Support Vector Data Descriptions and $k$ -Means Clustering: One Class?

We present ClusterSVDD, a methodology that unifies support vector data descriptions (SVDDs) and $k$ -means clustering into a single formulation. This allows both methods to benefit from one another, i.e., by adding flexibility using multiple spheres for SVDDs and increasing anomaly resistance and flexibility through kernels to $k$ -means. In particular, our approach leads to a new interpretation of $k$ -means as a regularized mode seeking algorithm. The unifying formulation further allows for deriving new algorithms by transferring knowledge from one-class learning settings to clustering settings and vice versa. As a showcase, we derive a clustering method for structured data based on a one-class learning scenario. Additionally, our formulation can be solved via a particularly simple optimization scheme. We evaluate our approach empirically to highlight some of the proposed benefits on artificially generated data, as well as on real-world problems, and provide a Python software package comprising various implementations of primal and dual SVDD as well as our proposed ClusterSVDD.