Heterogeneous complex data set-oriented multi-scale time entropy evaluation method

Abstract

The invention provides a heterogeneous complex data set-oriented multi-scale time entropy evaluation method, which belongs to the technical field of time sequence analysis, and comprises the following steps of: S1, performing down-sampling on an initial time sequence, dividing the initial time sequence into subsequences on different time scales, and then processing the subsequences by applying a time window method, obtaining a plurality of clustering windows; s2, calculating an entropy value in each clustering window, and averaging the entropy values of all the clustering windows to obtain a multi-scale time entropy; and S3, according to the obtained multi-scale time entropy, carrying out comprehensive evaluation on the initial time sequence. According to the multi-scale time entropy evaluation method for the heterogeneous complex data set, the method has extremely high generalization ability, so that the evaluation of the model performance is more accurate and reliable, and the method is suitable for wide practical application scenes.

Description

Technical Field

[0001] The present invention relates to the technical field of time series analysis, and in particular to a multi-scale time entropy evaluation method for heterogeneous and complex data sets. Background Art

[0002] In the modern data-driven world, the application of time series forecasting technology has become increasingly widespread and important. Whether it is predicting stock prices in financial markets, demand forecasting in the energy field, or predicting traffic flow in smart city management, these applications rely on accurate time series forecasting to support decision making and resource optimization. As the application areas continue to expand, the data sets involved have become more diverse and complex. This diversity and complexity of data has brought new challenges to the development, optimization, and application of time series forecasting models.

[0003] Traditional time series forecasting models, such as the Autoregressive Integrated Moving Average (ARIMA) model, have performed well in processing short-term linear data and have therefore been widely used in many fields. However, as the size and complexity of data increase, the limitations of traditional models have gradually become apparent. For example, the linear assumption of the ARIMA model may not be able to effectively handle data with nonlinear or long-term dependent features. To address these challenges, deep learning models such as long short-term memory networks (LSTM) and Transformer-based models (such as Fedformer, Autoformer, Pyraformer, and DynEformer) have become key tools in research and practice. These advanced models are able to better handle complex nonlinear and long-term dependent data by introducing innovative feature extraction and modeling mechanisms.

[0004] Although these advanced models perform well in processing complex time series data, their success often depends on the quality and characteristics of the dataset. During the forecasting process, the characteristics of different datasets (such as periodicity, trend, complexity, and information density) may lead to significant differences in forecast results. If the dataset characteristics are not analyzed in detail, it is difficult to determine whether these differences are caused by the dataset characteristics or the model itself. This uncertainty poses a challenge to the interpretability and application effect of the model, and may lead to misjudgment of the model performance, thus affecting its application in practical scenarios.

[0005] In addition, the prior art also has the following defects:

[0006] (1) Applicability issues caused by data set diversity: Different data sets may have different characteristics, such as linearity and nonlinearity, short-term and long-term, regularity and randomness. These characteristics directly affect the applicability of the selected model. For example, the traditional ARIMA model performs better when processing short-term linear data, while LSTM and Transformer perform better when processing nonlinear and long-term data. How to select an appropriate prediction model based on the characteristics of the data set has become a key challenge.

[0007] (2) The impact of dataset complexity on prediction accuracy: Complex datasets often contain multiple noises and abnormal patterns, which places higher demands on the prediction ability of the model. Existing prediction evaluation methods mainly rely on mean absolute error (MAE) and mean square error (MSE), but these methods may not fully reflect the complexity and inherent patterns of the dataset, resulting in decreased prediction accuracy. A tool that can comprehensively evaluate the complexity of the dataset is needed to ensure the prediction ability of the model in practical applications.

[0008] (3) Challenges of dataset characteristics to model interpretability: During the model prediction process, the characteristics of different datasets (such as periodicity, trend, complexity, and information density) may lead to significant differences in prediction results. Without a detailed analysis of the dataset characteristics, it is difficult to determine whether these differences are caused by the dataset characteristics or the model itself. This uncertainty poses a challenge to the interpretability and application effect of the model, and may lead to misjudgment of the model performance, thus affecting its application in practical scenarios. Summary of the invention

[0009] The purpose of the present invention is to provide a multi-scale time entropy evaluation method for heterogeneous and complex data sets. The method has extremely high generalization ability, making the evaluation of model performance more accurate and reliable, and suitable for a wide range of practical application scenarios.

