Time sequence fusion and classification method based on quantum evidence theory

Abstract

The invention discloses a time sequence fusion and classification method based on a quantum evidence theory. The method comprises the following steps: converting a time sequence to a frequency domain based on DFT; screening a front low-frequency component by using TFI; amplitude and phase features are extracted respectively, and a GFN model is established; the CDGFN is constructed to represent the two-dimensional uncertainty at the same time; generating a quantum basic probability amplitude QBPA function represented by a complex value in a quantum evidence theory (QET); using a quantum evidence combination rule (QECR) in the QET to fuse the multi-frequency information to generate quantum basic probability distribution (QBPD); and finally, performing classification decision based on the quantum Pignistic probability in the QET. According to the method, the complex number dual Gaussian fuzzy number (CDGFN) and the frequency domain feature extraction technology are introduced, so that the problems of missing of two-dimensional uncertainty expression, difficulty in time domain alignment, low small sample classification precision and the like in an existing time sequence classification method are effectively solved, and the classification accuracy is improved.

Description

Technical Field

[0001] This invention relates to the field of data mining and pattern recognition technology, and in particular to a time series fusion and classification method based on quantum evidence theory. Background Technology

[0002] Time series classification (TSC), a core task of artificial intelligence and data mining, has significant application value in fields such as smart medical diagnosis, industrial fault prediction, and financial analysis. However, in real-world scenarios, data often faces severe class imbalance and the challenge of small sample sizes. For example, in medical monitoring, the number of samples of specific pathological waveforms (such as epileptic seizures) is far fewer than the number of samples of normal rhythms. Although deep learning methods (such as CNN and Transformer) have powerful feature extraction capabilities, they are highly dependent on massive amounts of labeled data and are prone to overfitting under scarce samples. Traditional oversampling techniques (such as SMOTE) often ignore the strict temporal dependencies of time series, and the generated synthetic samples are prone to losing key dynamic features, making it difficult to fundamentally solve the problem of high-precision classification with small samples.

[0003] Furthermore, time series data commonly suffer from temporal misalignment and high-frequency noise interference. Events of the same category (such as heartbeats or equipment vibrations) often shift on the time axis due to differences in their starting points or durations, causing traditional point-to-point matching methods (such as Euclidean distance) to fail. Although algorithms such as Dynamic Time Warping (DTW) can partially alleviate the misalignment problem, they are computationally complex and extremely sensitive to noise. Existing technologies lack effective frequency filtering mechanisms, making it difficult to separate low-frequency components containing core patterns from random high-frequency noise, resulting in a significant decrease in the robustness of the model under complex conditions.

[0004] More critically, existing mainstream methods for handling uncertainty (such as the Triangular Ambiguity Number (TFN) or the Gaussian Ambiguity Number (GFN) based on Dempster-Shafer evidence theory) suffer from a severe lack of dimensionality. These methods are typically defined only in the real domain, capturing only one-dimensional intensity (amplitude) uncertainty of the data while completely ignoring phase information in the frequency domain. Phase is crucial for characterizing the synchronization, delay, and periodic structure of signals; its absence prevents models from fully describing the physical properties of complex signals. Summary of the Invention

[0005] In view of the above-mentioned problems in the existing technology, the technical problem to be solved by the present invention is to solve the problem of insufficient classification accuracy and robustness of existing time series classification methods.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: The present invention uses a publicly available time series dataset, and extracts and fuses the frequency domain features of the time series based on the Discrete Fourier Transform (DFT) and the complex dual Gaussian ambiguity number, thereby achieving accurate classification.

[0007] A time series fusion and classification method based on quantum evidence theory includes the following steps:

[0008] S1: Select several publicly available EEG time-series data. Each EEG time-series data is defined as a time-series sample. Each time-series sample is labeled as normal or abnormal. Several samples constitute an EEG time-series dataset. ;

[0009] S2: Will Each time-series sample is converted into a frequency domain sample via Discrete Fourier Transform (DFT). The time points in each time-series sample are then converted into frequency points in the frequency domain sample. The EEG data at each time point is converted into complex numbers at the frequency points. The label of each frequency domain sample is the same as the label of the corresponding time-domain sample.

