Time sequence classification method based on complex reliability Beta divergence
Through the time series classification method of complex reliability Beta divergence, the problem of unreliable information conflict in multi-source information fusion is solved, and more efficient pattern classification is achieved, especially on complex data sets, which show excellent classification accuracy.
Patent Information
- Application Number
- CN202510645678.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-20
- Publication Date
- 2025-07-25
AI Technical Summary
The prior art is difficult to effectively deal with conflicts caused by unreliable information in multi-source information fusion, affecting the accuracy and reliability of pattern classification results.
The time series classification method based on complex reliability Beta divergence is adopted to model uncertainty of the time series through time-frequency conversion and triangular fuzzy numbers, and conflict dissolution is used to realize information fusion and analysis, and finally the classification results are generated through complex Pignistic transformation.
It improves the accuracy and robustness of pattern classification, reduces the impact of data conflicts on the results, and shows better classification performance, especially on complex data sets, which significantly improves classification accuracy.
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Figure CN120372453A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a pattern classification method, and in particular to a time series classification method based on complex belief Beta divergence. Background Art
[0002] In the contemporary technological background of the deep integration of big data and artificial intelligence, classification, as the core preprocessing link for intelligent systems to process complex data, has become increasingly prominent. Facing a vast amount of heterogeneous data, how to extract discriminative features from high-dimensional, non-linear, and dynamically evolving data and achieve efficient information induction through pattern classification has become a fundamental challenge for intelligent systems to achieve cognition and decision-making. The essence of pattern classification lies in constructing a mapping relationship between the feature space and the category space to reveal the internal inter-class difference law of the data. Its core tasks include feature engineering, classifier optimization, and the construction of a performance evaluation system. However, a single data source is often limited by factors such as narrow information dimensions, significant noise interference, and environmental dynamics, making it difficult to break through the bottleneck of classification performance. In this context, multi-source information fusion technology provides a theoretical breakthrough direction for solving classification problems in complex scenarios by synergistically integrating heterogeneous sensors, multi-modal data, and cross-domain knowledge to construct a comprehensive information representation system that combines globality, complementarity, and redundancy.
[0003] Multi-source information fusion aims to improve the accuracy, completeness, and robustness of cognition as its core goal, and its methodology integrates information theory, statistics, artificial intelligence, and complex system theory. However, the heterogeneity, asynchrony, and uncertainty of multi-source data significantly increase the complexity of the fusion system. Among them, the uncertainty problem is particularly prominent, specifically manifested as data loss, noise interference, contradictions between modalities, and incomplete prior knowledge, resulting in a decrease in the credibility of the fusion result or even decision-making failure. In the field of pattern classification, it is crucial to achieve uncertainty modeling and reasoning. As an emerging means of uncertainty modeling and reasoning based on the complex plane, complex evidence theory presents extremely broad application prospects. However, there is a thorny problem in practical applications: the reliability of information sources is difficult to guarantee. The sensors used to collect information may experience temporary failures or be deliberately damaged by humans, thus providing unreliable information. There are often significant conflicts between this unreliable information and reliable information. In the framework of complex evidence theory, once this conflicting information is directly incorporated into the complex evidence combination rule for processing, the unreliable information may, due to improper factors in the evidence combination rule, cause the system to make completely unreasonable decisions. Summary of the Invention
[0004] Aiming at the above problems existing in the prior art, the technical problem to be solved by the present invention is: how to accurately classify time series.
