .

3. The center calculation method for a non-equal-length time series set according to claim 2, wherein the step S3 comprises: S31 : Calculate all time series separately Distance matrix between initial cluster centers sequence ;​ S32: based on the criteria of the minimum value path planning, determine the corresponding to the time series in the distance matrix planned path , represent the number of grid points through which the planned path passes. S33: determining the initial cluster center sequence based on the planning path corresponding to the set of time series and determining a set of similar sequences comprising all similar sequences corresponding to each time series of the set of time series ; representing the initial cluster center sequence corresponding to the similar sequences of the time series , ; S34: Calculate the average sequence of all similar sequences in the similar sequence set according to the similar sequence . S35: Calculate the average sequence of all similar sequences in the similar sequence set according to the similar sequence . S36: The calculation formula of the average sequence is as follows: .

4. The center calculation method for a non-equal-length time series set according to claim 3, wherein the step S4 comprises: S41: Calculate the initial cluster center sequence The Euclidean distance between the average sequence and the initial cluster center sequence, to obtain the distance vector ; Distance vector The formula for the calculation of the distance vector is shown below: ； and , the step S5 comprises: S51: judging the distance vector and the preset iteration error , if the distance vector is less than the preset iteration error , outputting the initial clustering center sequence as the clustering center; S52: if the distance vector is not smaller than a preset iteration error , the average sequence is updated into the initial clustering center sequence , and steps S3-S5 are iteratively executed until the distance vector is smaller than a preset iteration error .

5. The center calculation method for a non-equal-length time series set according to claim 1, wherein the step S2 comprises: S21: calculating the average of the sequence lengths of all time series according to the set of non-equally long time series all time series in the set ; The average of the sequence lengths is calculated The formula is as follows: ； wherein denotes the number of time series in the set of non-equi-length time series; denotes the sequence length of ; S22: selecting, from among the set of non-equal-length time sequences a time sequence with a sequence length closest to as the initial set of cluster center sequences ;​​ denotes a sequence of initial cluster centers, denotes a sequence of initial cluster centers of length n.

6. The center calculation method for a non-equal-length time series set according to claim 1, wherein the step S3 comprises: S31: calculate time series respectively with dtw distance between initial cluster center sequence , get matrix ; matrix As shown below: ； In the formulae, ; S32: Determine the average sequence set from the matrix determining an average sequence set ; denotes the average sequence, denotes the average sequence of length.

7. The method for center calculation on a set of non-equal-length time series according to claim 6, wherein the step S4 comprises: S41: respectively calculate Euclidean distances between the initial clustering center sequence and the average sequence , to obtain a distance vector set , , wherein the distance vector represents the distance between the initial clustering center sequence and the average sequence ; Distance vector The formula for the calculation of the distance vector is shown below: ； and , the step S5 comprises: S51: judging the distance vector and the preset iteration error , if the distance vector is less than the preset iteration error , outputting the corresponding time sequence as the clustering center; S52: if the distance vector is not smaller than a preset iteration error , the corresponding initial cluster center sequence is updated into an average sequence , and steps S2-S5 are iteratively executed until the corresponding distance vector is smaller than a preset iteration error .

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