Experiments in projection and clustering by simulated annealing

Simulated annealing is a stochastic relaxation algorithm which has been used successfully to optimize functions of many variables. This paper analyzes the simulated annealing algorithm when applied to the minimization of functions from two common problems encountered in exploratory pattern analysis, projection and clustering. The projection is a nonlinear mapping of patterns in high dimension to two dimensions. The simulated annealing mapping is compared to gradient descent minimization of the same objective function as well as eigenvector projection. The simulated annealing clustering is compared to a k-means algorithm. Empirical results show that simulated annealing can produce results as good as those obtained by conventional methods, but are impractical for small data sets because of the high computational cost. Simulated annealing does, in the case of the mapping problem, yield a better optimization and better retained structure for large data sets containing tight gaussian clusters.