基于自适应L2瓦瑟斯坦距离的分布值数据模糊聚类
Fuzzy clustering of distribution-valued data using adaptive L2 Wasserstein distances
摘要：
分布（或分布值）数据是一种新类型的数据，来自多个来源，被认为是分布变量的实现。提出了一种新的模糊c-均值算法。该算法使用分布之间的$L2$瓦瑟斯坦距离作为相异性度量。除了扩展的模糊c-均值算法的分布数据，并考虑到分解的平方$L2$瓦瑟斯坦距离，我们提出了一套算法，使用不同的自动方式来计算与变量以及与它们的组件，全球或集群明智的权重。在聚类过程中引入产品对一的约束，计算相关权重。相关性权重引入自适应距离，表达聚类过程中每个变量或每个分量的重要性，也可以作为聚类中的变量选择方法。我们已经测试了人工和真实世界的数据所提出的算法。结果证实，所提出的方法是能够更好地考虑到相对于标准的模糊c-均值，与非自适应距离的数据的聚类结构。
英文摘要：
Distributional (or distribution-valued) data are a new type of data arising from several sources and are considered as realizations of distributional variables. A new set of fuzzy c-means algorithms for data described by distributional variables is proposed. The algorithms use the $L2$ Wasserstein distance between distributions as dissimilarity measures. Beside the extension of the fuzzy c-means algorithm for distributional data, and considering a decomposition of the squared $L2$ Wasserstein distance, we propose a set of algorithms using different automatic way to compute the weights associated with the variables as well as with their components, globally or cluster-wise. The relevance weights are computed in the clustering process introducing product-to-one constraints. The relevance weights induce adaptive distances expressing the importance of each variable or of each component in the clustering process, acting also as a variable selection method in clustering. We have tested the proposed algorithms on artificial and real-world data. Results confirm that the proposed methods are able to better take into account the cluster structure of the data with respect to the standard fuzzy c-means, with non-adaptive distances.
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