[0010] To achieve the above object, the present invention provides a multi-scale temporal entropy evaluation method for heterogeneous and complex data sets, comprising the following steps:

[0011] Step S1, down-sample the initial time series, divide it into sub-sequences at different time scales, and then apply the time window method to process the sub-sequences to obtain multiple clustering windows;

[0012] Step S2, calculating the entropy value in each clustering window, and averaging the entropy values ​​of all clustering windows to obtain multi-scale time entropy;

[0013] Step S3: Comprehensively evaluate the initial time series based on the obtained multi-scale time entropy.

[0014] Preferably, in step S1, the initial time series is downsampled and divided into subsequences at different time scales, and then the subsequences are processed by applying a time window method to obtain multiple clustering windows. The specific operations are:

[0015] For a given initial time series {X1,X2,…,X N}, the downsampling scale τ and the clustering window length W are used to generate the downsampled subsequence. For each clustering window position, the clustering window contains:

[0016]

[0017] in, is obtained by starting from the initial time series {X1,X2,…,X N}, where x is the subsequence obtained by taking a sample every τ; kτ+1 Represents the sample point at position kτ+1 in the time series.

[0018] Preferably, in step S2, the entropy values ​​of all clustering windows are averaged to obtain multi-scale time entropy, and the specific operation is:

[0019]

[0020] Where M is the total number of clustering windows; j is the position index in the clustering window, indicating the position of a specific sample in the current clustering window. The value range of j is from k to k+W-1, indicating the index of each downsampled data point in clustering window k. H represents the number of times a specific pattern or data point appears at position j in the clustering window in the downsampled sequence; τ (X) represents the evaluation results of the multi-scale temporal entropy based paradigm under different downsampling scales τ.

[0021] Preferably, in step S3, a comprehensive evaluation is performed on the initial time series according to the obtained multi-scale time entropy, and the specific operation is as follows:

[0022]

[0023] Among them, α is the coefficient of the multi-scale time entropy based method; β is the coefficient of the regularization term; is the regularization term entropy of a specific feature F; It represents the final evaluation result of the multi-scale time entropy of the time series at different downsampling scales τ after considering the regularization effect of specific features.

[0024] Preferably, in step S3, four regularization terms are introduced, including a periodic regularization term, a trend regularization term, a complexity regularization term and an information regularization term.

[0025] Preferably, in step S3, the periodic regularization term calculation formula is as follows:

[0026]

[0027] in, represents the evaluation result of the multi-scale time entropy regularization term based on the ensemble empirical mode decomposition (EEMD); m is the number of intrinsic mode functions (IMFs) obtained by the ensemble empirical mode decomposition; N is the length of the time series; IMF i(τ,t) represents the value of the i-th intrinsic mode function at the downsampling scale τ and time point t. This formula measures the periodicity of the time series at different scales by calculating the energy share of each IMF and combining it with the logarithmic entropy function.

[0028] Preferably, in step S4, the trend regularization term calculation formula is as follows:

[0029]

[0030] in, Represents the evaluation result of the multi-scale time entropy regularization term based on the variational embedding multi-scale sample entropy; is the count of the downsampled sequence with embedding dimension θ at position j. This formula measures the trend of the time series under different downsample scales τ and embedding dimensions θ by calculating the probability of occurrence of different patterns in each clustering window and combining the logarithmic entropy function.

[0031] Preferably, in step S4, the complexity regularization term calculation formula is as follows:

[0032]

[0033] in, represents the evaluation result of the multi-scale time entropy regularization term based on the refined composite multi-scale permutation entropy; δ is the delay parameter; is the Φth subsequence of the kth permutation under the downsampling scale τ; represents the count of the k-th permutation in the Φ-th subsequence; N k is the total number of subsequences or permutations extracted from the time series in the kth clustering window under the downsampling scale τ and the delay parameter δ.

