Feature Representation and Similarity Measure Based on Covariance Sequence for Multivariate Time Series

The high dimension of multivariate time series (MTS) is one of the major factors that impact on the efficiency and effectiveness of data mining. It has two kinds of dimensions, time-based dimensionality, and variable-based dimensionality. They often cause most of the algorithms and techniques applied to the field of MTS data mining to be a failure. In view of the importance of the correlation between any two variables in an MTS, the covariances between any two variables are applied to analyze the extraction of the features for every MTS. In this way, a covariance sequence can be constructed to represent the characteristic of the MTS. Furthermore, an excellent method of dimensionality reduction, principal component analysis (PCA), is used to extract the features of the covariance sequences that derived from an MTS dataset. Thus Euclidean distance is suitable to measure the similarity between the features fast. The experimental results demonstrate that the proposed method not only can handle multivariate time series with different lengths but also is more efficient and effective than the existing methods for the MTS data mining.