Locally Constrained Support Vector Clustering

Support vector clustering transforms the data into a high dimensional feature space, where a decision function is computed. In the original space, the function outlines the boundaries of higher density regions, naturally splitting the data into individual clusters. The method, however, though theoretically sound, has certain drawbacks which make it not so appealing to the practitioner. Namely, it is unstable in the presence of outliers and it is hard to control the number of clusters that it identifies. Parametrizing the algorithm incorrectly in noisy settings, can either disguise some objectively present clusters in the data, or can identify a large number of small and nonintuitive clusters. Here, we explore the properties of the data in small regions building a mixture of factor analyzers. The obtained information is used to regularize the complexity of the outlined cluster boundaries, by assigning suitable weighting to each example. The approach is demonstrated to be less susceptible to noise and to outline better interpretable clusters than support vector clustering alone.