[0010] Set frequency domain threshold frequency index ;according to Each frequency domain sample is segmented, and each frequency domain sample is segmented from the first frequency point to... All frequency points B between the current location and the corresponding review points are used as training samples, and all training samples constitute the training set. The labels of the training samples are the same as those of the corresponding frequency domain samples.

[0011] S3: For all positive training samples with normal labels: using the rules of complex number operations, extract the amplitude of the complex number corresponding to each frequency point in each positive training sample. and phase Find the average amplitude and standard deviation of the complex values ​​corresponding to all positive training samples at the b-th frequency point, as well as the average phase and standard deviation of the phase. Then, construct the GFN amplitude membership function model based on the average amplitude and standard deviation of the amplitude at the b-th frequency point. A GFN phase membership function model is constructed based on the phase average value and phase standard deviation at the same frequency point. , B represents the total number of frequency points.

[0012] For all negative training samples labeled as anomaly, the same method as for positive training samples is used to obtain the average amplitude and standard deviation of the amplitude at the b-th frequency point, and a GFN amplitude membership function model is constructed. A GFN phase membership function model is constructed based on the phase average value and phase standard deviation at the b-th frequency point. , .

[0013] S4: For an EEG time series X corresponding to an unknown category, X is transformed into a frequency domain sequence X' using the method in S2, and then the method in S2 is used... Extract the sample to be predicted from X'; substitute the amplitude of the sample to be predicted at the b-th frequency point into... and get and Simultaneously, the phase corresponding to the sample to be predicted at the b-th frequency point is substituted into... and get and .

[0014] S5: Using the membership function values ​​obtained in S4, construct the second set of categories for "normal" and "abnormal" respectively. The membership function of the complex dual Gaussian fuzzy number (CDGFN) for the sample to be predicted when the labels are normal and abnormal is calculated using the frequency points. and The expression is as follows:

[0015] ,

[0016]

[0017] in, Represents the imaginary unit, satisfying .

[0018] S6: Calculate the squares of the amplitudes of the normal and abnormal CDGFN at the b-th frequency point, respectively. and The two squared modulus values ​​are sorted in descending order, and the quantum fundamental probability amplitude (QBPA) function in the initial quantum evidence theory (QET) at the b-th frequency point is generated based on the assignment law. Then, it is normalized to obtain... Repeat the above steps for B frequency points to obtain B sets of quantum fundamental probability amplitude (QBPA) functions.

[0019] S7: Using the quantum evidence combination rule QECR in QET, the B frequency points corresponding to the samples to be predicted are... By merging these components, the overall quantum fundamental probability distribution (QBPD) is obtained. The fusion expression is as follows:

[0020] ,

[0021] in This indicates a quantum interference fusion operation.

[0022] S8: Using the transformation law to fuse the results of S7 Convert to quantum probability Calculate the probability that the sample to be predicted belongs to the normal class. and the probability of belonging to an abnormal class The predicted label for X is the label corresponding to the higher probability value between the normal quantum probability and the abnormal quantum probability.

[0023] Preferably, in step S3, a GFN membership function model is constructed. The steps are as follows, where ,when hour, express ,when hour, express .

[0024] S3-1: Calculate the average amplitude and standard deviation of the amplitude, as well as the average phase and standard deviation of the phase, for the complex number at the b-th frequency point among all positive training samples with the label "normal". The calculation formula is as follows:

[0025] ,

[0026] in, express The mean at the b-th frequency point express The standard deviation at the b-th frequency point.

[0027] S3-2: Will and Substituting into the standard GFN membership function model, we get The calculation formula is as follows:

[0028] .

[0029] Compared with the prior art, the present invention has at least the following advantages:

[0030] This invention effectively addresses the problems of missing two-dimensional uncertainty representation, difficulty in time-domain alignment, and low classification accuracy for small samples in existing time series classification methods by introducing complex dual Gaussian fuzzy number (CDGFN) and frequency domain feature extraction technology, thereby improving the accuracy of classification.

