Separation of stationary and non-stationary sources with a generalized eigenvalue problem
Separation of stationary and non-stationary sources with a generalized eigenvalue problem
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DOI：
10.1016/j.neunet.2012.04.001
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发表时间：
2012-09-01
期刊：
影响因子：
7.8
通讯作者：
Yumoto, Kiyohumi
中科院分区：
文献类型：
--
作者：
Hara, Satoshi;Kawahara, Yoshinobu;Yumoto, Kiyohumi
非平稳效应在真实的世界数据中普遍存在。在许多情况下，观测到的信号是潜在的固定和非固定源的混合物，不能直接测量。例如，在EEG分析中，头皮上的电极记录来自位于大脑内部的几个来源的活动，这只能通过侵入性方式进行测量。辨别固定和非固定的贡献是揭示数据生成系统的机制的重要一步。为此，在平稳子空间分析（SSA）中，观测信号被建模为平稳和非平稳源的线性叠加，其目的是分离混合物中的两组。在本文中，我们提出了第一个SSA算法，有一个封闭的形式的解决方案。新的方法，解析SSA（ASSA），是超过100倍的速度比国家的最先进的，数值稳定，并保证是最佳的平稳和非平稳源之间的协方差是时间常数。在广泛的设置的数值模拟中，我们表明，我们的方法产生上级的结果，即使是随时间变化的组明智的协方差信号。在地球物理数据分析的应用中，ASSA提取了有意义的分量，为地磁场的Pi 2脉动提供了新的线索。(c)2012爱思唯尔有限公司保留所有权利。
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. (c) 2012 Elsevier Ltd. All rights reserved.