[0005] To solve the above technical problems, the present invention adopts the following technical solutions: a time series classification method based on complex belief Beta divergence. The present invention uses a publicly available time series dataset, models the uncertainty in the time series based on time-frequency conversion and triangular fuzzy numbers, performs information fusion and analysis on signals in different frequency domains, and resolves conflicts based on complex belief Beta divergence, thereby realizing the prediction of its category. The method includes the following steps:
[0006] S1: Obtain a number of time series data. Each time series data consists of a number of sampling points {t1, t2,..., t j ,..., t k ,..., t l} of the same number and a category label m. Each time series data forms a training sample, and the training samples form a training set;
[0007] S2: The training set is used to establish a complex basic belief assignment function generation model. Perform discrete Fourier transform on the training samples to transform the training samples into the frequency domain. Each training sample obtains l complex numbers, denoted as {n1, n2,..., n j ,..., n k ,..., n l}. To improve the classification efficiency and reduce noise interference, discard part of the high-frequency noise from the l complex numbers for each training sample, that is, discard l - k complex numbers starting from the tail. After discarding, it is denoted as {n1, n2,..., n j ,..., n k}, that is, each training sample contains k frequency features after transformation. n k represents the k-th frequency feature corresponding to the training sample. The category labels of the k frequency features in a training sample are all the category label of the training sample. Subsequently, establish a complex triangular fuzzy number κ cj for each frequency feature in each category according to the category label.
[0008] S3: Perform discrete Fourier transform on the sample to be predicted to transform it into the frequency domain, and discard the high-frequency noise of l - k complex numbers starting from the tail, that is, the sample to be predicted includes k frequency features after being transformed into the frequency domain. Establish a complex basic belief assignment function for each frequency feature in the sample to be predicted through the complex triangular fuzzy number κ cj to obtain a set of complex basic belief assignment functions
[0009] S4: Based on Calculate the similarity degree between any two complex basic belief assignment functions through complex belief Beta divergence
[0010] S5: Based on Construct the similarity matrix \(S\) of the set of complex basic belief assignment functions k×k ;
[0011] S6: Based on \(S\) k×k , calculate the support degree of the complex basic belief assignment function and normalize to obtain the credibility weight
[0012] S7: Based on calculate the modified average evidence of the set of complex basic belief assignment functions
[0013] S8: Based on perform \((k - 1)\) times of fusion to obtain the combined result
[0014] S9: Transform into a probability distribution through the complex belief Pignistic transformation
[0015] S10: Select the class with the maximum belief value as the predicted class \(\tau\) of the sample to be predicted based on the arg max method. Make a decision based on the principle of the maximum belief value, and the classification result is as follows
[0016]
[0017] That is, select the label class with the maximum belief value as the classification result.
[0018] Preferably, in the above S2, the process of establishing the complex triangular fuzzy number \(\kappa\) mj is as follows:
[0019] Perform a discrete Fourier transform on the training samples. The formula for the discrete Fourier transform is as follows:
[0020]
[0021] where \(e\) is the natural constant, and the transformed \(n\) k is a complex value. The result of this transformation is called the frequency-domain feature.
[0022] Discard \(l - k\) frequency-domain features from the tail to eliminate high-frequency noise. This step is called feature selection. A time-series sample after feature selection can be expressed as \(\{n_1, n_2,..., n\) j ,..., n k \}.
[0023] Perform the training of the complex triangular fuzzy number. The definition of the complex triangular fuzzy number is as follows:
[0024]
[0025] where κ mj (n j ) represents the membership degree of the training sample belonging to class m calculated based on the frequency domain feature n j , and this membership degree is a complex number, where i is the imaginary unit. The definitions of μ (a,b,e) (x) and μ (r,s,t) (y) are as follows:
[0026]
[0027] where x represents the modulus of the frequency domain feature n j , and y represents the phase of the frequency domain feature n j . a, b, and e respectively represent the lower bound, mean, and upper bound of the modulus of class m in the j-th frequency feature, and r, s, and t respectively represent the lower bound, mean, and upper bound of the phase of class m in the j-th frequency feature.
[0028] For the complex triangular fuzzy number κ mj used to calculate the membership degree of the j-th frequency domain feature to class m, its training process can be expressed by the following formula:
[0029] a = min(X mj ), b = mean(X mj ), c = max(X mj ),
[0030] r = min(Y mj ), s = mean(Y mj ), t = max(Y mj ).
[0031] where min, mean, and max respectively represent the minimum value, average value, and maximum value. X mj and Y mj respectively represent the sets of the j-th frequency features of all training samples with label m in the training set.
