A new nonlinear dimensionality reduction method with application to hyperspectral image analysis

Abstract

In this paper, we propose a new nonlinear dimensionality reduction method by combining Locally Linear Embedding (LLE) with Laplacian Eigenmaps, and apply it to hyperspectral data. LLE projects high dimensional data into a low-dimensional Euclidean space while preserving local topological structures. However, it may not keep the relative distance between data points in the dimension-reduced space as in the original data space. Laplacian Eigenmaps, on the other hand, can preserve the locality characteristics in terms of distances between data points. By combining these two methods, a better locality preserving method is created for nonlinear dimensionality reduction. Experiments conducted in this paper confirms the feasibility of the new method for hyperspectral dimensionality reduction. The new method can find the same number of endmembers as PCA and LLE, but it is more accurate than them in terms of endmember location. Moreover, the new method is better than Laplacian Eigenmap alone because it identifies more pure mineral endmembers.