Hierarchical Clustering of Hyperspectral Images using Rank-Two Nonnegative Matrix Factorization

In this paper, we design a fast hierarchical clustering algorithm for high-resolution hyperspectral images (HSI). At the core of the algorithm, a new rank-two nonnegative matrix factorization (NMF) algorithm is used to split the clusters, which is motivated by convex geometry concepts. The method starts with a single cluster containing all pixels and, at each step, performs the following: 1) selects a cluster in such a way that the error at the next step is minimized and 2) splits the selected cluster into two disjoint clusters using rank-two NMF in such a way that the clusters are well balanced and stable. The proposed method can also be used as an endmember extraction algorithm in the presence of pure pixels. The effectiveness of this approach is illustrated on several synthetic and real-world HSIs and is shown to outperform standard clustering techniques such as k-means, spherical k-means, and standard NMF.