Fast PCA via UTV decomposition and application on EEG analysis

In the mean square error sense, principal component analysis (PCA) or Karhunen-Loeve transform (KLT) can optimally summarize the high dimensional data into only a few meaningful ones. However, for the biomedical signal analysis, e.g. electroencephalogram (EEG), the data need to be updated or downdated very often. This fact makes the PCA impractical to be employed, especially in real-time signal analysis. In this paper, we propose the fast computational method for approximating the PCA such that the new transform, called fast PCA (fastPCA), can easily be updated and downdated. The fastPCA is calculated via the UTV decomposition which is the method normally used to approximate the rank-revealing property of the singular value decomposition (SVD). The merit of the fastPCA is also illustrated via the application on EEG analysis.