Dimension reduction and visualization of multiple time series data: a symbolic data analysis approach

Abstract

Exploratory analysis and visualization of multiple time series data are essential for discovering the underlying dynamics of a series before attempting modeling and forecasting. This study extends two dimension reduction methods - principal component analysis (PCA) and sliced inverse regression (SIR) - to multiple time series data. This is achieved through the innovative path point approach, a new addition to the symbolic data analysis framework. By transforming multiple time series data into time-dependent intervals marked by starting and ending values, each series is geometrically represented as successive directed segments with unique path points. These path points serve as the foundation of our novel representation approach. PCA and SIR are then applied to the data table formed by the coordinates of these path points, enabling visualization of temporal trajectories of objects within a reduced-dimensional subspace. Empirical studies encompassing simulations, microarray time series data from a yeast cell cycle, and financial data confirm the effectiveness of our path point approach in revealing the structure and behavior of objects within a 2D factorial plane. Comparative analyses with existing methods, such as the applied vector approach for PCA and SIR on time-dependent interval data, further underscore the strength and versatility of our path point representation in the realm of time series data.