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Kernel k-means is an extension of the standard k -means clustering algorithm that identifies nonlinearly separable clusters. In order to overcome the cluster initialization problem associated with this method, we propose the global kernel k-means algorithm, a deterministic and incremental approach to kernel-based clustering. Our method adds one cluster at each stage, through a global search procedure consisting of several executions of kernel k-means from suitable initializations. This algorithm does not depend on cluster initialization, identifies nonlinearly separable clusters, and, due to its incremental nature and search procedure, locates near-optimal solutions avoiding poor local minima. Furthermore, two modifications are developed to reduce the computational cost that do not significantly affect the solution quality. The proposed methods are extended to handle weighted data points, which enables their application to graph partitioning. We experiment with several data sets and the proposed approach compares favorably to kernel k -means with random restarts.

Kernel k-means is an extension of the standard kmeans clustering algorithm that identifies nonlinearly separable clusters. In order to overcome the cluster initialization problem associated with this method, in this work we propose the global kernel k-means algorithm, a deterministic and incremental approach to kernel-based clustering. Our method adds one cluster at each stage through a global search procedure consisting of several executions of kernel k-means from suitable initializations. This algorithm does not depend on cluster initialization, identifies nonlinearly separable clusters and, due to its incremental nature and search procedure, locates near optimal solutions avoiding poor local minima. Furthermore a modification is proposed to reduce the computational cost that does not significantly affect the solution quality. We test the proposed methods on artificial data and also for the first time we employ kernel k-means for MRI segmentation along with a novel kernel. The proposed methods compare favorably to kernel k-means with random restarts.

Multiview clustering partitions a dataset into groups by simultaneously considering multiple representations (views) for the same instances. Hence, the information available in all views is exploited and this may substantially improve the clustering result obtained by using a single representation. Usually, in multiview algorithms all views are considered equally important, something that may lead to bad cluster assignments if a view is of poor quality. To deal with this problem, we propose a method that is built upon exemplar-based mixture models, called convex mixture models (CMMs). More specifically, we present a multiview clustering algorithm, based on training a weighted multiview CMM, that associates a weight with each view and learns these weights automatically. Our approach is computationally efficient and easy to implement, involving simple iterative computations. Experiments with several datasets confirm the advantages of assigning weights to the views and the superiority of our framework over single-view and unweighted multiview CMMs, as well as over another multiview algorithm which is based on kernel canonical correlation analysis.