Maximum volume clustering: a new discriminative clustering approach
Maximum volume clustering: a new discriminative clustering approach
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DOI：
10.5555/2567709.2567746
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Gang Niu;Bo Dai;L. Shang;Masashi Sugiyama
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文献类型：
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作者：
Gang Niu;Bo Dai;L. Shang;Masashi Sugiyama
由弗拉基米尔Vapnik提出的大体积原理，主张假设躺在一个等价类具有更大的体积是更可取的，是一个有用的替代大边际原则。在本文中，我们介绍了一种新的判别式聚类模型的基础上的大容量原则称为最大容量聚类（MVC），然后提出了两个近似方案来解决这个MVC模型：软标签MVC方法使用序列二次规划和硬标签MVC方法使用半定规划，分别。所提出的MVC在理论上是有利的，原因有三。硬标签MVC中涉及的优化是凸的，并且在温和的条件下，软标签MVC中涉及的优化在所产生的集群方面类似于凸的。其次，软标签MVC方法具有聚类误差界。第三，MVC包括谱聚类，两个松弛的k-均值聚类和信息最大化聚类的优化问题作为其正则化参数趋于无穷大时的特殊极限情况。几个人工和基准数据集上的实验表明，所提出的MVC与最先进的聚类方法相比毫不逊色。
The large volume principle proposed by Vladimir Vapnik, which advocates that hypotheses lying in an equivalence class with a larger volume are more preferable, is a useful alternative to the large margin principle. In this paper, we introduce a new discriminative clustering model based on the large volume principle called maximum volume clustering (MVC), and then propose two approximation schemes to solve this MVC model: A soft-label MVC method using sequential quadratic programming and a hard-label MVC method using semi-definite programming, respectively. The proposed MVC is theoretically advantageous for three reasons. The optimization involved in hard-label MVC is convex, and under mild conditions, the optimization involved in soft-label MVC is akin to a convex one in terms of the resulting clusters. Secondly, the soft-label MVC method possesses a clustering error bound. Thirdly, MVC includes the optimization problems of a spectral clustering, two relaxed k-means clustering and an information-maximization clustering as special limit cases when its regularization parameter goes to infinity. Experiments on several artificial and benchmark data sets demonstrate that the proposed MVC compares favorably with state-of-the-art clustering methods.