Endmember Extraction on the Grassmannian
This addresses endmember extraction for hyperspectral image analysis, but appears incremental as it adapts existing concepts to a subspace setting.
The paper tackles the problem of extracting endmembers as subspaces in high-dimensional data like hyperspectral imagery, proposing an algorithm to identify subspaces near the convex hull boundary on a Grassmannian and demonstrating it on synthetic and real-world datasets.
Endmember extraction plays a prominent role in a variety of data analysis problems as endmembers often correspond to data representing the purest or best representative of some feature. Identifying endmembers then can be useful for further identification and classification tasks. In settings with high-dimensional data, such as hyperspectral imagery, it can be useful to consider endmembers that are subspaces as they are capable of capturing a wider range of variations of a signature. The endmember extraction problem in this setting thus translates to finding the vertices of the convex hull of a set of points on a Grassmannian. In the presence of noise, it can be less clear whether a point should be considered a vertex. In this paper, we propose an algorithm to extract endmembers on a Grassmannian, identify subspaces of interest that lie near the boundary of a convex hull, and demonstrate the use of the algorithm on a synthetic example and on the 220 spectral band AVIRIS Indian Pines hyperspectral image.