Determination of data dimensionality in hyperspectral imagery -- A noise-adjusted transformed Derschgorin disk approach

Abstract

In hyperspectral image analysis, determining a distinct material number is an important task for subsequent classification processes. Identifying the number of distinct materials is essentially the same task as determining the intrinsic dimensionality of the imaging spectrometer data. Minimum noise fraction (MNF) transformation or noise-adjusted principal component analysis (NAPCA) is a highly effective means of determining the inherent dimensionality of image data. However, inaccuracy in the noise estimation degrades the validity of this estimation. To effectively resolve this problem, this work presents a Noise-Adjusted Transformed Gerschgorin Disk approach (NATGD) which incorporates the NAPCA method into a transformed Gerschgorin disk (TGD) approach. By noise-adjusted, Gerschgorin disks in NATGD can be formed into two distinct, non-overlapping collections; one for signals and the other for noises. Hence, the number of distinct materials can be visually determined by counting the number of Gerschgorin disks for signals. Experimental results demonstrate that the method proposed herein can effectively solve the intrinsic dimensionality problem.