Pattern discovery from multivariate time series data

Abstract

A multivariate time series (MTS) is made up of data collected by monitoring the values of a set of temporarily related or interrelated variables over a period of time at successive instants spaced at uniform time intervals. Therefore it consists of a set of component univariate time series (CUTS) which corresponds to the series of values taken by a variable over the monitoring period of time. Given a set of MTS, the problem of classification or clustering such data is concerned with discovering inherent groupings of the data according to how similar or dissimilar the time series are to each other. Two main challenges to processing MTS are multiple variables and high dimensions. Although existing feature extraction methods can effectively reduce the dimensions, the methods may lose certain important correlations among the variables while reducing high dimensions of MTS. In view of the growing need to deal with MTS in many application domains, we propose a generic and application-independent method capable of discovering, classifying and clustering phases associated with pattern discovery from data. Firstly, a new feature extraction method resulting in a feature vector is proposed to reduce high dimensions of MTS. Next, with a view to reducing the dimensions of the feature vector, we propose an unsupervised feature selection method capable of reducing the computation time, improve classification performance, and facilitate a better understanding of datasets. Finally, the classifier and the clustering methods are applied. Specifically, the proposed algorithms address the following issues. i) A general algorithm is proposed to discover the inter-temporal and intra-temporal patterns associated with an MTS. ii) In order to discover patterns from the MTS, discretization is needed to transform numerical data into level value. Hence, a fuzzy approach is proposed to discover fuzzy temporal patterns using fuzzy membership functions. iii) After discovering temporal patterns, a feature vector is constructed by combining diverse measurements of intra-/inter-temporal patterns for each MTS. iv) Classify and cluster MTS using feature vectors after selecting the appropriate number of features using an unsupervised attribute clustering algorithm. In addition, since MTS data are commonly found in business and finance, social and biological sciences, engineering and computing, medicine and healthcare, etc., effective classification of such data has many potential applications in a wide range of problem domains. The performance of the proposed algorithm has been tested using both synthetic and real-world datasets. It is also applied in several real case studies, viz. classification for single-trial EEG and association analysis, clustering and portfolio management for stock markets. Both experimental results and practical solutions have shown that the proposed algorithm can be a promising algorithm for MTS analysis.