Exploration of virtual dimensionality in hyperspectral image analysis

Virtual dimensionality (VD) is a new concept which was developed to estimate the number of spectrally distinct signatures present in hyperspectral image data. Unlike intrinsic dimensionality which is mainly of theoretical interest, the VD is a very useful and practical notion. It is derived from the Neyman-Pearson detection theory. Unfortunately, its utility in hyperspectral data exploitation has yet to be explored. This paper presents several applications to which the VD is applied successfully. Since the VD is derived from a binary hypothesis testing problem for each spectral band, it can be used for band selection. When the test fails for a band, it indicates that there is a signal source in that particular band which must be selected. By the same token it can be further used for dimensionality reduction. For principal components analysis (PCA) or independent component analysis (ICA), the VD helps to determine the number of principal components or independent components are required for exploitation such as detection, classification, compression, etc. For unsupervised target detection and classification, the VD can be used to determine how many unwanted signal sources present in the image data so that they can be eliminated prior to detection and classification. For endmember extraction, the VD provides a good estimate of the number of endmembers needed to be extracted. All these applications are justified by experiments.