A hierarchical clustering method integrating distance features, shape features and timing features

Abstract

The application belongs to the technical field of data processing, and discloses a hierarchical clustering method combining distance features, shape features and time sequence features, which comprises: in an initial stage, each time sequence process is regarded as an independent cluster, and the distances between different features of each time sequence process are calculated; a composite similarity index DST of the combined distance, shape and time sequence features is constructed according to the contribution degrees of the distances; the distances between different clusters are calculated according to the constructed composite similarity index and the determined inter-cluster connection mode, and the nearest clusters are continuously iterated and merged; when all the clusters are merged into a large cluster, the clustering is completed, and the optimal clustering number is determined according to the contour coefficients after each merging. The composite similarity index DST is constructed, the weights are automatically calculated according to the contribution degrees of different features to the current time sequence process, the multi-dimensional differences between the time sequence processes can be more comprehensively reflected, and the clustering result is more in line with the actual dynamic evolution law of the time sequence process.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field related to data processing, and more particularly relates to a hierarchical clustering method integrating distance features, shape features and time sequence features. BACKGROUND

[0002] The hierarchical clustering method is a clustering method for constructing a multi-level tree structure by gradually merging or splitting data points. The core principle is to form a hierarchical relationship of clusters from bottom to top or from top to bottom according to the similarity measurement between data points, and finally to display the multi-scale clustering structure of data through a tree diagram.

[0003] The similarity index is commonly used to measure the similarity or difference between data points in clustering analysis. Its core role is to determine the similarity between data points, thereby guiding the algorithm to classify samples with inherent similarity into the same class. Therefore, the selection of the similarity index will directly affect the recognition and division effect of the clustering algorithm on the internal structure of the data. In the prior art, the standard hierarchical clustering method uses Euclidean distance as the similarity index. The Euclidean distance mainly focuses on the absolute spatial distance between data points, and it is difficult to capture the inherent dynamic changes of time sequence data. Therefore, in order to achieve more accurate and effective clustering of time sequence data, in view of the characteristics of water level process which shows multi-scale fluctuations and also considers overall trend and local detail changes, it is urgent to propose a hierarchical clustering method integrating distance features, shape features and time sequence features. The method sets a composite similarity index of distance features, shape features and time sequence features, automatically calculates the weight according to the contribution of different features to the current time sequence process, and is used to reveal the internal structural characteristics and dynamic evolution of the water level process. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a hierarchical clustering method integrating distance features, shape features and time sequence features. The purpose is to fully capture the similarity between different time sequence processes in the three dimensions of amplitude, shape and time sequence, so as to overcome the defect that the standard hierarchical clustering method cannot capture the complex dynamic characteristics of time sequence process only by Euclidean distance, thereby solving the technical problems of low clustering accuracy, ignoring structure information and large intra-class heterogeneity of time sequence process.

[0005] To achieve the above purpose, according to one aspect of the present application, a hierarchical clustering method integrating distance features, shape features and time sequence features is provided, comprising the following steps:

[0006] S1: In the initial stage, each time sequence process is regarded as an independent cluster, and the distances between different features of each time sequence process are calculated;

[0007] S2: Based on the calculated distances of different features, a composite similarity index of distance features, shape features and time sequence features is constructed according to the contribution of each distance.

[0008] S3: Determine the connection mode between clusters and the distance calculation method between different clusters;

[0009] S4: Calculate the distance between different clusters according to the constructed composite similarity index and the determined connection mode between clusters, and constantly iterate and merge the nearest clusters;

[0010] S5: When all clusters are merged into one large cluster, the clustering is completed, and the optimal cluster number is determined according to the silhouette coefficient after each merging.