[0032] Preferably, in S3, the process of obtaining is as follows:
[0033] For the sample to be predicted, the same Fourier transform and feature extraction steps of discarding high-frequency features as in S2 are adopted. Taking a sample {n′1, n′2,..., n′ j ,..., n′ k} after feature extraction as an example, the generation process of the complex basic belief assignment function set is introduced:
[0034] Let the complex number n′ j = xe iy, that is, x and y are the modulus and phase angle of n′ respectively j The membership degree of the category m can be calculated by the complex triangular fuzzy number as follows: j For other category labels, and so on, generating the same number of membership degrees as the number of categories.
[0035]
[0036] For other category labels, and so on, generating the same number of membership degrees as the number of categories.
[0037] The membership degree also needs a certain transformation process to obtain the complex basic belief assignment function. The process is as follows:
[0038] First, distribute the membership degree to obtain
[0039]
[0040] where 2 C represents the power set of the set C of all category labels, and min represents the minimum value. Here, c is a subset of 2 C This process distributes the membership degree originally assigned to a single category label to the power set of the category label set C.
[0041] For Perform normalization to obtain the complex basic belief assignment function
[0042]
[0043] where c and d represent different sets, and both are subsets of 2 C of the subset.
[0044] Performing the above operations on each frequency feature can obtain the set of complex basic belief assignment functions corresponding to the sample to be predicted
[0045] Preferably, in the S4, the process of calculating is as follows:
[0046] The definition of the complex belief Beta divergence is as follows:
[0047]
[0048] where and are the j-th and p-th complex basic belief assignment functions, cos is the cosine function, and θ Δ is and phase difference, and respectively represent and Let \( \alpha \) be the modulus, and \( \beta \) be a real parameter less than 1, which can be selected from real numbers other than 1 according to the actual situation.
[0049] Based on the above definitions, define the similarity between two complex basic belief assignment functions and is calculated by the following formula:
[0050]
[0051] Preferably, in the step S5, the process of obtaining S k×k is as follows:
[0052] Based on organize the similarity matrix S of the set of complex basic belief assignment functions in the following way k×k :
[0053]
[0054] Preferably, in the step S6, the process of obtaining is as follows:
[0055] Based on S k×k , calculate according to the following formula:
[0056]
[0057] Normalize to obtain The formula for is:
[0058]
[0059] Preferably, in the step S7, the process of obtaining is as follows:
[0060] Based on the idea of weighted average, perform weighted average on the complex basic belief assignment functions according to the credibility weight to implement the conflict resolution strategy.
[0061]
[0062] Preferably, in the step S8, the process of obtaining is as follows:
[0063] To achieve the convergence of the decision result, it is still necessary to fuse the weighted average evidence. According to the complex evidence combination rule, the fusion formula is:
[0064] The complex evidence combination rule is defined as follows:
[0065]
[0066] wherein represents the empty set, represents the degree of support for set d, represents the conflict coefficient, which is calculated by the following formula:
[0067]
[0068] Preferably, in S9, the process of obtaining is as follows:
[0069] Divide the belief belonging to multiple subsets, and use the complex Pignistic transformation for belief assignment to obtain the corresponding probability distribution. The formula is:
[0070]
[0071] where |c| represents the cardinality of set c.
[0072] Preferably, the several time series data are electrocardiogram beat signal ECG time series data, and the category c includes normal signals and certain special disease signals; the complex basic belief assignment function set of electrocardiogram signals is established by the steps of S1 - S2 For a new electrocardiogram beat signal ECG time series data, use the steps of S3 - S10 to finally obtain its predicted category τ.
[0073] Compared with the prior art, the present invention has at least the following advantages:
[0074] 1. The present invention innovatively transforms the time series classification task to the complex domain through the discrete Fourier transform and uses complex methods to solve the time series classification problem throughout the process. In the process of data modeling, the present invention not only depicts the modulus of the frequency characteristics, but also effectively depicts the phase characteristics by virtue of the high - dimensional characteristics of complex numbers. The present invention fully considers the data conflict problem that may occur in the complex evidence theory framework, and proposes an effective conflict management and conflict resolution strategy based on the complex belief BETA divergence, reducing the impact of data conflict on the pattern classification result.
