Ranking Tensor Subspaces in Weighted Multilinear Principal Component Analysis
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2017-07-01
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FILISBINO, T. A.
GIRALDI, G. A.
Carlos E. Thomaz
GIRALDI, G. A.
Carlos E. Thomaz
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International Journal of Pattern Recognition and Artificial Intelligence
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FILISBINO, T. A.; GIRALDI, G. A.; THOMAZ, C. E. Ranking Tensor Subspaces in Weighted Multilinear Principal Component Analysis. International Journal of Pattern Recognition and Artificial Intelligence, v. 31, n. 7, Jul, 2017.
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© 2017 World Scientific Publishing Company.Multilinear principal component analysis (MPCA) has been applied for tensor decomposition and dimensionality reduction in image databases modeled through higher order tensors. Despite the well-known attractive properties of MPCA, the traditional approach does not incorporate prior information in order to steer its subspace computation. In this paper, we propose a method to explicitly incorporate such semantics in the MPCA framework to allow an automatic selective treatment of the variables that compose the patterns of interest. The method relies on spatial weights calculated, in this work, by separating hyperplanes and Fisher criterion. In this way, we can perform feature extraction and dimensionality reduction taking advantage of high level information in the form of labeled data. Besides, the corresponding tensor components are ranked in order to identify the principal weighted tensor subspaces for classification tasks. In the computational results we consider gender and facial expression experiments to illustrate the capabilities of the method for dimensionality reduction, classification and reconstruction of face images.