[0011] Preferably, S1 comprises the following steps:

[0012] S11: Obtain an initial time series process data set, and regard each process in the data set as an independent cluster as the starting point of clustering;

[0013] S12: Calculate the distance between different features between each time series process, including complexity invariant distance, first-order difference Euclidean distance, and dynamic time warping distance;

[0014] Preferably, the calculation formula of the complexity invariant distance is as follows:

[0015]

[0016] wherein, and denote different two sequences, denotes the Euclidean distance between sequences and , denotes the complexity estimate value, denotes the complexity invariant distance between and ; Preferably, the calculation formula of the first-order difference Euclidean distance is as follows:

[0017]

[0018]

[0019] wherein, denotes the sequence length, and denote the first-order derivative of different sequences at a certain time, which can be regarded as the basic approximation of the local slope, denotes the first-order difference Euclidean distance between and ;

[0020] Preferably, the calculation formula of the dynamic time warping distance is as follows:

[0021] ​

[0022] wherein, and are two points in two time series and , denotes and the dynamic time warping distance between , with initial condition ;

[0023] Preferably, S2 comprises the following steps:

[0024] S21: Normalization is performed on the complexity invariant distance, the first-order difference Euclidean distance and the dynamic time warping distance calculated in S1, and the calculation formula is as follows:

[0025]

[0026] wherein, denotes the normalized distance, denotes the original distance, and denote the maximum and minimum values of the original distance, respectively;

[0027] S22: The normalized complexity invariant distance in step S21 is the distance feature , the normalized first-order difference Euclidean distance is the shape feature , and the normalized dynamic time warping distance is the time series feature ; the weight of each feature index is calculated according to the contribution degree of each feature index to the similarity between different time series processes, and the calculation formula is as follows:

[0028]

[0029]

[0030] wherein: denotes the weight of different feature indexes, denotes the relative ranking under different feature indexes, is the value of the sample, is the average value of the sample, is the standard deviation of the sample;

[0031] If the Z-score is less than 0, the weight of the distance will be greater than 1, and the contribution of the distance measure will be enhanced; if the Z-score is 0, the feature index will remain unchanged; otherwise, the weight of the feature will be less than 1, and the contribution of the distance measure will be reduced;

[0032] S23: Constructing a composite similarity index DST according to the weight of different feature indexes calculated in step S22, and the calculation formula is as follows:

[0033]

[0034] wherein: 、 、 respectively represent the distance feature distance, shape feature distance and time sequence feature distance between different time sequence processes, 、 、 respectively represent the weight of distance feature, shape feature and time sequence feature in constructing the comprehensive distance measurement index;

[0035] Preferably, S3 comprises the following steps:

[0036] S31: Selecting the average connection as the connection mode between different clusters for revealing the inherent hierarchy and similarity of data, and the calculation formula of the distance between clusters is as follows:

[0037]

[0038] wherein: and respectively represent the number of samples in the cluster, represents the distance between different sequences, represents the distance between clusters of and ;

[0039] S32: In the initial stage of clustering, each time sequence process is regarded as an independent cluster, and the composite similarity index DST between the time sequence processes is the distance between two clusters;

[0040] Preferably, S4 comprises the following steps:

[0041] S41: Merging the two clusters with the smallest DST distance in the distance matrix D in the first iteration and to form a new cluster ;

[0042] S42: The distance between the new cluster and other clusters is calculated according to the constructed composite similarity index DST and the selected average connection mode, and the corresponding row and column of and are deleted, the distance between the new cluster and all other clusters is added, and the distance matrix D is updated;

[0043] S43: merging the two closest clusters according to the new distance matrix in each iteration, constantly repeating S42, updating the distance matrix and performing the next merging after each iteration, and calculating the silhouette coefficient under the current clustering situation after each iteration .

[0044] Preferably, the silhouette coefficient The calculation formula is as follows:

[0045]

[0046] Wherein, represents the average distance of sample to all other samples in the same cluster, represents the average distance of sample to all samples in the other cluster closest to it.

[0047] Overall, compared with the prior art, the hierarchical clustering method of the present application which combines distance features, shape features and time sequence features mainly has the following beneficial effects:

[0048] 1. The accuracy is significantly improved: the composite similarity index DST of distance features, shape features and time sequence features is constructed, the weight is automatically calculated according to the contribution of different features to the current time sequence process, which can more comprehensively reflect the multi-dimensional difference between time sequence processes, and the clustering effect is better than that of single-dimensional index, and the clustering precision is significantly improved.

