Classification improvement by dimensionality reduction based on multilinear algebra tools

Hyperspectral images (HSI) are multidimensional and multicomponent data with a huge number of spectral bands. To improve classifiers efficiency the principal component analysis (PCA), referred to as PCA_dr, the maximum noise fraction (MNF) and more recently the independent component analysis (ICA) are the most commonly used techniques for dimensionality reduction. But to apply those techniques, and in general when dealing with multi-way data, a standard technique consists in vectorizing images provide two-way data. As an alternative, in this paper, we propose to consider HSI as array data or tensor-instead of matrix- which offers multiple ways to decompose data orthogonally. This new method is based on multilinear algebra tools which generalize the PCA to higher order. We show that the result of classification is improved by taking advantage of jointly spatial and spectral information and by performing simultaneously a dimensionality reduction on the spectral way and a projection onto a lower dimensional subspace of the two spatial ways.