Multitask Principal Component Analysis
Multitask Principal Component Analysis
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发表时间：
2016-11
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通讯作者：
Ikko Yamane;F. Yger;Maxime Bérar;Masashi Sugiyama
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作者：
Ikko Yamane;F. Yger;Maxime Bérar;Masashi Sugiyama
主成分分析（PCA）是一种典型的和研究得很好的降维工具。然而，当数据很少时，协方差估计器的核心质量差可能会影响其性能。我们利用这个问题，铸造成一个多任务框架的PCA，这样做，我们展示了如何同时解决几个相关的PCA问题。因此，我们提出了一种新的制剂的PCA问题依赖于一种新的正则化。这种正则化是基于子空间之间的距离，整个问题作为黎曼流形上的优化问题来解决。我们的实验证明了我们的方法的实用性，为脑电信号的预处理。
Principal Component Analysis (PCA) is a canonical and well-studied tool for dimension- ality reduction. However, when few data are available, the poor quality of the covariance estimator at its core may compromise its performance. We leverage this issue by casting the PCA into a multitask framework, and doing so, we show how to solve simultaneously several related PCA problems. Hence, we propose a novel formulation of the PCA prob- lem relying on a novel regularization. This regularization is based on a distance between subspaces, and the whole problem is solved as an optimization problem over a Riemannian manifold. We experimentally demonstrate the usefulness of our approach as pre-processing for EEG signals.