[0049] 2. The structure information is more complete: the traditional distance measurement index such as Euclidean distance emphasizes the amplitude, and the dynamic time warping rearranges the time structure, which is easy to ignore the shape and time sequence features, while the composite similarity index DST considers the amplitude, the change trend and the shape at the same time, so that the clustering result is more consistent with the actual dynamic evolution law of time sequence process.

[0050] 3. Higher flexibility: the combination of the composite similarity index DST does not use fixed or subjective weights, but automatically calculates the weight according to the contribution of different features to the current time sequence process. This data-driven adaptive weighting mechanism can avoid human bias and better adapt to different types and characteristics of time sequence data, which can significantly improve the clustering quality and generalization ability. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 is a flow chart of hierarchical clustering method combined with composite similarity index DST for clustering;

[0052] Figure 2 is the change trend of the silhouette coefficient of 200 groups of water level processes under different similarity indexes and different clustering numbers;

[0053] Figure 3 This is a clustering result diagram of 200 water level processes using Euclidean distance as the similarity index;

[0054] Figure 4 This is a clustering result diagram of 200 water level processes using dynamic time warping as a similarity index;

[0055] Figure 5 This is a clustering result diagram of 200 water level processes using Chebyshev distance as the similarity index;

[0056] Figure 6 This is a clustering result diagram of 200 water level processes using the composite similarity index DST as the distance metric. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0058] Please see Figure 1 A hierarchical clustering method that integrates distance features, shape features, and temporal features includes the following steps:

[0059] S1: In the initial stage, each time series process is treated as an independent cluster, and the distance between different features of each time series process is calculated;

[0060] S2: Based on the calculated distances of different features, construct a composite similarity index DST that integrates distance, shape, and temporal features according to the contribution of each distance;

[0061] S3: Define the inter-cluster connection method and determine the distance calculation method between different clusters;

[0062] S4: Calculate the distance between different clusters based on the constructed composite similarity index and the determined inter-cluster connection method, and iteratively merge the nearest clusters;

[0063] S5: Clustering is complete when all clusters are merged into one large cluster. The optimal number of clusters is determined based on the silhouette coefficients after each merge.

[0064] S1 includes the following steps:

[0065] S11: Obtain the initial time series process dataset and treat each process in the dataset as an independent cluster as the starting point for clustering;

[0066] S12: sequentially calculate the distance of different features between each time sequence, including complexity invariant distance, first-order difference Euclidean distance and dynamic time warping distance;

[0067] The complexity invariant distance calculation formula is as follows:

[0068]

[0069] wherein, and denote two different sequences, denote the Euclidean distance between sequences and , and denote the complexity estimate value, denote and the complexity invariant distance between

[0070] The first-order difference Euclidean distance calculation formula is as follows:

[0071]

[0072] wherein, denote the sequence length, and denote the first derivative of different sequences at a certain time, which can be regarded as the basic approximation of local slope, denote and the first-order difference Euclidean distance between

[0073] The dynamic time warping distance calculation formula is as follows:

[0074]

[0075] wherein, and are two points in two time sequences and , and denote the dynamic time warping distance between and , the initial condition is , and the final result is ;

[0076] Preferably, S2 comprises the following steps:

[0077] S21: normalize the complexity invariant distance, first-order difference Euclidean distance and dynamic time warping distance calculated in S1, and the calculation formula is as follows:

[0078]

[0079] wherein, denotes the normalized distance, denotes the original distance, and denotes the maximum and minimum value of the original distance, respectively;

[0080] S22: the normalized complexity-invariant distance in step S21 is the distance feature , the normalized first-order difference Euclidean distance is the shape feature , and the normalized dynamic time warping distance is the time sequence feature ; the weight of each feature index is calculated according to the contribution degree of each feature index to the similarity between different time sequence processes, and the calculation formula is as follows:

