Robust Multiple Kernel k-means Clustering using Min-Max Optimization

Abstract: Multiple kernel learning is a type of multiview learning that combines different data modalities by capturing view-specific patterns using kernels. Although supervised multiple kernel learning has been extensively studied, until recently, only a few unsupervised approaches have been proposed. In the meanwhile, adversarial learning has recently received much attention. Many works have been proposed to defend against adversarial examples. However, little is known about the effect of adversarial perturbation in the context of multiview learning, and even less in the unsupervised case. In this study, we show that adversarial features added to a view can make the existing approaches with the min-max formulation in multiple kernel clustering yield unfavorable clusters. To address this problem and inspired by recent works in adversarial learning, we propose a multiple kernel clustering method with the min-max framework that aims to be robust to such adversarial perturbation. We evaluate the robustness of our method on simulation data under different types of adversarial perturbations and show that it outperforms several compared existing methods. In the real data analysis, We demonstrate the utility of our method on a real-world problem.