Kernel-based hard clustering methods in the feature space with automatic variable weighting

• The paper gives kernel-based hard clustering algorithms in the feature space.
• The algorithms learn a relevance weight for each variable.
• Partition and cluster interpretation tools are given.
• Applications on synthetic and real datasets corroborate the proposed algorithms.

This paper presents variable-wise kernel hard clustering algorithms in the feature space in which dissimilarity measures are obtained as sums of squared distances between patterns and centroids computed individually for each variable by means of kernels. The methods proposed in this paper are supported by the fact that a kernel function can be written as a sum of kernel functions evaluated on each variable separately. The main advantage of this approach is that it allows the use of adaptive distances, which are suitable to learn the weights of the variables on each cluster, providing a better performance. Moreover, various partition and cluster interpretation tools are introduced. Experiments with synthetic and benchmark datasets show the usefulness of the proposed algorithms and the merit of the partition and cluster interpretation tools.