An introduction to spectral graph techniques for the analysis of hyperspectral image data

Abstract

Two of the biggest challenges in analyzing HyperSpectral Image (HSI) data are that, first, the data is very high-dimensional, and secondly, by its very nature, HSI contains both spatial and spectral information. In order to make full use of this information, models and algorithms should incorporate both aspects of the data; unfortunately, this is a decidedly non-trivial problem. In recent years, spectral graph theory (including manifold learning) has proven to be a very successful technique for analyzing high-dimensional data sets. Given the highly abstract nature of graphs, many of these techniques are easily applied to HSI data; moreover, by carefully choosing how the graph is constructed, both the spatial and spectral nature of the data can be included in the model. In this note, we present a general background overview of spectral graph theory, with an emphasis on how it can be used to analyze HSI data (in particular, to perform nonlinear dimensionality reduction as well as segmentation and classification). We include examples from real-world data, and also point out some of the issues (such as computational complexity and storage requirements) that need to be addressed.