Nonlocal Total Variation with Primal Dual Algorithm and Stable Simplex Clustering in Unsupervised Hyperspectral Imagery Analysis

We focus on implementing a nonlocal total variational method for unsupervised classification of hyperspectral imagery. We minimize the energy directly using a primal dual algorithm, which we modified for the non-local gradient and weighted centroid recalculation. By squaring the labeling function in the fidelity term before re-calculating the cluster centroids, we can implement an unsupervised clustering method with random initialization. We stabilize this method with stable simplex clustering. To better differentiate clusters, we use a linear combination of the cosine and Euclidean distance between spectral signatures instead of the traditional cosine distance. Finally, we speed up the calculation using a k-d tree and approximate nearest neighbor search algorithm for calculation of the weight matrix for distances between pixel signatures. We implement our method on six different datasets and compare results to traditional clustering methods like kmeans, non-negative matrix factorization, and the graph-based MBO scheme.