[0034] The formula measures the complexity of the time series at different downsampling scales τ and delay parameters δ by calculating the probability of occurrence of different arrangement patterns in each clustering window and combining it with the logarithmic entropy function.

[0035] Preferably, in step S4, the information density regularization term calculation formula is as follows:

[0036]

[0037] in, It represents the evaluation result of the multi-scale time entropy regularization term based on Tsallis permutation entropy, which is used to evaluate the information density of time series at different downsampling scales τ. q is an adjustable parameter of Tsallis entropy; represents the number of occurrences of a certain pattern within a given clustering window; λ represents the embedding dimension for the jth subsequence at the downsampling scale τ in time series analysis.

[0038] Therefore, the present invention adopts the above-mentioned multi-scale time entropy evaluation method for heterogeneous and complex data sets, and the beneficial technical effects are as follows:

[0039] (1) This paper proposes a multi-scale time entropy evaluation method, which aims to overcome the limitation of relying solely on traditional indicators such as MAE and MSE to measure model performance. This method can not only deeply analyze the objective characteristics of time series data sets from multiple perspectives, but also pre-evaluate model performance through comprehensive analysis, providing an important basis for subsequent model optimization.

[0040] (2) By adopting a multi-scale and time window approach, the present invention can carefully evaluate time series data sets at different time scales. This method can not only fully capture long-term trends and short-term fluctuations, but also effectively reveal the complex dynamic characteristics in the data, thereby more comprehensively understanding the data behavior.

[0041] (3) The present invention can identify and analyze the characteristics of different data sets and explain the root causes of differences in model performance. By comprehensively evaluating multiple characteristics of time series, the method demonstrates extremely high generalization ability, making the evaluation of model performance more accurate and reliable, and applicable to a wide range of practical application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A flowchart of a multi-scale temporal entropy evaluation method for heterogeneous and complex data sets according to the present invention;

[0043] Figure 2 This is a diagram illustrating the principle of the multi-scale time entropy evaluation method;

[0044] Figure 3 This is a diagram showing the effectiveness of the multi-scale time evaluation results and model prediction results; Figure 3 (a) is the comparison of MSE results of each model; Figure 3 (b) is the comparison of MAE results of each model; Figure 3 (c) in the figure is a comparison of the multi-scale time entropy evaluation results of each data set. DETAILED DESCRIPTION

[0045] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0046] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0047] Embodiment 1

[0048] The present invention improves the Shannon entropy formula by introducing multi-scale and time window methods, forming a new theoretical framework. While retaining the core advantage of Shannon entropy in measuring information uncertainty, this framework is optimized for the specific needs of time series data sets. This improved method allows for more flexible adjustment of the time scale and window size of the evaluation to accommodate time series data of different types and characteristics. When processing time series data, the traditional Shannon entropy method often fails to fully capture the changes and complexity of the data in the time dimension. To solve this problem, the present invention introduces a multi-scale analysis method to decompose and analyze the time series data set at different time scales, thereby being able to more comprehensively capture the multi-level structure and dynamic characteristics of the data. At the same time, the time window method is adopted, so that the window size can be flexibly adjusted as needed during the analysis process, so as to better adapt to local changes and long-term trends in the data. Its principle diagram is shown as follows Figure 2 As shown. In addition, the framework of the present invention allows the integration of regularization terms based on multi-scale analysis to take into account the diverse characteristics of time series. This approach makes the assessment of trends, periodicity, complexity and information density in the data more comprehensive and precise.

[0049] Specifically, Figure 1 FIG. 1 is a flowchart of a multi-scale time entropy evaluation method for heterogeneous and complex data sets according to the present invention, comprising the following steps:

[0050] Step S1: downsample the initial time series, divide it into subsequences at different time scales, and then process the subsequences using the time window method to obtain multiple clustering windows. The specific operations are as follows:

[0051] For a given initial time series {X1,X2,…,X N}, the downsampling scale τ and the clustering window length W are used to generate the downsampled subsequence. For each clustering window position, the clustering window contains:

[0052]

[0053] in, is obtained by starting from the initial time series {X1,X2,…,X N}, where x is the subsequence obtained by taking a sample every τ; kτ+1 Represents the sample point at position kτ+1 in the time series.

