Time Series Data Classification on Grassmann Manifold

Abstract

Time Series Classification has become one of the most challenging problems in many signal processing and machine learning applications, e.g., audio/video signal processing and EEG signal processing. We propose a novel method of extracting features from data for classification and representing data on a Grassmann manifold by parameterizing it using the autoregressive moving model (ARMA). Then we perform classification on these extracted features by training support vector machines (SVM), with appropriate kernels on the Grassmann manifold. We performed tests on several publicly available datasets. We found that an SVM with a proper kernel on the Grassmann manifold consistently performs better than an SVM using a typical Gaussian kernel that acts on the data in Euclidean space. Furthermore, we found that the Grassmann SVM technique overperforms the literature in some high-dimensional datasets, without the need for any other preprocessing techniques. This work demonstrates the power of data-based manifold techniques in improving the performance of existing algorithms.