Paper AS-WeM11
SVD + Factor Rotation: A Powerful Alternative to PCA for Spectral Image Analysis

Wednesday, October 22, 2008, 11:20 am, Room 207

Factor analysis has proven an effective approach for distilling high dimensional spectral-image data into a limited number of components that describe the spatial and spectral characteristics of the imaged sample. Principal Component Analysis (PCA) is the most commonly used factor analysis tool; however, PCA constrains both the spectral and abundance factors to be orthogonal, and forces the components to serially maximize the variance that each accounts for. Neither constraint has any basis in physical reality; thus, principal components are abstract and not easily interpreted. The mathematical properties of PCA scores and loadings also differ subtly, which has implications for how they can be used in abstract factor “rotation” procedures such as Varimax. The Singular Value Decomposition (SVD) is a mathematical technique that is frequently used to compute PCA. In this talk, we will argue that SVD itself provides a more flexible framework for spectral image analysis since spatial-domain and spectral-domain singular vectors are treated in a symmetrical fashion. We will also show that applying an abstract rotation in our choice of either the spatial or spectral domain relaxes the orthogonality requirement in the complementary domain. For instance, samples are often approximately orthogonal in a spatial sense, that is, they consist of relatively discrete chemical phases. In such cases, rotating the singular vectors in a way designed to maximize the simplicity of the spatial representation yields physically acceptable and readily interpretable estimates of the pure-component spectra. This talk will demonstrate that this approach can achieve excellent results for difficult-to-analyze data sets obtained by a variety of spectroscopic imaging techniques. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.