Stationary Subspace Analysis as a Generalized Eigenvalue Problem
Understanding non-stationary effects is one of the key challenges in data analysis. However, in many settings the observation is a mixture of stationary and non-stationary sources. The aim of Stationary Subspace Analysis (SSA) is to factorize multivariate data into its stationary and non-stationary components. In this paper, we propose a novel SSA algorithm (ASSA) that extracts stationary sources from multiple time series blocks. It has a globally optimal solution under certain assumptions that can be obtained by solving a generalized eigenvalue problem. Apart from the numerical advantages, we also show that compared to the existing method, fewer blocks are required in ASSA to guarantee the identifiability of the solution. We demonstrate the validity of our approach in simulations and in an application to domain adaptation.
KeywordsNon-stationarity Dimensionality Reduction Feature Extraction Eigenvalue Problem Stationary Subspace Analysis
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