[0075] 2. Compared with the classical machine learning strategy, the present invention has better classification performance on time series data, and the classification accuracy is significantly improved compared with the classical machine learning strategy. BRIEF DESCRIPTION OF THE DRAWINGS
[0076] Figure 1 is a flow chart of the method of the present invention.
[0077] Figure 2This is the overall framework of the method of the present invention.
[0078] Figure 3 For experimental effect comparison (based on accuracy), where (a), (b), (c), and (d) are the accuracy experimental results on different data sets respectively. Specific implementation manners
[0079] The present invention will be further described in detail below.
[0080] To improve the reliability and accuracy of the complex evidence theory in practical applications, it is necessary to propose targeted conflict management strategies. The conflict management strategy for complex evidence can not only optimize the application effect of the complex evidence theory, but also contribute to the further development of the pattern classification method based on the complex evidence theory, enabling it to operate more robustly and accurately when facing complex and changeable real-world situations.
[0081] See Figure 1 and Figure 2 Example 1: A time series classification method based on complex belief Beta divergence, which uses the publicly available electrocardiogram (ECG) data time series as the training set, models the uncertainty in the time series based on time-frequency conversion and triangular fuzzy numbers, performs information fusion and analysis on signals in different frequency domains, and resolves conflicts based on complex belief Beta divergence, thereby realizing the prediction of its category. The method includes the following steps:
[0082] S1: Obtain the ECG time series data of the cardiac rhythm signal. Each ECG time series data of the cardiac rhythm signal consists of a number of sampling points {t1, t2,..., t k ,..., t l} and the category m (including normal signals and certain special disease signals). Each ECG time series data forms a training sample, and the training samples form a training set.
[0083] S2: Perform discrete Fourier transform on the training set and discard the high-frequency noise. Subsequently, establish complex triangular fuzzy numbers according to the training set, in the same way as the claims.
[0084] S3: Perform the same discrete Fourier transform on the new ECG time series data, i.e., the sample to be predicted, and discard the high-frequency noise in the same part. Subsequently, establish a complex basic belief assignment function through the complex triangular fuzzy numbers established in S2 to obtain the set of complex basic belief assignment functions of the ECG signals
[0085] S4: Based on Calculate the similarity degree between any two complex belief assignment functions of the ECG signals
[0086] S5: Based on Establish the similarity matrix of the set of complex basic belief assignment functions of electrocardiogram signals
[0087] S6: Based on Calculate the support degree of any complex belief assignment function of electrocardiogram signals And for Perform normalization to obtain the credibility weight
[0088] S7: Based on Calculate the modified average evidence of the set of complex belief assignment functions of electrocardiogram signals
[0089] S8: Based on Perform (k - 1) times of fusion to obtain the combined result
[0090] S9: Convert to the probability distribution CBet through the complex belief Pignistic transformation.
[0091] S10: Select the category with the maximum belief value as the predicted category τ of the new ECG time series data based on the arg max method ECG .
[0092] Specifically, the process of calculating in S4 is as follows:
[0093] Based on the definition of complex belief Beta divergence:
[0094]
[0095] And based on the formula Calculate the similarity between any two complex belief assignment functions of electrocardiogram signals.