[0054] Step S2: Calculate the entropy value in each clustering window and average the entropy values ​​of all clustering windows to obtain multi-scale time entropy. The specific operation is:

[0055]

[0056] Where M is the total number of clustering windows; j is the position index in the clustering window, indicating the position of a specific sample in the current clustering window. The value range of j is from k to k+W-1, indicating the index of each downsampled data point in clustering window k. H represents the number of times a specific pattern or data point appears at position j in the clustering window in the downsampled sequence; τ (X) represents the evaluation results of the multi-scale temporal entropy based paradigm under different downsampling scales τ.

[0057] This method effectively integrates the information of time series at different scales, thereby revealing the overall complexity and structural characteristics of the time series.

[0058] Step S3: Based on the obtained multi-scale time entropy, a comprehensive evaluation is performed on the initial time series. The specific operation is as follows:

[0059]

[0060] Among them, α is the coefficient of the multi-scale time entropy based method; β is the coefficient of the regularization term; is the regularization term entropy of a specific feature F; It represents the final evaluation result of the multi-scale time entropy of the time series at different downsampling scales τ after considering the regularization effect of specific features.

[0061] This improved approach enables detailed assessment of features such as periodicity, trend, stability, and information density at multiple scales, revealing the deep characteristics and complexity of the data.

[0062] The present invention also introduces four regularization terms, including a periodic regularization term, a trend regularization term, a complexity regularization term and an information regularization term.

[0063] Periodic regularity:

[0064] Periodicity is a common feature in time series, which refers to patterns that repeat at regular time intervals. This repeatability usually reflects certain regular behaviors or periodic processes, such as seasonal changes, diurnal cycles, economic cycles, etc. Ensemble empirical mode decomposition (EEMD) is an improved method of empirical mode decomposition (EMD). By introducing white noise and averaging multiple decomposition results, EEMD overcomes the inherent mode aliasing problem in EMD. Due to its strong adaptability, multi-scale decomposition capability and noise resistance, EEMD has unique advantages in the periodic analysis of time series. It can accurately extract the periodic components in the data and quantify the energy distribution of these components, providing an effective method for the periodic analysis of time series. Combining the EEMD transformation with the original formula, the specific steps are as follows:

[0065] First, the time series {X1,X2,…,X N} to obtain m intrinsic mode functions (IMFs). For each IMF, the ratio of its energy to the total energy is calculated, denoted by p i :

[0066]

[0067] Based on the multi-scale time entropy paradigm, EEMD decomposition is introduced and the entropy is calculated by considering the energy ratio of each IMF. The transformed formula is as follows:

[0068]

[0069] in, represents the evaluation result of the multi-scale time entropy regularization term based on the ensemble empirical mode decomposition (EEMD); m is the number of intrinsic mode functions (IMFs) obtained by the ensemble empirical mode decomposition; N is the length of the time series; IMF i(τ,t) represents the value of the i-th intrinsic mode function at the downsampling scale τ and time point t. This formula measures the periodicity of the time series at different scales by calculating the energy share of each IMF and combining it with the logarithmic entropy function.

[0070] Trend regularization term:

[0071] Trend is an important feature in time series, manifested as a pattern of increase, decrease or stability that persists over a long time frame. Unlike seasonality, which reflects a periodic pattern, trend reflects the global characteristics of the time series and is usually observed on a larger time scale. Variational Embedding Multiscale Sample Entropy (VEMSE) is an advanced algorithm for analyzing multi-channel systems. It addresses the imbalance of traditional multiscale sample entropy (MMSE) in these aspects through variational processing of embedding dimension and data length. VEMSE is able to capture long-term trends in time series data more accurately by combining multiscale analysis and variational embedding. The change in entropy values ​​at different scales and embedding dimensions quantifies the trend of the time series. Trend leads to significant entropy changes at larger scales, thereby achieving effective extraction and quantification of trend features.

