主成分分析の固有ベクトルと時空間データパターンとの関係について

概要

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The principal component analysis (PCA) has been widely used for spatio-temporal analysis of multichannel data such as multichannel biomedical signals. The purpose of the present study was to elucidate the physical meaning of the eigenvector of the PCA. In the present theoretical analysis, the multichannel bioinformation was modeled using multiple sinusoidal signals, and independence among the data patterns produced by the multiple sources is assumed. It is found that the vector axis of each eigenvector of PCA is consistent with the independent pattern axis which each dipole sources produces, when analyzing the spatio-temporal data generated by the one or several dipole source by means of PCA. In the simulation study, the head volume conductor was approximated by a homogeneous sphere model and 19 electrodes were used over the spherical surface. Dipole source of sinusoidal distribution in their strength were used to simulate brain electrical activity. As the result, it is found that the axis of each eigenvector is consistent with the pattern axis which each dipole source produces, when the pattern axis which each dipole source produces was independent. It is also found that there is little effect of white noise on the eigenvector of large eigenvalue. The present theoretical and simulation study promises to further our understanding on the PCA.
2013-03-01