[0096] Specifically, S5 includes the following specific steps:
[0097] Based on Organize the similarity matrix of the set of complex belief assignment functions of electrocardiogram signals in the following way
[0098]
[0099] Specifically, S6 includes the following specific steps:
[0100] Based on Define the support degree of the complex belief assignment function of electrocardiogram signals Calculate according to the following formula
[0101]
[0102] Normalize to obtain the credibility weight of the complex belief assignment function of the electrocardiogram signal The formula is:
[0103]
[0104] Specifically, S7 includes the following specific steps:
[0105] Based on the idea of weighted average, according to the credibility weight Perform weighted average on the complex basic belief assignment function of the electrocardiogram signal to implement the conflict resolution strategy. The modified average evidence of the electrocardiogram signal can be calculated by the following formula:
[0106]
[0107] Specifically, S8 includes the following specific steps:
[0108] To achieve the convergence of the decision result, it is still necessary to fuse the modified average evidence of the electrocardiogram signal According to the complex evidence combination rule, the fusion formula is:
[0109]
[0110] Specifically, S9 includes the following specific steps:
[0111] Divide the belief belonging to multiple subsets, and use the complex Pignistic transformation to perform belief assignment to obtain the corresponding probability distribution. The formula is:
[0112]
[0113] where |c| represents the cardinality of set c.
[0114] Specifically, S9 includes the following specific steps:
[0115] Make a decision based on the principle of the maximum belief value to obtain the classification result
[0116]
[0117] In summary, the embodiment realizes pattern classification of the electrocardiogram signal time series. It includes the following steps: modeling the electrocardiogram signal of the training set based on triangular fuzzy numbers to obtain the corresponding triangular fuzzy number model, and establishing a set of complex belief assignment functions of the electrocardiogram signal for the test set based on this Calculate the similarity of the set of complex belief assignment functions of the electrocardiogram signal based on the complex belief Beta divergence Calculate the support degree of each complex belief assignment function of the electrocardiogram signal And obtain the credibility weight through normalization Perform weighted averaging on the original data based on the credibility weight to obtain the modified average evidence of the electrocardiogram signal Further calculate the fusion result Perform belief assignment based on the complex Pignistic transform to obtain the corresponding probability distribution CBet; then make a decision based on the maximum belief value to generate the pattern classification result τ ECG 。
[0118] Experiment and analysis:
[0119] The datasets selected for the experiment come from the website UCR Time Series. Four datasets are mainly selected: the Two-Lead Electrocardiogram (TLE) dataset, the ECG Five Days (E5D) dataset, the Large Kitchen Appliances (LKA) dataset, and the Worms Two Class (WTC) dataset. And perform pattern classification tasks on these datasets
[0120] The evaluation metric is accuracy Acc. The accuracy is calculated based on the formula, and the formula is
[0121]
[0122] where C is the total number of classes, and N ij represents the number of samples in the i-th class predicted as the j-th class. Accuracy is the core benchmark for measuring the overall classification effect of the model, providing a basic reference for subsequent more detailed performance analysis. Its importance is reflected in the intuitive quantification of the basic capabilities of the classifier and its key role in scenarios with balanced classes and equal error costs
[0123] To optimize the performance of the present invention, in this experiment, the proportional coefficient of the frequency domain features is selected as 0.125. The determination of this value aims to ensure that while reducing noise interference as much as possible, the execution efficiency of the algorithm is optimized, so as to achieve the best balance between the two on the premise of ensuring a certain classification accuracy
[0124] To further verify the effectiveness of the present invention, it is compared with popular mainstream pattern classification algorithms, which are as follows
[0125] DT: Decision tree algorithm
[0126] NB: Naive Bayes algorithm
[0127] SVM: Support vector machine algorithm
[0128] KNN: k-nearest neighbor algorithm
[0129] RF: Random Forest algorithm.
[0130] MLP: Feedforward neural network multi-layer perceptron.
[0131] The time series classification method based on complex reliability Beta divergence proposed in the present invention is called CBB-MSIF.
