On various types of controlled-sized clustering based on optimization
On various types of controlled-sized clustering based on optimization
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DOI：
10.1109/fuzz-ieee.2017.8015556
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发表时间：
2017-07
期刊：
影响因子：
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通讯作者：
Y. Endo;Sachiko Ishida;Naohiko Kinoshita;Y. Hamasuna
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文献类型：
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作者：
Y. Endo;Sachiko Ishida;Naohiko Kinoshita;Y. Hamasuna
聚类是无监督分类方法之一，即在没有任何外部标准的情况下将数据集分类为一些簇。典型的聚类方法，例如k 均值 (KM) 或模糊 c 均值 (FCM) 是基于给定目标函数的优化构建的。许多聚类方法以及 KM 和 FCM 都被表述为具有典型目标函数和约束的优化问题。目标函数本身也是聚类方法结果的评价准则。考虑到其理论可扩展性，在优化框架中构建聚类方法具有巨大的优势。一些作者从优化的角度出发，提出了一种对簇大小有严格约束的基于优化的偶数聚类方法（ECBO），并构造了ECBO的一些变体。 ECBO中考虑的约束是每个簇大小为K或K+1，并且在每次迭代中通过单纯形法计算每个对象对簇的归属度。认为ECBO在聚类精度、聚类大小、优化框架等方面比其他类似方法具有优势。然而，ECBO对簇大小的约束在簇大小的意义上是严格的，因此在允许簇大小有一些额外余量的情况下可能会不方便。此外，预计可以控制每个簇大小的新聚类算法可以处理更多不同的数据集。从以上观点出发，我们提出了两种基于ECBO的新的聚类算法。一种是基于优化的COtrolled-sized Clustering（COCBO），另一种是扩展的COCBO，称为基于优化的COtrolled-sized Clustering++（COCBO++）。每个簇的大小可以在算法中控制。然而，这些算法存在一些问题。在本文中，我们将描述各种类型的COCBO来解决上述问题，并在一些数值示例中评估方法。
Clustering is one of unsupervised classification method, that is, it classifies a data set into some clusters without any external criterion. Typical clustering methods, e.g. k-means (KM) or fuzzy c-means (FCM) are constructed based on optimization of the given objective function. Many clustering methods as well as KM and FCM are formulated as optimization problems with typical objective functions and constraints. The objective function itself is also an evaluation guideline of results of clustering methods. Considered together with its theoretical extensibility, there is the great advantage to construct clustering methods in the framework of optimization. From the viewpoint of optimization, some of the authors proposed an Even-sized Clustering method Based on Optimization (ECBO), which is with tight constraints of cluster size, and constructed some variations of ECBO. The constraint considered in ECBO is that each cluster size is K or K + 1, and the belongingness of each object to clusters is calculated by the simplex method in each iteration. It is considered that ECBO has the advantage in the viewpoint of clustering accuracy, cluster size, and optimization framework than other similar methods. However, the constraint of cluster sizes of ECBO is tight in the meaning of cluster size so that it may be inconvenient in case that some extra margin of cluster size is allowed. Moreover, it is expected that new clustering algorithms in which each cluster size can be controlled deal with more various datasets. From the above view point, we proposed two new clustering algorithms based on ECBO. One is COntrolled-sized Clustering Based on Optimization (COCBO), and the other is an extended COCBO, which is referred to as COntrolled-sized Clustering Based on Optimization++ (COCBO++). Each cluster size can be controlled in the algorithms. However, these algorithms have some problems. In this paper, we will describe various types of COCBO to solve the above problems and estimate the methods in some numerical examples.