Clustering based on hyperplanes

In machine learning, clustering is of pivotal importance and there is a growing research interest directed towards it. Many clustering algorithms have been proposed using a wide range of approaches. In this study, we focus on high-dimensional data clustering and adopt the maximum margin clustering approach. To this end, we introduced two methods: The first proposed method uses the classical maximum margin clustering approach, and it splits the data into two clusters with the largest margin between them. The second proposed method takes the cluster compactness into consideration, and it searches for two parallel hyperplanes that best fit the cluster samples but at the same time as far as possible from each other. In addition, we introduced the variants of these clustering methods that are more robust to the outliers and noise within the data samples. We use the stochastic gradient (SG) algorithm to solve the resulting optimization problems, therefore all proposed clustering methods scale well with large-scale data. The experimental results show that the proposed methods significantly outperform the existing maximum margin clustering methods, especially on high-dimensional clustering problems, which shows the efficacy of the proposed methods.