[0132] The experimental results show that, see Figure 3 , the CBB-MSIF method constructed based on the complex reliability Beta divergence stood out among all the experimental method systems and successfully achieved the highest average accuracy. This result preliminarily demonstrates the performance of the CBB-MSIF method in dealing with complex data classification tasks. In order to further analyze the performance advantages of the CBB-MSIF method and explore the potential mechanism behind it, a comprehensive comparative analysis of the data of each time series set was further carried out. In the process of studying all time series data sets, it was found that the CBB-MSIF method showed better performance than the classic machine learning algorithm. Taking the E5D data set as an example, the classification accuracy of the CBB-MSIF method on this data set is as high as 0.9884, while the highest accuracy that the classic method can achieve on this data set is only 0.8037, and there is a clear gap between the two. Compared with the MLP algorithm based on neural networks, the CBB-MSIF method also has certain advantages. For example, in the WTC data set, the accuracy of the CBB-MSIF method in this data environment is $0.7662$. The highest accuracy of the classic method on this data set is only 0.6234. Despite the complex characteristics of the WTC dataset, the CBB-MSIF method can still stand out in the data classification process by virtue of its effective use of the complex reliability Beta divergence. Similarly, in each time series dataset, the CBB-MSIF method is shown to be leading or has unique advantages in key performance indicators such as classification accuracy, model stability or computational efficiency. This series of detailed data comparison and analysis results strongly demonstrates the advancement and superiority of the CBB-MSIF method in the field of time series data classification, and provides solid data support and theoretical basis for the promotion and expansion of this method in practical applications.
[0133] In short, the present invention proposes a time series classification method based on complex reliability Beta divergence, which, on the one hand, alleviates the conflict problem that is common in complex evidence theory, and on the other hand, makes the pattern classification results reasonable and fully interpretable. The performance of the present invention is better than the current popular mainstream pattern classification algorithm, and can be applied to actual engineering scenarios, making contributions to practical scenarios such as fault diagnosis.
[0134] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.
Claims
1. A time series classification method based on complex confidence Beta divergence, characterized in that: It includes the following steps: S1: Obtain a number of time series data; each time series data consists of a number of sampling points {t1, t2,..., t j ,..., t k ,..., t l} and a class label m. Each time series data forms a training sample, and the training samples form a training set; S2: The training set is used to establish a complex basic belief assignment function generation model. The training samples are subjected to discrete Fourier transform to convert them into the frequency domain. Each training sample obtains l complex numbers, denoted as {n1, n2,..., n j ,..., n k ,..., n l}; For each training sample, part of the high-frequency noise is discarded from the l complex numbers, that is, l - k complex numbers are discarded starting from the tail. After discarding, it is denoted as {n1, n2,..., n j ,..., n k}, that is, each training sample contains k frequency features after conversion. n k represents the k-th frequency feature corresponding to the training sample. The class labels of the k frequency features in a training sample are all the class labels of the training sample. Subsequently, a complex triangular fuzzy number κ cj is established for each frequency feature in each category according to the class label; S3: Perform a discrete Fourier transform on the sample to be predicted, convert it to the frequency domain, and discard the high-frequency noise of l-k complex numbers starting from the tail, that is, the sample to be predicted includes k frequency features after being converted to the frequency domain; through the complex triangular fuzzy number κ cj Establish a complex basic belief assignment function for each frequency feature in the sample to be predicted to obtain a set of complex basic belief assignment functions S4: Based on calculate the similarity between any two complex basic belief assignment functions through the complex reliability Beta divergence S5: Based on establish the similarity matrix S of the set of complex basic belief assignment functions k×k ; S6: Based on S k×k , calculate the support degree of the complex basic belief assignment function and normalize it to obtain the credibility weight S7: Based on calculate the modified average evidence of the set of complex basic belief assignment functions S8: Based on Perform (k - 1) fusions to obtain the combined result S9: Convert to a probability distribution through the complex belief Pignistic transformation S10: Select the class with the maximum confidence value as the predicted class τ of the sample to be predicted based on the arg max method.
