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静止的子空间分析

Stationary Subspace Analysis
课程网址: http://videolectures.net/aml08_bunau_ssa/  
主讲教师: Klaus-Robert Müller; Paul von Bunau; Frank C. Meinecke
开课单位: 柏林工业大学
开课时间: 2008-12-20
课程语种: 英语
中文简介:
非平稳性是现实数据中普遍存在的现象,但它们挑战了标准的机器学习方法:如果训练和测试分布不同,原则上我们不能从观察到的训练样本生成测试分布。这会影响有监督和无监督的学习算法。例如,在一个分类问题中,我们可以从训练样本中推断出数据和标签之间的虚假依赖性,而这些训练样本仅仅是非平稳性的人工制品。相反,为了更好地理解分析的系统,识别非平稳行为的来源往往是一个科学问题的核心。为此,我们提出了一种新的无监督范式:平稳子空间分析(SSA)。SSA将一个多变量时间序列分解为一个平稳子空间和一个非平稳子空间。我们推导了一种基于特殊正交群优化过程的高效算法。利用优化流形的李群结构,可以显式地分解出问题的固有对称性,从而将参数个数减少到精确的自由度。我们的方法在脑-机接口(BCI)的应用中得到了证明。
课程简介: Non-stationarities are an ubiquitous phenomenon in real-world data, yet they challenge standard Machine Learning methods: if training and test distributions differ we cannot, in principle, gen- eralise from the observed training sample to the test distribution. This affects both supervised and unsupervised learning algorithms. In a classification problem, for instance, we may infer spurious dependen- cies between data and label from the the training sample that are mere artefacts of the non-stationarities. Conversely, identifying the sources of non-stationary behaviour in order to better understand the analyzed system often lies at the heart of a scientific question. To this end, we propose a novel unsupervised paradigm: Stationary Subspace Analysis (SSA). SSA decomposes a multi-variate time-series into a stationary and a non-stationary subspace. We derive an efficient algorithm that hinges on an optimization procedure in the Special Orthogonal Group. By exploiting the Lie group structure of the optimization manifold, we can explicitly factor out the inherent symmetries of the problem and thereby reduce the number of parameters to the exact degrees of freedom. The practical utility of our approach is demonstrated in an application to Brain Computer-Interfacing (BCI).
关 键 词: 计算机应用; 固定子空间分析; 脑机接口
课程来源: 视频讲座网
最后编审: 2020-05-22:吴雨秋(课程编辑志愿者)
阅读次数: 89