Determining hyperspectral data-intrinsic dimensionality via a modified Gram-Schmidt process

The overdetermined nature of hyperspectral data constitutes a serious obstacle in many applicative fields. A vital step in dimensionality reduction is determining the intrinsic number of dimensions the signal resides in. This work proposes a modified Gram-Schmidt (MGS) process which iteratively finds the most distant pixels within the data in terms of an orthogonal complement norm (OCN) to a subspace spanned by the extreme pixels found in previous iterations. We analyze the distribution of extreme OCN using extreme values theory (EVT) and derive a termination condition for the MGS process. The dimensionality is determined by the number of found extreme pixels, which provide an estimation for the signal subspace.