[0072] In the VEMSE algorithm, each subsequence The embedding dimension m j is variable, not fixed. Therefore, based on the original formula, a unique embedding dimension m is introduced for each subsequence j , and recalculate the probability distribution and entropy value accordingly. Therefore, the formula for processing trend can be expressed as:

[0073]

[0074] in, Represents the evaluation result of the multi-scale time entropy regularization term based on the variational embedding multi-scale sample entropy; is the count of the downsampled sequence with embedding dimension θ at position j. This formula measures the trend of the time series under different downsample scales τ and embedding dimensions θ by calculating the probability of occurrence of different patterns in each clustering window and combining the logarithmic entropy function.

[0075] Complexity regularization term:

[0076] In time series analysis, complexity usually refers to the comprehensive manifestation of chaotic, random and nonlinear characteristics of time series. Complex time series exhibit dynamic changes, nonlinear characteristics and a certain degree of randomness, making their prediction and analysis challenging. Refined Composite Multiscale Permutation Entropy (RCMPE) is a method further developed on the basis of Multiscale Permutation Entropy (MPE). RCMPE combines the advantages of multiscale analysis and permutation entropy, and can capture the nonlinear dynamic characteristics and complexity of time series in more detail. By calculating the permutation entropy at different time scales and combining the results, RCMPE provides a more comprehensive description of the complexity of the series. It can thoroughly evaluate the complexity of time series and avoid the problem of over-simplification or smoothing of time scales in traditional methods. RCMPE is suitable for analyzing complex and nonlinear time series, and effectively deals with series with multiple dynamic characteristics. The formula is as follows:

[0077]

[0078] in, represents the evaluation result of the multi-scale time entropy regularization term based on the refined composite multi-scale permutation entropy; δ is the delay parameter; is the Φth subsequence of the kth permutation under the downsampling scale τ; represents the count of the k-th permutation in the Φ-th subsequence; N k is the total number of subsequences or permutations extracted from the time series in the kth clustering window under the downsampling scale τ and the delay parameter δ.

[0079] The formula measures the complexity of the time series at different downsampling scales τ and delay parameters δ by calculating the probability of occurrence of different arrangement patterns in each clustering window and combining it with the logarithmic entropy function.

[0080] Information density rule:

[0081] In time series analysis, information density describes the distribution and variation of information in time series data, revealing trends, seasonality, and complexity. Challenges in analyzing information density include the nonlinearity and nonstationarity of time series, multi-scale characteristics, noise and outliers, and computational complexity. Multiscale Tsallis permutation entropy (MTPE) has significant advantages in analyzing information density because Tsallis entropy is a non-additive entropy that can better handle complex systems with long-range dependencies and fractal characteristics. MTPE is able to capture the multi-fractal characteristics and potential patterns of time series at different time scales. By introducing the concept of permutation entropy, it enhances resistance to noise and outliers. In addition, the adjustable parameter q in Tsallis entropy makes the calculation more flexible and can adapt to different types of time series. Introducing the MTPE framework into the original formula, the formula is as follows:

[0082]

[0083] in, It represents the evaluation result of the multi-scale time entropy regularization term based on Tsallis permutation entropy, which is used to evaluate the information density of time series at different downsampling scales τ. q is an adjustable parameter of Tsallis entropy; represents the number of occurrences of a certain pattern within a given clustering window; λ represents the embedding dimension for the jth subsequence at the downsampling scale τ in time series analysis.

[0084] The present invention will be further described below through specific examples.

[0085] 1) Experimental design

[0086] Six representative time series forecasting models are selected as benchmarks in this experiment: Fedformer, Pyraformer, Informer, Autoformer, Reformer, and ETSformer. In order to comprehensively evaluate the performance of these models on different time series data, nine datasets from multiple fields are selected, including network, traffic, weather, energy, and economy. These datasets are used to test the effectiveness of multi-scale time entropy evaluation methods in identifying time series features and evaluating model performance.

