Convex clustering with metric learning
Convex clustering with metric learning
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DOI：
10.1016/j.patcog.2018.04.019
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
Xiaopeng Lucia Sui;Li Xu;Xiaoning Qian;Tie Liu
中科院分区：
文献类型：
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作者：
Xiaopeng Lucia Sui;Li Xu;Xiaoning Qian;Tie Liu
重温了Chii和Lange(2015)的凸聚类公式。虽然这一公式可以精确而有效地求解，但它使用标准欧几里德度量来衡量数据点与其对应的聚类中心之间的距离，因此在存在离群点特征时，其性能会显著恶化。为了解决这个问题，本文考虑了一种将凸聚类和度量学习相结合的公式。结果表明：(1)对于任意给定的正定马氏距离度量，利用乘子交替方向法可以精确有效地解决凸聚类问题；(2)学习正定马氏距离度量的问题存在一个闭合解；(3)一种在凸聚类和度量学习之间交替的算法不仅比原来的凸聚类公式有显著的性能提升，而且比Wang等人最近提出的鲁棒凸聚类公式有显著的性能提升。(2017年)。
The convex clustering formulation of Chi and Lange (2015) is revisited. While this formulation can be precisely and efficiently solved, it uses the standard Euclidean metric to measure the distance between the data points and their corresponding cluster centers and hence its performance deteriorates significantly in the presence of outlier features. To address this issue, this paper considers a formulation that combines convex clustering with metric learning. It is shown that: (1) for any given positive definite Mahalanobis distance metric, the problem of convex clustering can be precisely and efficiently solved using the Alternating Direction Method of Multipliers; (2) the problem of learning a positive definite Mahalanobis distance metric admits a closed-form solution; (3) an algorithm that alternates between convex clustering and metric learning can provide a significant performance boost over not only the original convex clustering formulation but also the recently proposed robust convex clustering formulation of Wang et al. (2017).