Multivariate time series-density peaks clustering and its applications

• 1.It introduces a hybrid dissimilarity measure, fusing Euclidean and correlation distance, to better capture both the magnitude and shape of time series data. • 2.The method is built on the Density Peaks Clustering (DPC) framework, focusing on the overall data distribution and inherent trends rather than just pairwise distances. • 3.Its feasibility and broad applicability are proven through tests on benchmark datasets and real-world problems from medicine and molecular dynamics. • 4.The algorithm's computational complexity is formally analyzed to assess its scalability and practical efficiency. In traditional approaches to the multivariate time series (MTS) clustering problem, most methods primarily rely on distance measures to distinguish between samples, which often overlooks the inherent change trends of the sequences and the distribution relationships among samples. To address this limitation, the multivariate time series-density peaks clustering (MTS-DPC) algorithm is proposed based on the DPC framework. In MTS-DPC, the Euclidean distance and correlation distance between samples are combined with different weights to form a new measure of sample dissimilarity. Based on this fused measure, the clustering process is performed using the DPC algorithm. To validate the feasibility and applicability of MTS-DPC, tests were conducted on artificially generated benchmarks of multivariate time series with diverse variation patterns and a real-world MTS benchmark. The evaluations were performed using general metrics. Additionally, the computational complexity of MTS-DPC in both spatial and temporal aspects were statically analyzed. Finally, MTS-DPC was applied to analyze two MTS problems, which are the metabolic indicators clustering problems in the medical field and the molecular trajectory clustering problems in molecular dynamics (MD) simulation. The results demonstrate that MTS-DPC accurately clusters the samples with different features. Both the clustering results of benchmarks and practical problems showed the feasibility of MTS-DPC. And it can be applied to other MTS clustering problems.