A comparison of deterministic and probabilistic approaches to endmember representation

The piece-wise convex multiple model endmember detection algorithm (P-COMMEND) and the Piece-wise Convex End-member detection (PCE) algorithm autonomously estimate many sets of endmembers to represent a hyperspectral image. A piece-wise convex model with several sets of endmembers is more effective for representing non-convex hyperspectral imagery over the standard convex geometry model (or linear mixing model). The terms of the objective function in P-COMMEND are based on geometric properties of the input data and the endmember estimates. In this paper, the P-COMMEND algorithm is extended to autonomously determine the number of sets of endmembers needed. The number of sets of endmembers, or convex regions, is determined by incorporating the competitive agglomeration algorithm into P-COMMEND. Results are shown comparing the Competitive Agglomeration P-COMMEND (CAP) algorithm to results found using the statistical PCE endmember detection method.