Tensor Multi-Elastic Kernel Self-Paced Learning for Time Series Clustering

Time series clustering has attracted growing attention due to the abundant data accessible and extensive value in various applications. The unique characteristics of time series, including high-dimension, warping, and the integration of multiple elastic measures, pose challenges for the present clustering algorithms, most of which take into account only part of these difficulties. In this paper, we make an effort to simultaneously address all aforementioned issues in time series clustering under a unified multiple kernels clustering (MKC) framework. Specifically, we first implicitly map the raw time series space into multiple kernel spaces via elastic distance measure functions. In such high-dimensional spaces, we resort to the tensor constraint based self-representation subspace clustering approach, which involves the self-paced learning paradigm, to explore the essential low-dimensional structure of the data, as well as the high-order complementary information from different elastic kernels. The proposed approach can be extended to more challenging multivariate time series clustering scenario in a direct but elegant way. Extensive experiments on 85 univariate and 10 multivariate time series datasets demonstrate the significant superiority of the proposed approach beyond the baseline and several state-of-the-art MKC methods.