[0031] This invention employs Discrete Fourier Transform (DFT) to convert time-domain features into frequency-domain features. Leveraging the alignment properties of frequency-domain components, it fundamentally eliminates matching errors caused by time-domain feature misalignment, thus improving the reliability of feature fusion. Simultaneously, by constructing CDGFN, this invention achieves, for the first time, simultaneous modeling of frequency-domain amplitude and phase information within the framework of evidence theory. Compared to traditional methods that only utilize real-valued data, this provides a more complete description of the periodicity and volatility of the data. Extensive validation on multiple public datasets demonstrates that the method achieves an average classification accuracy of 88.19%, representing a performance improvement of nearly 20% compared to existing similar evidence theory methods (such as GFN-MSIF and TFN-MSIF), with a standard deviation of only 10.01%, exhibiting extremely high stability.

[0032] This method does not rely on massive amounts of data for parameter iteration. It combines the Threshold Frequency Index (TFI) mechanism to accurately filter low-frequency key information and remove high-frequency noise, making the model significantly superior in scenarios with scarce samples. For example, it achieved a classification accuracy of 100.00% on a dataset (Coffee) with only 56 samples, which is significantly better than deep learning models such as MCNN. This strongly demonstrates its excellent robustness and generalization ability in small sample and high noise interference environments. Attached Figure Description

[0033] Figure 1 This is a schematic diagram illustrating the steps of the model of the present invention.

[0034] Figure 2 This is a schematic diagram of the overall framework of the method of the present invention.

[0035] Figure 3 This is a schematic diagram of the two-dimensional features of a single sample in this invention—amplitude and phase.

[0036] Figure 4 This is a schematic diagram illustrating the construction process of the GFN membership function model of this invention.

[0037] Figure 5 The bar charts show the accuracy comparison between the method of this invention and different classification methods on eight datasets. Figures (a)-(h) respectively show the comparison of classification accuracy on the Wafer, FordA, FordB, TwoLeadECG, ECGFiveDays, WormsTwoClass, ToeSegmentation2, and Coffee datasets.

[0038] Figure 6This is a graph showing the impact of the optimal threshold frequency index (TFI) on classification accuracy in this invention. Figures (a) to (h) respectively show the trend of classification accuracy as a function of TFI on the Wafer, FordA, FordB, TwoLeadECG, ECGFiveDays, WormsTwoClass, ToeSegmentation2, and Coffee datasets. Detailed Implementation

[0039] The present invention will now be described in further detail.

[0040] The method described in this invention can be applied to electroencephalogram (EEG) signal monitoring and diagnosis in smart healthcare. Specifically, the acquired EEG time series is first converted to the frequency domain using Discrete Fourier Transform (DFT) to eliminate time-domain misalignment. Then, low-frequency components containing key physiological rhythms (such as alpha and beta waves) are filtered out using Threshold Frequency Index (TFI), effectively eliminating high-frequency noise such as electromyography artifacts. Subsequently, the energy amplitude and phase synchronization characteristics of brain waves are simultaneously modeled using Complex Dual Gaussian Blur Number (CDGFN), and multi-frequency information is fused using the Quantum Evidence Combination Rule (QECR). This enables high-precision automatic classification and assisted diagnosis of pathological states such as epileptic seizure detection and sleep staging, even in environments with scarce samples or high noise levels.

[0041] See Figures 1-6 The time series fusion and classification method based on quantum evidence theory includes the following steps:

[0042] S1: Select several publicly available EEG time-series data. Each EEG time-series data is defined as a time-series sample. Each time-series sample is labeled as normal or abnormal. Several samples constitute an EEG time-series dataset. ;

[0043] S2: Will Each time-series sample is converted into a frequency domain sample via Discrete Fourier Transform (DFT). The time points in each time-series sample are then converted into frequency points in the frequency domain sample. The EEG data at each time point is converted into complex numbers at the frequency points. The label of each frequency domain sample is the same as the label of the corresponding time-domain sample.

