Stationary subspace analysis for spatial data

TL;DR

This paper extends stationary subspace analysis to spatial data, introducing spatial SSA with three estimation procedures, combined via joint diagonalization, and proposes a new method to estimate the nonstationary subspace dimension.

Contribution

It introduces spatial stationary subspace analysis (spSSA), develops three estimation procedures, and proposes a novel data augmentation method for dimension estimation.

Findings

Combined estimation procedures improve separation performance.

Methods reliably recover stationary and nonstationary components when dimension is known.

New data augmentation approach effectively estimates the nonstationary subspace dimension.

Abstract

Stationary subspace analysis (SSA) is a blind source separation framework that decomposes linearly mixed multivariate data into stationary and nonstationary components. We extend SSA to spatially indexed data by introducing spatial stationary subspace analysis (spSSA), which explicitly accounts for spatial dependence. We propose three estimation procedures for the unmixing matrix based on first- and second-order spatial statistics. Each procedure targets a different type of nonstationarity and can be formulated as the solution to a generalized eigenvalue problem. To address situations where multiple forms of nonstationarity are present simultaneously, we combine the three procedures using approximate joint diagonalization. Simulation studies demonstrate that this combined approach yields superior separation performance. When the dimension of the nonstationary subspace is known, the proposed methods reliably recover the latent stationary and nonstationary components. However, determining this dimension remains a fundamental challenge in SSA, for which no generally accepted solution currently exists. Building on our estimation procedures, we propose a novel data augmentation approach to estimate the dimension of the nonstationary subspace and demonstrate its effectiveness through simulation studies. The proposed methodology is easily transferable to time series settings, making it of broader methodological interest.