[0087] 2) Dataset selection

[0088] Edge cloud upload bandwidth workload data:

[0089] Datasets of commercial crowdsourced edge clouds ECW-08 and ECW-09: The edge cloud infrastructure consists of self-built, recruited, and user-rented heterogeneous devices. The platform contains 5,174 devices distributed across the country and serves more than 40 typical applications.

[0090] ECW-New App dataset: This dataset contains workload sequences of applications that have never appeared in ECW and is used to verify the ability of the proposed method to evaluate new network datasets.

[0091] ETTm1 and ETTm2 datasets: record the operation data of power transformers and are used to study the prediction of energy consumption and equipment maintenance.

[0092] ECL dataset: provides electricity consumption information of a large number of customers, which helps in energy demand forecasting and load management.

[0093] Exchange dataset: Contains exchange rate data from multiple countries, suitable for financial market forecasting and risk management.

[0094] Traffic dataset: provides traffic flow information and is suitable for traffic flow prediction and optimization.

[0095] Weather dataset: records various meteorological parameters, providing a rich source of data for weather forecasting and climate research.

[0096] 3) Experimental methods

[0097] The multi-scale time entropy evaluation method is used to analyze these time series data to evaluate their seasonality, trend, stability and information density. In order to effectively test the impact of the regularization term designed for a specific feature, the regularization parameter α is set to 0. Subsequently, the multi-scale time entropy evaluation results are compared with the mean absolute error (MAE) and mean square error (MSE) of each model on different data sets. This comparison aims to verify the effectiveness of the multi-scale time entropy evaluation method in identifying time series features and evaluating model performance.

[0098] 4) Experimental results

[0099] Table 1 Model prediction results

[0100]

[0101] Table 2 Multi-scale time entropy evaluation results

[0102] Characterisic ETTm1 ETTm2 ECL Weather Traffic Exchange ECW_08 ECW_newapp ECW_09 Trend 0.399 0.531 0.806 0.436 1.179 0.174 0.673 0.753 0.926 Seasonal 0.824 0.953 0.983 1.155 1.307 0.703 1.223 1.080 0.946 Information density 0.813 0.808 0.775 0.770 0.814 0.776 0.811 0.667 0.806 Complex 1.594 1.139 1.286 1.357 1.389 1.629 1.379 1.600 1.384

[0103] For the multi-scale temporal entropy evaluation method, the size of the eigenvalue reflects the complexity of the dataset in terms of seasonality, trend, stability, and information density. Smaller eigenvalues ​​indicate that the dataset is relatively simple in terms of these features and is therefore easier to evaluate and predict. Therefore, these datasets usually perform better on models designed to target these features. Figure 3 Visual analysis results are presented.

[0104] For models that were improved to capture seasonality, such as Fedformer, Autoformer, and Pyraformer, these models showed excellent forecasting performance on datasets with strong seasonality estimates, such as ETTm1, ETTm2, ECW-09, and Exchange. However, due to the high complexity of the Exchange dataset, models designed for complexity, such as Informer and Reformer, did not perform well. Similarly, the ECW-New App dataset also has high complexity, resulting in lower forecasting accuracy for Reformer. However, since this dataset performs best in terms of information density, the Informer model, which combines temporal fusion encoding to enhance the perception of temporal information, performs exceptionally well.

[0105] In contrast, the Traffic dataset performs poorly on all four evaluation metrics, with the MAE and MSE of its model predictions significantly lower than those of the other datasets. These results validate the effectiveness of the proposed method, as it reflects the objective characteristics of the dataset through evaluation.

[0106] Therefore, the present invention adopts the above-mentioned multi-scale time entropy evaluation method for heterogeneous and complex data sets. This method has extremely high generalization ability, making the evaluation of model performance more accurate and reliable, and suitable for a wide range of practical application scenarios.

