Piecewise Flat Embeddings for Hyperspectral Image Analysis

Graph-based dimensionality reduction techniques such as Laplacian Eigenmaps (LE), Local Linear Embedding (LLE), Isometric Feature Mapping (ISOMAP), and Kernel Principal Components Analysis (KPCA) have been used in a variety of hyperspectral image analysis applications for generating smooth data embeddings. Recently, Piecewise Flat Embeddings (PIKE) were introduced in the computer vision community as a technique for generating constant eitibeddings that make data clustering / image segmentation a straightforward process. In this paper, we show how PFE arises by modifying I I yielding- a constrained l(1)-minimization problem that can be solved iteratively. Using publicly available data, we carry out experiments to illustrate the implications of applying PEE to pixel-based hyperspectral image clustering and classification.