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 (PFE) were introduced in the computer vision community as a technique for generating piecewise constant embeddings that make data clustering / image segmentation a straightforward process. In this paper, we show how PFE arises by modifying LE, yielding a constrained ℓ1-minimization problem that can be solved iteratively. Using publicly available data, we carry out experiments to illustrate the implications of applying PFE to pixel-based hyperspectral image clustering and classification.
Tyler L. Hayes, Renee T. Meinhold, John F. Hamilton, and Nathan D. Cahill, "Piecewise flat embeddings for hyperspectral image analysis," Proc. SPIE 10198, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXIII, 101980O (Presented at SPIE Defense + Security: April 12, 2017; Published: 5 May 2017); https://doi.org/10.1117/12.2262302.
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