Unsupervised dimensionality reduction method for multivariate time series based on global and local scatter

Abstract

To solve the problem that the traditional dimensionality reduction methods cannot be directly applied to multivariate time series, and for the existing approaches, it is difficult to ensure the effectiveness of dimensionality reduction while significantly reducing the dimension, an unsupervised dimensionality reduction method of multivariate time series based on global and local scatter was proposed.Firstly, a feature series extraction method was proposed to extract the upper triangular elements of the co-variance matrix of each multivariate time series and combine them into a feature sequence.Then, based on the idea of “minimum local scatter and maximum global scatter,” an unsupervised dimensionality reduction model was presented, which preserved the global information as much as possible while maintaining the local nearest neighbor relationship.Using the feature sequence as the input, the sum of the neighborhood variances of all sample points was minimized, and the variance of all the neighborhood centroids were maximized.The projection matrix obtained by solving the proposed model could be used to perform the dimensionality reduction.Finally, the proposed method was evaluated with experiments on 20 public data sets.The results show that the proposed method can significantly reduce the dimension of multivariate time series, while ensuring the effectiveness of dimensionality reduction.

Keywords

• multivariate time series;graph structure;feature extraction;unsupervised dimensionality reduction;classification accuracy