A Partition Noise-Adjusted Principal Components Analysis for Determining Data Dimensionality in Hyperspectral Imagery

Abstract

In this paper, we apply noise-adjusted principla component analysis (NAPCA) to a partitioned data space to resolve the inaccuracy of the noise estimation and properly estimate the data dimensionality. This approach is referred to herein as PNAPCA. In contrast to the PCA-based approaches which consider interrelationships within a set of variables, PNAPCA focuses on the relationship between two distinct subspaces which are parititioned from the data space of the original image by a simultaneous transformation. This partitioning causes the gap between the group of eigenvalues for signal plus noise and noise only to become larger than all other PCA based approaches. The number of endmembers can then be determined by a designed union-intersection margin testing (UIMT).