Gornitz Nico, Lima Luiz Alberto, Muller Klaus-Robert, Kloft Marius, Nakajima Shinichi
IEEE Trans Neural Netw Learn Syst. 2018 Sep;29(9):3994-4006. doi: 10.1109/TNNLS.2017.2737941. Epub 2017 Sep 27.
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.
我们提出了聚类支持向量数据描述（ClusterSVDD），这是一种将支持向量数据描述（SVDD）和k均值聚类统一为单一公式的方法。这使得两种方法能够相互受益，即通过为SVDD使用多个球体增加灵活性，并通过核函数提高k均值的抗异常能力和灵活性。特别是，我们的方法为k均值提供了一种新的解释，即作为一种正则化模式搜索算法。这种统一的公式还允许通过将知识从单类学习设置转移到聚类设置，反之亦然，从而推导出新的算法。作为一个展示，我们基于单类学习场景推导出一种用于结构化数据的聚类方法。此外，我们的公式可以通过一种特别简单的优化方案来求解。我们通过实证评估我们的方法，以突出在人工生成的数据以及现实世界问题上所提出的一些优点，并提供一个Python软件包，其中包括原始和对偶SVDD的各种实现以及我们提出的ClusterSVDD。