[0044] Set frequency domain threshold frequency index ,generally The value of is much smaller than half the sequence length. ), Indicates the length of the time series of the sample data; according to Each frequency domain sample is segmented, and each frequency domain sample is segmented from the first frequency point to... All frequency points B between the current location and the corresponding review points are used as training samples, and all training samples constitute the training set. The labels of the training samples are the same as those of the corresponding frequency domain samples. This data selection method retains the "low frequency band" frequency component data. The "low frequency band" frequency component data is in complex form. This is based on the principle that the low frequency component contains the main features of the time series, while the high frequency component contains mostly noise.

[0045] S3: For all positive training samples with normal labels: using the rules of complex number operations, extract the amplitude of the complex number corresponding to each frequency point in each positive training sample. and phase Find the average amplitude and standard deviation of the complex values ​​corresponding to all positive training samples at the b-th frequency point, as well as the average phase and standard deviation of the phase. Then, construct the GFN amplitude membership function model based on the average amplitude and standard deviation of the amplitude at the b-th frequency point. A GFN phase membership function model is constructed based on the phase average value and phase standard deviation at the same frequency point. , B represents the total number of frequency points; the same method is used to construct corresponding frequency points for each of the B frequency points. and ;

[0046] For all negative training samples labeled as anomaly, the same method as for positive training samples is used to obtain the average amplitude and standard deviation of the amplitude at the b-th frequency point, and a GFN amplitude membership function model is constructed. A GFN phase membership function model is constructed based on the phase average value and phase standard deviation at the b-th frequency point. , ;

[0047] S4: For an EEG time series X corresponding to an unknown category, X is transformed into a frequency domain sequence X' using the method in S2, and then the method in S2 is used... Extract the sample to be predicted from X'; substitute the amplitude of the sample to be predicted at the b-th frequency point into... and get and Simultaneously, the phase corresponding to the sample to be predicted at the b-th frequency point is substituted into... and get and ;

[0048] S5: Using the membership function values ​​obtained in S4, construct the second set of categories for "normal" and "abnormal" respectively. The membership function of the complex dual Gaussian fuzzy number (CDGFN) for the sample to be predicted when the labels are normal and abnormal is calculated using the frequency points. and The expression is as follows:

[0049] ,

[0050]

[0051] in, Represents the imaginary unit, satisfying This step combines the magnitude membership degree and phase membership degree in the real number field to generate complex membership degrees that contain two-dimensional uncertainty information.

[0052] S6: Calculate the squares of the amplitudes of the normal and abnormal CDGFN at the b-th frequency point, respectively. and The two squared modulus values ​​are sorted in descending order, and the initial quantum fundamental probability amplitude (QBPA) function at the b-th frequency point is generated based on the assignment law. Then, it is normalized to obtain... Repeat the above steps for B frequency points to obtain B sets of quantum fundamental probability amplitude (QBPA) functions.

[0053] S7: Using the quantum evidence combination rule QECR, the B frequency points corresponding to the samples to be predicted are... By merging these components, the overall quantum fundamental probability distribution (QBPD) is obtained. The fusion expression is as follows:

[0054] ,

[0055] in This indicates a quantum interference fusion operation; this section uses the principle of quantum interference for fusion, which utilizes the interference properties of complex numbers to enhance consistent evidence and weaken conflicting evidence.

[0056] S8: Using the transformation law to fuse the results of S7 Convert to quantum probability Calculate the probability that the sample to be predicted belongs to the normal class. and the probability of belonging to an abnormal class The predicted label for X is the label corresponding to the larger probability value between the normal quantum probability and the abnormal quantum probability. The conversion law is existing technology.

[0057] Specifically, in S3, a GFN membership function model is constructed. The steps are as follows, where ,when hour, express ,when hour, express ;

[0058] S3-1: Calculate the average amplitude and standard deviation of the amplitude, as well as the average phase and standard deviation of the phase, for the complex number at the b-th frequency point among all positive training samples with the label "normal". The calculation formula is as follows:

[0059] ,

[0060] in, express The mean at the b-th frequency point express The standard deviation at the b-th frequency point;

[0061] S3-2: Will and Substituting into the standard GFN membership function model, we get The calculation formula is as follows:

[0062] .

