Optimization of Graph Affinity Matrix with Heuristic Methods in Dimensionality Reduction of Hypespectral Images

Hyperspectral images include hundreds of spectral bands, adjacent ones of which are often highly correlated and noisy, leading to a decrease in classification performance as well as a high increase in computational time. Dimensionality reduction techniques, especially the nonlinear ones, are very effective tools to solve these issues. Locality preserving projection (LPP) is one of those graph based methods providing a better representation of the high dimensional data in the low-dimensional space compared to linear methods. However, its performance heavily depends on the parameters of the affinity matrix, that are k-nearest neighbor and heat kernel parameters. Using simple methods like grid-search, optimization of these parameters becomes very computationally demanding process especially when considering a generalized heat kernel, including an exclusive parameter per feature in the high dimensional space. The aim of this paper is to show the effectiveness of the heuristic methods, including harmony search (HS) and particle swarm optimization (PSO), in graph affinity optimization constructed with a generalized heat kernel. The preliminary results obtained with the experiments on the hyperspectral images showed that HS performs better than PSO, and the heat kernel with multiple parameters achieves better performance than the heat kernel with a single parameter.