[0107] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A multi-scale temporal entropy evaluation method for heterogeneous and complex data sets, characterized by: The following steps are involved: Step S1, down-sample the initial time series, divide it into sub-sequences at different time scales, and then apply the time window method to process the sub-sequences to obtain multiple clustering windows; Step S2, calculating the entropy value in each clustering window, and averaging the entropy values ​​of all clustering windows to obtain multi-scale time entropy; Step S3: Comprehensively evaluate the initial time series based on the obtained multi-scale time entropy.

2. According to claim 1, a multi-scale temporal entropy evaluation method for heterogeneous and complex data sets is characterized in that: In step S1, the initial time series is downsampled and divided into subsequences at different time scales. Then, the subsequences are processed using the time window method to obtain multiple clustering windows. The specific operations are as follows: For a given initial time series {X1,X2,…,X N }, the downsampling scale τ and the clustering window length W are used to generate the downsampled subsequence. For each clustering window position, the clustering window contains: in, is obtained by starting from the initial time series {X1,X2,…,X N }, where x is the subsequence obtained by taking a sample every τ; kτ+1 Represents the sample point at position kτ+1 in the time series.

3. The multi-scale temporal entropy evaluation method for heterogeneous and complex data sets according to claim 2 is characterized in that: In step S2, the entropy values ​​of all clustering windows are averaged to obtain multi-scale time entropy. The specific operation is: Where M is the total number of clustering windows; j is the position index in the clustering window; H represents the number of times a specific pattern or data point appears at position j in the clustering window in the downsampled sequence; τ (X) represents the evaluation results of the multi-scale temporal entropy based paradigm under different downsampling scales τ.

4. The multi-scale temporal entropy evaluation method for heterogeneous and complex data sets according to claim 3 is characterized in that: In step S3, the initial time series is comprehensively evaluated based on the obtained multi-scale time entropy. The specific operations are as follows: Among them, α is the coefficient of the multi-scale time entropy based method; β is the coefficient of the regularization term; is the regularization term entropy of a specific feature F; It represents the final evaluation result of the multi-scale time entropy of the time series at different downsampling scales τ after considering the regularization effect of specific features.

5. The multi-scale temporal entropy evaluation method for heterogeneous and complex data sets according to claim 4, characterized in that: In step S3, four regularization terms are introduced, including a periodic regularization term, a trend regularization term, a complexity regularization term, and an information regularization term.

6. The multi-scale temporal entropy evaluation method for heterogeneous and complex data sets according to claim 5, characterized in that: In step S3, the periodic regularization term calculation formula is as follows: in, represents the evaluation result of the multi-scale time entropy regularization term based on integrated empirical mode decomposition; m is the number of intrinsic mode functions obtained by integrated empirical mode decomposition; N is the length of the time series; IMF i (τ, t) represents the value of the i-th IMF at the downsampling scale τ and time point t.

7. The multi-scale temporal entropy evaluation method for heterogeneous and complex data sets according to claim 6, characterized in that: In step S4, the trend regularization term calculation formula is as follows: in, Represents the evaluation result of the multi-scale time entropy regularization term based on the variational embedding multi-scale sample entropy; is the downsampled sequence count of embedding dimension θ at position j.

8. The multi-scale temporal entropy evaluation method for heterogeneous and complex data sets according to claim 7, characterized in that: In step S4, the complexity regularization term calculation formula is as follows: in, represents the evaluation result of the multi-scale time entropy regularization term based on the refined composite multi-scale permutation entropy; δ is the delay parameter; is the Φth subsequence of the kth permutation under the downsampling scale τ; represents the count of the k-th permutation in the Φ-th subsequence; N k is the total number of subsequences or permutations extracted from the time series in the kth clustering window under the downsampling scale τ and the delay parameter δ.

9. The multi-scale temporal entropy evaluation method for heterogeneous and complex data sets according to claim 8, characterized in that: In step S4, the information density regularization term calculation formula is as follows: in, represents the evaluation result of the multi-scale time entropy regularization term based on Tsallis permutation entropy; q is the adjustable parameter of Tsallis entropy; represents the number of occurrences of a certain pattern within a given clustering window, and λ represents the embedding dimension for the jth subsequence at the downsampling scale τ in time series analysis.

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