[0063] Experimental content and results

[0064] To verify the effectiveness of this invention, experiments were conducted using eight publicly available datasets from different domains in the UCR time series repository, including Wafer, FordA, FordB, TwoLeadECG, ECGFiveDays, WormsTwoClass, ToeSegmentation2, and Coffee. These datasets cover sequence lengths ranging from 152 to 500 and sample sizes ranging from 56 to 7164. Coffee (56 samples) and ToeSegmentation2 (166 samples), among others, are typical small-sample datasets, effectively testing the model's adaptability to different data scales. The experiments employed ten-fold cross-validation as the evaluation mechanism and compared the proposed method (CDGFN-MSIF, CM) with three existing mainstream methods: evidence-based methods (TFN-MSIF, GFN-MSIF), deep learning-based methods (MLP, MCNN, t-LeNet, MCDCNN), and traditional machine learning methods (decision trees, SVM, AdaBoost, gradient boosting).

[0065] Experimental results show that this invention significantly improves overall classification accuracy. For example... Figure 5As shown in the figure, this bar chart with error bars visually compares the classification accuracy of the proposed method (CM) with decision trees, SVM, deep learning models (MCNN, etc.), and existing evidence theory methods (GM, TM) on eight different datasets. In the comparison of these eight datasets, the red bar representing the proposed method (CM) achieved the best classification results in six datasets, including FordA and FordB. Statistical data shows that the average accuracy of the proposed method reached 88.19%, and... Figure 5 The shorter error bars corresponding to the red bars in the graph (standard deviation of only 10.01%) visually reflect the algorithm's extremely high stability. Compared with existing methods within the same evidence theory framework, this invention significantly surpasses the GM method's 66.36% and the TM method's 64.89%, representing an improvement of nearly 20%. This fully demonstrates the overwhelming advantage of introducing CDGFN to capture two-dimensional information (amplitude and phase) in the frequency domain compared to methods using only one-dimensional real-valued features.

[0066] Furthermore, this invention demonstrates superior performance advantages in small sample scenarios. For example... Figure 5 Subplot (h) (i.e., the test results for the Coffee dataset) highlights the performance differences of various models with extremely small sample sizes. On the Coffee dataset with only 56 samples, the accuracy of deep learning-based MCNN is only 38.00%, and t-LeNet is only 53.60% (as shown by the yellow bars in the figure), while the present invention (red bars) achieves 100.00% accuracy. Similarly, on the WormsTwoClass dataset, the present invention also outperforms models such as MCDCNN. This result strongly demonstrates that the present invention can still extract effective features and make accurate decisions even in the absence of a large amount of labeled data, filling the gap in deep learning in the small sample domain.

[0067] Finally, multiple analytical experiments further verified the effectiveness and design rationality of the core components of this invention. For example... Figure 6As shown in the line trend graph, this graph depicts the trajectory of classification accuracy in various datasets as the Threshold Frequency Index (TFI) increases from low frequency to the full frequency band. With the increase of TFI (i.e., the introduction of more high-frequency components), the classification accuracy of most datasets (such as FordA and ToeSegmentation2) shows a downward trend. This demonstrates that the high-frequency part of the time series is mainly composed of noise. The present invention uses the TFI mechanism to filter the initial low-frequency components, which can effectively filter noise and significantly improve classification robustness. Simultaneously, ablation experiments based on this invention also demonstrate the numerical comparison of accuracy between the complete model (CM) and variant models after removing different core components. Data shows that if the frequency selection mechanism is removed (W / o frequency selection), the average accuracy of the model drops significantly from 88.19% to 72.80%; if the CDGFN structure is removed (only real GFN separation processing is used, W / o CDGFN), the average accuracy drops to 80.15%. This quantitatively demonstrates that the joint representation in the complex domain enhances the fusion effect of multi-source information through quantum interference effects. Furthermore, this invention also examines the final classification accuracy when using Discrete Fourier Transform (DFT) and Hilbert Transform as preprocessing methods. Results show that the DFT method (average accuracy 88.19%) significantly outperforms the Hilbert Transform method (average accuracy 69.67%), and DFT achieves higher accuracy on all eight datasets, validating the rationality and efficiency of choosing DFT as the frequency domain feature extraction method.

[0068] In summary, this invention proposes a time series classification method based on CDGFN and quantum multi-source information fusion, which outperforms current popular mainstream algorithms in terms of accuracy, stability, and small sample adaptability, and has extremely high practical application value.