[0081]

[0082] wherein: denotes the weight of different feature indexes, denotes the relative ranking under different feature indexes, is the value of the sample, is the average value of the sample, is the standard deviation of the sample;

[0083] If the Z-score is less than 0, the weight of the distance will be greater than 1, and the contribution of the distance measure will be enhanced; if the Z-score is 0, the feature index will remain unchanged; otherwise, the weight of the feature will be less than 1, and the contribution of the distance measure will be reduced;

[0084] S23: a composite similarity index DST is constructed according to the weight of different feature indexes calculated in step S22, and the calculation formula is as follows:

[0085]

[0086] wherein: , , denote the distance feature distance, shape feature distance and time sequence feature distance between different time sequence processes, respectively, , , denote the weight of the distance feature, shape feature and time sequence feature in constructing the comprehensive distance measure index, respectively;

[0087] S3 includes the following steps:

[0088] S31: the average connection is selected as the connection mode between different clusters, which is used to reveal the inherent hierarchy and similarity of the data, and the calculation formula of the distance between clusters is as follows:

[0089]

[0090] wherein: and respectively represent the number of samples in the cluster, represents the distance between different sequences, represents and the inter-cluster distance of

[0091] S32: In the initial stage of clustering, each time series process is regarded as an independent cluster, and the composite similarity index DST between the time series processes is the inter-cluster distance between two clusters;

[0092] S4 includes the following steps:

[0093] S41: In the first iteration, the two clusters with the smallest DST distance in the distance matrix D are merged and to form a new cluster ;

[0094] S42: The distance between the new cluster and other clusters is calculated according to the constructed composite similarity index DST and the selected average connection method, and the corresponding rows and columns of and are deleted, and the distances of the new cluster to all other clusters are added, and the distance matrix D is updated;

[0095] S43: In each iteration process, the two clusters with the closest distance are merged according to the new distance matrix, and S42 is repeatedly repeated, the distance matrix is updated after each iteration and the next merging is performed, and the silhouette coefficient under the current clustering condition is calculated after each iteration, and the calculation formula is as follows:

[0096]

[0097] wherein, represents the average distance of sample to all other samples in the same cluster, represents the average distance of sample to all samples in the other cluster closest to it.

[0098] This embodiment takes 200 groups of water level processes corresponding to 200 groups of pareto solutions obtained by multi-objective scheduling of Baihetan Power Station in September 2022 as original data, aims to deeply mine the inherent spatio-temporal correlation of different water level processes through an efficient clustering method, more finely capture the differences in shape and trend of the water level processes, and more scientifically and reasonably cluster, so as to more deeply analyze the typical water level processes.

[0099] The hierarchical clustering method is used to cluster 200 groups of water level processes by combining the composite similarity index DST of the constructed comprehensive distance feature, shape feature and time sequence feature. To verify the advantage of the composite similarity index DST in capturing subtle differences in water level curves compared to traditional distance metrics, Euclidean distance (EU), dynamic time warping (DTW) and Chebyshev distance (Cheb) are selected as control groups by combining the hierarchical clustering method. The silhouette coefficient, CH index and DB index are selected as clustering effect evaluation indexes.

[0100] Since the optimal cluster number of the hierarchical clustering method is obtained by calculating the silhouette coefficient under different clustering numbers rather than being set by humans, to avoid excessive dispersion due to a too large k value or excessive roughness due to a too small k value, the clustering number k is limited to 2-10 in this embodiment. The change trend of the silhouette coefficient under different similarity indexes with the clustering number k is as shown in FIG. 2. It can be seen that the traditional single similarity index starts to decline after reaching the maximum silhouette coefficient under a low clustering number, indicating that these indexes are prone to underfitting or oversimplification. The change trend of the silhouette coefficient corresponding to the composite similarity index shows a more stable and significant clustering separation degree. Figure 2

[0101] The clustering evaluation index results under the optimal clustering number are shown in Table 1. As can be seen from the table, under the optimal clustering number, the clustering results of the water level process using DST as the similarity index show significant advantages over the traditional single similarity index, in which the optimal values of the silhouette coefficient, CH index and DB index obtained by using DST for clustering the water level process are improved by 9.9%, 15.7% and 6.6% respectively, indicating that DST can strengthen the separability between classes while ensuring the compactness within classes, significantly improving the overall quality and stability of water level clustering.

