Ising-Based Combinatorial Clustering Using the Kernel Method

Combinatorial clustering based on the Ising model is getting attention as a method to obtain high-quality clustering results. Furthermore, combinatorial clustering using the kernel method can handle any irregular data type by using a kernel trick. The kernel trick is an approach to the extension of the data to an arbitrary high-dimensional feature space by switching the kernel function. However, the conventional kernel clustering based on the Ising model can only be used in the limited case where the number of clusters is two. This is because the Ising model is composed of decision variables that represent binary values. This paper proposes Ising-based combinatorial clustering using a kernel method that can handle two or more clusters. The key idea of the proposed method is to represent clustering results using one-hot encoding. One-hot encoding represents a cluster to which a single data belongs by using bits whose number is the same as that of clusters. However, the one-hot constraint caused by the use of one-hot encoding decreases the quality of clustering. To this problem, in this paper, combinatorial clustering based on an externally defined one-hot constraint is used. The proposed kernel-based combinatorial clustering works with more than two clusters. Therefore, the proposed method is compared with Euclidean distance-based combinatorial clustering that divides the data into two or more clusters as the conventional method. Through experiments, it is clarified that the quality of the clustering results of the proposed method for irregular data is significantly better than that of the conventional method.