Diffusion Map Kernel Analysis for Target Classification

Given a high dimensional dataset, one would like to be able to represent this data using fewer parameters while preserving relevant information, previously this was done with principal component analysis, factor analysis, or feature selection. However, if we assume the original data actually exists on a lower dimensional manifold embedded in a high dimensional feature space, then recently popularized approaches based in graph-theory and differential geometry allow us to learn the underlying manifold that generates the data. One such manifold-learning technique, called Diffusion Maps, is said to preserve the local proximity between data points by first constructing a representation for the underlying manifold. This work examines binary target classification problems using Diffusion Maps to embed the data with various kernel representations for the diffusion parameter. Results demonstrate that specific kernels are well suited for Diffusion Map applications on some sonar feature sets and in general certain kernels outperform the standard Gaussian and Polynomial kernels, on several of the higher dimensional data sets including the sonar data contrasting with their performance on the lower-dimensional publicly available data sets.