Hybrid manifold clustering with evolutionary tuning

Abstract

Manifold clustering, also known as submanifold learning, is the task to embed patterns in submanifolds with different characteristics. This paper proposes a hybrid approach of clustering the data set, computing a global map of cluster centers, embedding each cluster, and then merging the scaled submanifolds with the global map. We introduce various instantiations of cluster and embedding algorithms based on hybridization of k-means, principal component analysis, isometric mapping, and locally linear embedding. A (1+1)-ES is employed to tune the submanifolds by rotation and scaling. The submanifold learning algorithms are compared w.r.t. the nearest neighbor classification performance on various experimental data sets.