Hybrid Genetic Algorithms Are Better for Spatial Clustering

Abstract

Iterative methods and genetic algorithms have been used separately to minimize the loss function of representative-based clustering formulations. Neither of them alone seems to be significantly better. Moreover, the trade-off of effort versus quality slightly favors gradient descent. We present a unifying view for the three most popular loss functions: least sum of squares, its fuzzy version and the log likelihood function. We identify commonalities in gradient descent algorithms for the three loss functions and the evaluation of the loss function itself. We can then construct hybrids (genetic algorithms with a mutation operation that performs few gradient descent steps) for all three clustering approaches. We demonstrate that these hybrids are much efficient and effective (significantly render better performance as normalized by the number of function evaluations or CPU time).