Dimension reduction for hyperspectral imaging using laplacian eigenmaps and randomized principal component analysis:Midyear Report

Hyperspectral imaging has attracted researchers’ interests in recent years. Because of its high dimensionality and complexity, the reduction of dimension of hyperspectral data sets has become crucial in processing and categorizing the data. In this project, I will apply two methods of dimension reduction: laplacian eigenmaps and randomized principal component analysis in order to reduce the dimension of hyperspectral imaging data. Laplacian eigenmaps is a method developed in 2002 for dimension reduction. It is widely used and is essential in understanding dimension reduction. Randomized principal component analysis is a method that is developed later in 2008. It takes an approach different from laplacian eigenmaps, but is more efficient in dealing with large matrices. My goal is to implement these two methods to some hyperspectral data sets, and study in order to understand the differences and similarities between these two methods. This project will also assists me in understanding hyperspectral imaging and in analyzing hyperspectral data sets.