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A time series fusion and classification method based on quantum evidence theory, characterized by: Includes the following steps: S1: Select several publicly available EEG time-series data. Each EEG time-series data is defined as a time-series sample. Each time-series sample is labeled as normal or abnormal. Several samples constitute an EEG time-series dataset. ; S2: Will Each time-series sample is converted into a frequency domain sample via Discrete Fourier Transform (DFT). The time points in each time-series sample are then converted into frequency points in the frequency domain sample. The EEG data at each time point is converted into complex numbers at the frequency points. The label of each frequency domain sample is the same as the label of the corresponding time-domain sample. Set frequency domain threshold frequency index ;according to Each frequency domain sample is segmented, and each frequency domain sample is segmented from the first frequency point to... All frequency points B between the current location and the corresponding review points are used as training samples, and all training samples constitute the training set. The labels of the training samples are the same as those of the corresponding frequency domain samples; S3: For all positive training samples with normal labels: using the rules of complex number operations, extract the amplitude of the complex number corresponding to each frequency point in each positive training sample. and phase Find the average amplitude and standard deviation of the complex values ​​corresponding to all positive training samples at the b-th frequency point, as well as the average phase and standard deviation of the phase. Then, construct the GFN amplitude membership function model based on the average amplitude and standard deviation of the amplitude at the b-th frequency point. A GFN phase membership function model is constructed based on the phase average value and phase standard deviation at the same frequency point. , B represents the total number of frequency points; For all negative training samples labeled as anomaly, the same method as for positive training samples is used to obtain the average amplitude and standard deviation of the amplitude at the b-th frequency point, and a GFN amplitude membership function model is constructed. A GFN phase membership function model is constructed based on the phase average value and phase standard deviation at the b-th frequency point. , ; S4: For an EEG time series X corresponding to an unknown category, X is transformed into a frequency domain sequence X' using the method in S2, and then the method in S2 is used... Extract the sample to be predicted from X'; substitute the amplitude of the sample to be predicted at the b-th frequency point into... and get and Simultaneously, the phase corresponding to the sample to be predicted at the b-th frequency point is substituted into... and get and ; S5: Using the membership function values ​​obtained in S4, construct the second set of categories for "normal" and "abnormal" respectively. The membership function of the complex dual Gaussian fuzzy number (CDGFN) for the sample to be predicted when the labels are normal and abnormal is calculated using the frequency points. and The expression is as follows: ， in, Represents the imaginary unit, satisfying ; S6: Calculate the squares of the amplitudes of the normal and abnormal CDGFN at the b-th frequency point, respectively. and The two squared modulus values ​​are sorted in descending order, and the quantum fundamental probability amplitude (QBPA) function for the initial quantum evidence theory at the b-th frequency point is generated based on the assignment law. Then, it is normalized to obtain... Repeat the above steps for B frequency points to obtain B sets of quantum fundamental probability amplitude (QBPA) functions. S7: Using the quantum evidence combination rule QECR in QET, the B frequency points corresponding to the samples to be predicted are... By merging them, the overall quantum fundamental probability distribution is obtained. The fusion expression is as follows: ， in This indicates a quantum interference fusion operation; S8: Using the transformation law to fuse the results of S7 Convert to quantum probability Calculate the probability that the sample to be predicted belongs to the normal class. and the probability of belonging to an abnormal class The predicted label for X is the label corresponding to the higher probability value between the normal quantum probability and the abnormal quantum probability.

2. The time series fusion and classification method based on quantum evidence theory as described in claim 1, characterized in that: In S3, a GFN membership function model is constructed. The steps are as follows, where ,when hour, express ,when hour, express ; S3-1: Calculate the average amplitude and standard deviation of the amplitude, as well as the average phase and standard deviation of the phase, for the complex number at the b-th frequency point among all positive training samples with the label "normal". The calculation formula is as follows: ， in, express The mean at the b-th frequency point express The standard deviation at the b-th frequency point; S3-2: Will and Substituting into the standard GFN membership function model, we get The calculation formula is as follows: 。

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