Improvement of Classification Using a Joint Spectral Dimensionality Reduction and Lower Rank Spatial Approximation for Hyperspectral Images

Abstract

Hyperspectral images (HSI) are multidimensional and multicomponent data with a huge number of spectral bands providing spectral redundancy. To improve the efficiency of the classifiers the principal component analysis (PCA), referred to as PCA _dr , the maximum noise fraction (MNF) and more recently the independent component analysis (ICA), referred to as ICA _dr are the most commonly used techniques for dimensionality reduction (DR). But, in HSI and in general when dealing with multi-way data, these techniques are applied on the vectorized images, providing a two-way data. The spatial representation is lost and the spectral components are selected using only spectral information. 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.We develop two news DR methods based on multilinear algebra tools which perform the DR using the PCA _dr for the first one and using the ICA _dr for the second one. We show that the result of spectral angle mapper (SAM) 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.