Discriminative Learning on Exemplary Patterns of Sequential Numerical Data

One of the effective methodologies for time series classification is to identify informative subsequence patterns in time series and exploit them as discriminative features. Previous studies on this methodology have achieved promising results using a small number of individually selected patterns. However, there remain difficulties in finding a set of related patterns or patterns of a minor class, which can be critical in real-world applications. In this paper, we exploit the sparse learning technique for the support vector machine (SVM) to identify informative and exemplary patterns. We first present a representation of time series as a vector of distances to exemplary patterns. It allows a structural SVM to handle distance space data and function as the nearest neighbor classifier, the combination of which is known to be highly competitive in time series classification. We then extend the zero-norm approximation method for the structural SVM, which can eliminate non-essential patterns from the classification model. The resulting model makes predictions by a simple modified nearest neighbor rule, yet has a strong mathematical support for empirical risk minimization and feature selection. We conduct an empirical study on real-world behavior and sequential data to evaluate the effectiveness of the proposed method and graphically examine the exemplary patterns.