Time series data analysis, especially forecasting, classification, imputation, and anomaly detection, has gained a lot of research attention in recent years due to its prevalence and wide application. Compared to classification, clustering is an unsupervised task and thus more applicable for analyzing massive time series without labels. One latest way is based on the idea of graph community detection: first transforming a time series set into a graph (or a network), in which a node represents a time series instance and an edge denotes that the two connected nodes (thus the represented time series) are more similar to each other; then, running a community detection algorithm on the graph to discover a community structure, that gives out a clustering result. Recently, there are several works based on the graph community detection idea to cluster multivariate time series. However, such works focus only on specific methods in each step, and a performance comparison of combinations of methods in different steps is lacking. This paper outlines the process of graph-based multivariate time clustering as four phases (referred to as framework), namely representation learning, similarity computing, relation network construction, and clustering, lists typical methods in each phase, and makes a comparison study of combinations of each phase methods (called strategies in this paper). Recent time series deep neural network models are introduced to the framework as time series representation learning methods as well. In addition, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10489_2025_6444_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$\varvec{\varepsilon } \varvec{k}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mi mathvariant="bold-italic">ε</mi> </mrow> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> </mrow> </math></EquationSource> </InlineEquation>NN, an improvement of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10489_2025_6444_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\varvec{k}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> </math></EquationSource> </InlineEquation>NN by filtering out unnecessary low similarity connections during network construction, is proposed. A great number of experiments are conducted on eight real-world multivariate time series with various properties to verify the performance of different strategy combinations. The results suggest that proper deep neural network is a promising way for learning time series vector representations to compute similarities, and strategies including <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10489_2025_6444_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$\varvec{\varepsilon } \varvec{k}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mi mathvariant="bold-italic">ε</mi> </mrow> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> </mrow> </math></EquationSource> </InlineEquation>NN for network construction, average for multi-layer network merging and Louvain for clustering are more effective from a statistical perspective.

A comparison study of several strategies in multivariate time series clustering based on graph community detection

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发表日期：

2025年3月14日

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Hanlin Sun,
Wei Jie,
Yanping Chen,
Zhongmin Wang

摘要

Time series data analysis, especially forecasting, classification, imputation, and anomaly detection, has gained a lot of research attention in recent years due to its prevalence and wide application. Compared to classification, clustering is an unsupervised task and thus more applicable for analyzing massive time series without labels. One latest way is based on the idea of graph community detection: first transforming a time series set into a graph (or a network), in which a node represents a time series instance and an edge denotes that the two connected nodes (thus the represented time series) are more similar to each other; then, running a community detection algorithm on the graph to discover a community structure, that gives out a clustering result. Recently, there are several works based on the graph community detection idea to cluster multivariate time series. However, such works focus only on specific methods in each step, and a performance comparison of combinations of methods in different steps is lacking. This paper outlines the process of graph-based multivariate time clustering as four phases (referred to as framework), namely representation learning, similarity computing, relation network construction, and clustering, lists typical methods in each phase, and makes a comparison study of combinations of each phase methods (called strategies in this paper). Recent time series deep neural network models are introduced to the framework as time series representation learning methods as well. In addition, $\varvec{\varepsilon } \varvec{k}$ $ε k$ NN, an improvement of $\varvec{k}$ $k$ NN by filtering out unnecessary low similarity connections during network construction, is proposed. A great number of experiments are conducted on eight real-world multivariate time series with various properties to verify the performance of different strategy combinations. The results suggest that proper deep neural network is a promising way for learning time series vector representations to compute similarities, and strategies including $\varvec{\varepsilon } \varvec{k}$ $ε k$ NN for network construction, average for multi-layer network merging and Louvain for clustering are more effective from a statistical perspective.