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Virtual Dimensionality of Hyperspectral Data

The term of virtual dimensionality (VD) was first coined in Chang (2003a) as a new concept defined as the number of spectrally distinct signatures in hyperspectral imagery. It was later published in Chang and Du (2004) and has received considerable interest since then. There are reasons of why VD has become a widespread and acceptable concept in hyperspectral imaging community. First, due to significantly improved spectral and spatial resolutions a hyperspectral image sensor can now uncover many unknown subtle material substances, referred to as signal sources that cannot be identified by a priori knowledge or visual inspection. Determining the number of such substances in the data is very challenging and extremely difficult, if not impossible. Second, there exists no concept in hyperspectral imaging similar to intrinsic dimensionality (ID) (Fukunaga, 1982, 1990) used in statistical signal processing, pattern recognition, and classification that can be used for hyperspectral data exploitation where ID, also known as effective dimensionality (ED), is defined as the minimal number of parameters used to characterize data. Third, the techniques developed for determining ID in multivariate data have been shown to be inapplicable to hyperspectral data. Finally and most importantly, before VD was introduced, there were few techniques available in the literature that can be used to effectively determine the number of unknown signal sources in hyperspectral data. VD was originally proposed to address these issues. Like many other new concepts VD has evolved through several stages where it has been examined and studied extensively for its use in various applications. As expected, some controversial issues also arise in how VD is used and interpreted. This chapter revisits and reexamines the concept of VD and further explores its utility in hyperspectral data exploitation, while clarifying some issues that may have misled users to misinterpreting VD.