title: Separation of stationary and non-stationary sources with a generalized eigenvalue problem.
abstract: Non-stationary effects are ubiquitous in real world data. In many settings, the observed signals are a mixture of underlying stationary and non-stationary sources that cannot be measured directly. For example, in EEG analysis, electrodes on the scalp record the activity from several sources located inside the brain, which one could only measure invasively. Discerning stationary and non-stationary contributions is an important step towards uncovering the mechanisms of the data generating system. To that end, in Stationary Subspace Analysis (SSA), the observed signal is modeled as a linear superposition of stationary and non-stationary sources, where the aim is to separate the two groups in the mixture. In this paper, we propose the first SSA algorithm that has a closed form solution. The novel method, Analytic SSA (ASSA), is more than 100 times faster than the state-of-the-art, numerically stable, and guaranteed to be optimal when the covariance between stationary and non-stationary sources is time-constant. In numerical simulations on wide range of settings, we show that our method yields superior results, even for signals with time-varying group-wise covariance. In an application to geophysical data analysis, ASSA extracts meaningful components that shed new light on the Pi 2 pulsations of the geomagnetic field.
authors.affiliation: Institute of Scientific and Industrial Research (ISIR), Osaka University, Osaka 5670047, Japan. hara@ar.sanken.osaka-u.ac.jp
authors.forename: Satoshi
authors.initials: S
authors.lastname: Hara
authors.forename: Yoshinobu
authors.initials: Y
authors.lastname: Kawahara
authors.forename: Takashi
authors.initials: T
authors.lastname: Washio
authors.forename: Paul
authors.initials: P
authors.lastname: von Bünau
authors.forename: Terumasa
authors.initials: T
authors.lastname: Tokunaga
authors.forename: Kiyohumi
authors.initials: K
authors.lastname: Yumoto
mesh_terms: D000465:Algorithms; D001921:Brain / Q000502:physiology; D004569:Electroencephalography / Q000379:methods; D016011:Normal Distribution; D011340:Problem Solving