2. The time series classification method based on complex belief BETA divergence according to claim 1, wherein: In the above S2, a complex triangular fuzzy number κ is established mj The process is as follows: Perform a discrete Fourier transform on the training samples. The formula for the discrete Fourier transform is as follows: where e is the natural constant, and the transformed n k is a complex value; Conduct training on complex triangular fuzzy numbers. The definition of complex triangular fuzzy numbers is as follows: where k mj (n j ) represents the membership degree of the training sample belonging to category m calculated based on the frequency domain feature n j , where i is the imaginary unit; μ (a,b,e) (x) and μ (r,s,t) (y) are defined as follows: where x represents the modulus of the frequency-domain feature n j and y represents the phase of the frequency-domain feature n j The lower bound, mean, and upper bound of the modulus of the m category in the jth frequency feature are represented by a, b, and e respectively, and the lower bound, mean, and upper bound of the phase of the m category in the jth frequency feature are represented by r, s, and t respectively; For the complex triangular fuzzy number κ used to calculate the membership degree of the j-th frequency domain feature to category m mj , its training process can be expressed by the following formula: a = min(X mj ), b = mean(X mj ), c = max(X mj ), r = min(Y mj ), s = mean(Y mj ), t = max(Y mj ). where min, mean, and max represent the minimum value, average value, and maximum value respectively; X mj and Y mj represent the sets of the j-th frequency features of all training samples with label m in the training set respectively.
3. The time series classification method based on complex belief BETA divergence according to claim 2, characterized in that: In S3, obtaining is as follows: For the sample to be predicted, the same Fourier transform and feature extraction steps of discarding high-frequency features as in S2 are adopted. Taking a sample {n′1, n′2,..., n′ j ,..., n′ k} after feature extraction as an example, the generation process of the set of complex basic belief assignment functions is introduced: Let the complex number be \(n'\) j = \(xe\) iy , that is, \(x\) and \(y\) are the modulus and phase angle of \(n'\) j respectively. Then, the membership degree of \(n'\) to category \(m\) can be calculated by complex trigonometric fuzzy numbers as follows: j For other class labels, and so on, generate the same number of membership degrees as the number of classes. The membership degree also requires a certain conversion process to obtain the complex basic belief assignment function. The process is as follows: First, the membership degree is assigned to obtain Among them, 2 C represents the power set of the set C of all category labels, and min represents the minimum value; here c is 2 C is a subset of, and this process distributes the membership degrees originally assigned to a single category label to the power set of the set C of category labels; For perform normalization to obtain a complex basic belief assignment function where c and d represent different sets and are both subsets of 2 C ; Performing the above operations on each frequency feature can obtain the set of complex basic belief assignment functions corresponding to the sample to be predicted.
4. The time series classification method based on complex belief BETA divergence according to claim 3, characterized in that: In S4, the calculation of is as follows: The definition of the complex belief Beta divergence is as follows: where and are the j-th and p-th complex basic belief assignment functions, cos is the cosine function, and θ Δ is and 's phase difference, and respectively represent and 's modulus, and β is a real number parameter less than 1; Based on the above definitions, the similarity between two basic belief assignment functions of complex numbers and is calculated by the following formula:
5. The time series classification method based on complex belief BETA divergence according to claim 4, characterized in that: In S5, obtaining S k×k is as follows: Based on Organize the similarity matrix S of the set of complex basic belief assignment functions in the following way k×k :
6. A time series classification method based on complex belief BETA divergence according to claim 5, characterized in that: In S6, obtaining is as follows: Based on S k×k , calculate according to the following formula: For perform normalization to obtain The formula is:
7. The time series classification method based on complex belief BETA divergence according to claim 6, characterized in that: In the above S7, obtaining is as follows:
8. The time series classification method based on complex belief BETA divergence according to claim 7, characterized in that: In the above S8, obtaining is carried out as follows: According to the plural evidence combination rule, the fusion formula is: The said complex evidence combination rule is defined as follows: Among them represents the empty set, represents the degree of support for set d, represents the conflict coefficient, which is calculated by the following formula:
9. The time series classification method based on complex belief BETA divergence according to claim 8, wherein: In S9, obtaining is as follows: Where |c| represents the cardinality of the set c.
10. The time series classification method based on complex belief BETA divergence as claimed in claim 9, wherein: The several time series data are electrocardiogram (ECG) beat signal time series data, and the category c includes normal signals and certain special disease signals; the complex basic belief assignment function set of the ECG signal is established by steps S1 - S2. For a new ECG beat signal time series data, the steps S3 - S10 are adopted, and finally its predicted category τ is obtained.