Kernelized evolutionary distance metric learning for semi-supervised clustering

This study proposes a novel distance metric learning method called evolutionary distance metric learning (EDML) to improve clustering quality that simultaneously evaluates inter- and intra-clusters. While we also provide an extension which integrates kernelization technique to the proposed method namely kernelized evolutionary distance metric learning (K-EDML). Hence, the non-linear transformation of distance metric can be performed while maintaining all properties of EDML. The proposed methods are able to handle either class label or pairwise constraints and directly improve any clustering index as an objective function. Both can be viewed as utilization of cluster-level soft constraints, unlike other instance-level hard constraints which sometimes collapse the clustering. Also, maintaining neighbor relation of clusters can lead to better visualization of the clustering result. For multimodality problem of the objective function, an evolutionary algorithm (EA), differential evolution with self-adapting control parameters and generalized opposition-based learning (GOjDE), is employed to optimize a metric transform matrix based on the Mahalanobis distance. We empirically demonstrate the drawback of EDML in non-linearly separable input space and illustrate the benefit of kernel function to extension K-EDML method by showing its superior result benefits to other clustering algorithms in the semi-supervised clustering on various real-world datasets.