[0102]

[0103] Figure 3 The clustering results under the optimal clustering number for the standard hierarchical clustering method, i.e., using Euclidean distance (EU) as the similarity index, can be seen from the clustering results. When using Euclidean distance as the similarity index, the algorithm only roughly divides the 200 groups of water level processes into three categories, making it difficult to distinguish the subtle differences between them. This is mainly because Euclidean distance only focuses on the overall distance between processes in the numerical space, without deeply mining the shape features of time series curves such as inflection point position, amplitude and time sequence of wave peaks and troughs. Therefore, when different water level processes have similar numerical ranges but different shape trends, Euclidean distance often cannot distinguish them, leading to a too simple clustering result that cannot meet the needs of fine-grained analysis of water level time series patterns.

[0104] Figure 4 ​For the clustering result under the optimal clustering number when using dynamic time warping (DTW) as the similarity index, it can be seen from the clustering result that the algorithm can better align the phase difference and local time shift in each water level process when using dynamic time warping as the similarity index. However, since dynamic time warping only pursues the minimization of cumulative alignment error in the optimization process, it does not impose constraints on the global shape or local geometric features of the sequence, and therefore it is still difficult to distinguish the differences in micro details, which is insufficient to meet the demand for high-precision time series clustering.

[0105] Figure 5 For the clustering result under the optimal clustering number when using Chebyshev distance (Cheb) as the similarity index, it can be seen from the clustering result that the algorithm can quickly identify water level processes that deviate significantly at a certain time by virtue of the sensitivity to the maximum coordinate difference at any time in the sequence when using Chebyshev distance as the similarity index. However, since Chebyshev distance only measures the overall similarity by the maximum deviation of a single point, it completely ignores the cumulative difference and overall shape trend of the two curves at other time points, so when the water level process presents moderate fluctuations in multiple periods, this measure cannot reflect these scattered changes, and therefore it cannot meet the demand for fine clustering of the overall evolution and local microstructure of the water level time series.

[0106] Figure 6 For the clustering result under the optimal clustering number when using the composite similarity index DST constructed as the distance measure, it can be seen from the clustering result that using DST as the similarity index for water level process clustering can not only take into account the three features of distance difference, curve shape and time series evolution, but also can divide the 200 water level processes into several categories relatively evenly, and the water level processes within each category have high aggregation, while the center curves between categories exhibit significant evolutionary differences. This shows that DST, driven by the data-driven similarity contribution, continuously adjusts the weights of each feature to ensure that it can capture local wave peaks, troughs and slope changes and other microstructures sensitively while aligning the global trend at each iteration, avoiding the problems of too rough clustering under Euclidean distance and excessive sensitivity to single-point deviation under Chebyshev distance. At the same time, compared with DTW which only focuses on minimizing the alignment path, DST also improves the recognition ability of sudden jumps and inflection point distribution through the weighted fusion of shape and time series features, thereby achieving higher discrimination and classification accuracy in diverse water level patterns.

