Unsupervised Classification of Multivariate Time Series Using VPCA and Fuzzy Clustering With Spatial Weighted Matrix Distance

Due to high dimensionality and multiple variables, unsupervised classification of multivariate time series (MTS) involves more challenging problems than those of univariate ones. Unlike the vectorization of a feature matrix in traditional clustering algorithms, an unsupervised pattern recognition scheme based on matrix data is proposed for MTS samples in this paper. To reduce the computational load and time consumption, a novel variable-based principal component analysis (VPCA) is first devised for the dimensionality reduction of MTS samples. Afterward, a spatial weighted matrix distance-based fuzzy clustering (SWMDFC) algorithm is proposed to directly group MTS samples into clusters as well as preserve the structure of the data matrix. The spatial weighted matrix distance (SWMD) integrates the spatial dimensionality difference of elements of data into the distance of MST pairs. In terms of the SWMD, the MTS samples are clustered without vectorization in the dimensionality-reduced feature matrix space. Finally, three open-access datasets are utilized for the validation of the proposed unsupervised classification scheme. The results show that the VPCA can capture more features of MTS data than principal component analysis (PCA) and 2-D PCA. Furthermore, the clustering performance of SWMDFC is superior to that of fuzzy ${c}$ -means clustering algorithms based on the Euclidean distance or image Euclidean distance.