Paper:

# Hard *c*-Means Using Quadratic Penalty-Vector Regularization for Uncertain Data

## Yasunori Endo^{*}, Arisa Taniguchi^{**}, and Yukihiro Hamasuna^{***}

^{*}Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

^{**}Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

^{***}Department of Informatics, Kinki University, 3-4-1 Kowakae, Higashiosaka, Osaka 577-8502, Japan

*c*-means, quadratic penalty-vector regularization, sequential extraction

Clustering is an unsupervised classification technique for data analysis. In general, each datum in real space is transformed into a point in a pattern space to apply clustering methods. Data cannot often be represented by a point, however, because of its uncertainty, e.g., measurement error margin and missing values in data. In this paper, we will introduce quadratic penalty-vector regularization to handle such uncertain data using Hard *c*-Means (HCM), which is one of the most typical clustering algorithms. We first propose a new clustering algorithm called hard c-means using quadratic penalty-vector regularization for uncertain data (HCMP). Second, we propose sequential extraction hard c-means using quadratic penalty-vector regularization (SHCMP) to handle datasets whose cluster number is unknown. Furthermore, we verify the effectiveness of our proposed algorithms through numerical examples.

*c*-Means Using Quadratic Penalty-Vector Regularization for Uncertain Data,”

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.16, No.7, pp. 831-840, 2012.

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