[0107] Those skilled in the art will readily understand that the above description is only the preferred embodiment of the present application, and is not intended to limit the present application. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A hierarchical clustering method integrating distance features, shape features, and time series features, applied to the field of water level process detection, characterized in that: The method comprises the following steps: S1: In the initial stage, each water level time series process is regarded as an independent cluster, and the distances of different features between the water level time series processes are calculated; S1 comprises the following steps: S11: Obtain an initial water level time series process data set, and regard each process in the data set as an independent cluster as the starting point of clustering; S12: Calculate the distances of different features between the water level time series processes in turn, including the complexity invariant distance, the first-order difference Euclidean distance and the dynamic time warping distance; The calculation formula of the complexity invariant distance is as follows: wherein, and denote two different sequences, denotes a sequence and the Euclidean distance between, denotes a complexity estimate, denotes and the complexity-invariant distance between; The calculation formula of the first-order difference Euclidean distance is as follows: wherein, denotes the sequence length, and denotes the first derivative of different sequences at a certain time, which can be regarded as a basic approximation of the local slope, denotes and the first difference Euclidean distance between The calculation formula of the dynamic time warping distance is as follows: wherein, and are two points in two time series and , denotes and the dynamic time warping distance between with initial condition and final result ; S2: Based on the distances of different features calculated, a composite similarity index of the integrated distance, shape and time series features is constructed according to the contribution degrees of the distances to the similarity of the current water level time series process; S2 comprises the following steps: S21: The complexity invariant distance, the first-order difference Euclidean distance and the dynamic time warping distance calculated in S1 are normalized, and the calculation formula is as follows: wherein, denotes the normalized distance, denotes the original distance, and denotes the maximum and minimum of the original distance, respectively; S22: the normalized complexity-invariant distance in step S21 is a distance feature , the normalized first-order difference Euclidean distance is a shape feature , and the normalized dynamic time warping distance is a time sequence feature ; the weight of each feature index is calculated according to the contribution of each feature index to the similarity between the time sequence processes at different water levels, and the calculation formula is as follows: wherein: represents the weight of different characteristic indicators, represents the relative ranking under different characteristic indicators, is the value of the sample, is the sample mean, is the standard deviation of the sample; S23: The composite similarity index DST is constructed according to the weights of the different feature indexes calculated in step S22, and the calculation formula is as follows: wherein: , , respectively represent the distance characteristic distance, shape characteristic distance and time sequence characteristic distance between different water level time sequence processes, , , respectively represent the weight of the distance characteristic, shape characteristic and time sequence characteristic when constructing the comprehensive distance measurement index. S3: The connection mode between clusters is determined, and the distance calculation method between different clusters is determined; S4: The distance between different clusters is calculated according to the constructed composite similarity index and the determined connection mode between clusters, and the nearest clusters are iteratively merged; S5: When all the clusters are merged into one large cluster, the clustering is completed, and the best clustering number is determined according to the silhouette coefficient after each merging, so as to identify the typical evolution mode in the water level process.

2. The hierarchical clustering method integrating distance features, shape features, and temporal features as described in claim 1, characterized in that: S3 comprises the following steps: S31: The average connection is selected as the connection mode between different clusters, which is used to reveal the inherent hierarchical structure and similarity of data, and the calculation formula of the distance between clusters is as follows: wherein: and denote the number of samples within a cluster, denotes the distance between different sequences, denotes and the inter-cluster distance. S32: In the initial stage of clustering, each water level time series process is regarded as an independent cluster, and the composite similarity index DST between the water level time series processes is the distance between clusters.

3. The hierarchical clustering method integrating distance features, shape features, and temporal features as described in claim 1, characterized in that: S4 comprises the following steps: S41: merging the two clusters with the smallest DST distance in the distance matrix D in the first iteration and , forming a new cluster ; S42: the distance between the new cluster and other clusters is calculated according to the constructed composite similarity index DST and the selected average connection mode, and the distance matrix D is updated and corresponding row and column, add a new cluster the distance from all other clusters, update the distance matrix D; S43: merge the two closest clusters according to the new distance matrix in each iteration, constantly repeat S42, update the distance matrix and perform the next merging after each iteration, and calculate the silhouette coefficient under the current clustering situation after each iteration .

4. The hierarchical clustering method integrating distance features, shape features, and temporal features as described in claim 3, characterized in that: The profile coefficient The calculation formula is as follows: wherein, represents the sample the average distance to all other samples within the same cluster, represents the sample the average distance to all samples within the other cluster closest to it.

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