Sammon mapping for preliminary analysis in Hyperspectral Imagery

Abstract

The main goal of this paper is to present the implementation of the Sammon algorithm developed for finding N points in a lower m-dimensional subspace, where the original points are from a high n-dimensional space. This mapping is done so interpoints Euclidian distances in m-space correspond to the distances measured in the n-dimensional space. This method known as non-linear projection method or multidimensional scaling (MDS) aims to preserve the global properties of points. The method is based on the idea of transforming the original, n-dimensional input space into a reduced, m-dimensional one, where m<n, and it may be used to clustering hyperspectral data. The Principal Component Analysis (PCA) may be applied as a pre-processing procedure for starting, in order to obtain the N points in the lower subspace. The algorithm was tested on hyperspectral data with spectra of various lengths. Depending of the size of the input data (number of points), the number of learning iterations and computational facilities available, Sammon mapping might be computationally expensive.

Keywords

• hyperspectral data
• Sammon mapping method
• Euclidian distances
• non-linear mapping techniques