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Chunk #45 — Componential Analyses of ERPs — PCA

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Advances in Electrophysiological Research.
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The central idea of the principal component analysis is to reduce the dimensionality of a dataset consisting of a large number of interrelated variables, while retaining as much as possible of the variation present in the dataset. This is done by transforming the data into a new set of variables, called the principal components, which are uncorrelated and often orthogonal and which are ordered so that the first few retain most of the variation present in all of the original variables (Jolliffe 2005). The PCA method decomposes the entire ERP dataset into individual elementary curves or components, and the sum of the derived components should approximate the waveform of the measured ERP (Begleiter et al. 1987b). PCA components (i.e., factor loadings or factor waveforms), together with their associated weights (i.e., topography of factor scores), can each be represented in terms of their accounted variance and interpreted based on their topographic significance (Kayser and Tenke 2006). Often, the initially derived components are further subjected to factor rotation (e.g., varimax rotation) to achieve/improve factor structure while maintaining factor orthogonality (being perpendicular from