Spectral-Density-Based Graph Construction Techniques for Hyperspectral Image Analysis

Abstract

The past decade has seen the emergence of many hyperspectral image (HSI) analysis algorithms based on graph theory and derived manifold coordinates. The performance of these algorithms is inextricably tied to the graphical model constructed from the spectral data, i.e., the community structure of the spectral data must be well represented to extract meaningful information. This paper provides a survey of many spectral graph construction techniques currently used by the hyperspectral community and discusses their advantages and disadvantages for hyperspectral analyses. A focus is provided on techniques influenced by spectral density from which the concept of community structure arises. Two inherently density-weighted graph construction techniques from the data mining literature, shared nearest neighbor (NN) and mutual proximity, are also introduced and compared as they have not been previously employed in HSI analyses. Density-based edge allocation is demonstrated to produce more uniform NN lists than nondensity-based techniques by demonstrating an increase in the number of intracluster edges and improved $k$ -NN classification performance. Imposing the mutuality constraint to symmetrify an adjacency matrix is demonstrated to be beneficial in most circumstances, especially in rural (less cluttered) scenes. Surprisingly, many complex edge-reweighting techniques are shown to slightly degrade NN list characteristics. An analysis suggests this condition is possibly attributable to the validity of characterizing spectral density by a single variable representing data scale. As such, these complex edge-reweighting techniques may need to be modified to increase their effectiveness, or simply not be used.