Modularity versus Laplacian Eigenmaps for dimensionality reduction and classification of hyperspectral imagery

Since hyperspectral imagery typically contains information from hundreds of spectral bands, dimensionality reduction is often used as a pre-processing step in algorithms for classifying pixels/regions. A popular algorithm for dimensionality reduction is Laplacian Eigenmaps (LE), which uses a graph-based model of the hyperspectral data and constructs a basis for the reduced-dimensional space from a few generalized eigenvectors of the graph Laplacian matrix. A related matrix that can be constructed from the same graph-based model is the modularity matrix, which has been used in complex network problems to detect “community” structures in graphs. In this paper, we use the modularity matrix to construct a basis for dimensionality reduction, yielding an algorithm called Modularity Eigenmaps (ME). We then assess the performance of ME versus LE on the subsequent classification of publicly available hyperspectral imagery with known ground truth labels, illustrating a tradeoff between accuracy/precision measures and computational speed.