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.
| Original language | English |
|---|---|
| Pages (from-to) | 7-20 |
| Number of pages | 14 |
| Journal | Neural Networks |
| Volume | 33 |
| DOIs | |
| Publication status | Published - Sep 1 2012 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Cognitive Neuroscience
- Artificial Intelligence
Cite this
Separation of stationary and non-stationary sources with a generalized eigenvalue problem. / Hara, Satoshi; Kawahara, Yoshinobu; Washio, Takashi; von Bünau, Paul; Tokunaga, Terumasa; Yumoto, Kiyohumi.
In: Neural Networks, Vol. 33, 01.09.2012, p. 7-20.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Separation of stationary and non-stationary sources with a generalized eigenvalue problem
AU - Hara, Satoshi
AU - Kawahara, Yoshinobu
AU - Washio, Takashi
AU - von Bünau, Paul
AU - Tokunaga, Terumasa
AU - Yumoto, Kiyohumi
PY - 2012/9/1
Y1 - 2012/9/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.neunet.2012.04.001
DO - 10.1016/j.neunet.2012.04.001
M3 - Article
C2 - 22551683
AN - SCOPUS:84863869958
VL - 33
SP - 7
EP - 20
JO - Neural Networks
JF - Neural Networks
SN - 0893-6080
ER -