Graph optimized locality preserving projection via heuristic optimization algorithms

Dimensionality reduction has been an active research topic in hyperspectral image analysis due to complexity and nonlinearity of the hundreds of the spectral bands. Locality preserving projection (LPP) is a linear extension of the manifold learning and has been very effective in dimensionality reduction compared to linear methods. However, its performance heavily depends on construction of the graph affinity matrix, which has two parameters need to be optimized: k-nearest neighbor parameter and heat kernel parameter. These two parameters might be optimally chosen simply based on a grid search when using only one representative kernel parameter for all the features, but this solution is not feasible when considering a generalized heat kernel in construction the affinity matrix. In this paper, we propose to use heuristic methods, including harmony search (HS) and particle swarm optimization (PSO), in exploring the effects of the heat kernel parameters on embedding quality in terms of classification accuracy. 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 isotropic kernel with single parameter.