A PCA-based Kernel for Kernel PCA on Multivariate Time Series

Multivariate time series (MTS) data sets are common in various multimedia, medical and financial application domains. These applications perform several data-analysis operations on large number of MTS data sets such as similarity searches, feature-subset-selection, clustering and classification. Inherently, an MTS item has a large number of dimensions. Hence, before applying data mining techniques, some form of dimension reduction, e.g., feature extraction, should be performed. Principal Component Analysis (PCA) is one of the techniques that have been frequently utilized for dimension reduction. However, traditional PCA does not scale well in terms of dimensionality, and therefore may not be applied to MTS data sets. The Kernel PCA technique addresses this problem of scalability by utilizing the kernel trick. In this paper, we propose a PCA based kernel to be employed for the Kernel PCA technique on the MTS data sets, termed KEros, which is based on Eros, a PCA based similarity measure for MTS data sets. We evaluate the performance of KEros using Support Vector Machine (SVM), and compare the performance with Kernel PCA using linear kernel and Generalized Principal Component (GPCA). The experimental results show that KEros outperforms these other techniques in terms of classification