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JACIII Vol.20 No.4 pp. 571-579
doi: 10.20965/jaciii.2016.p0571
(2016)

Paper:

On Fuzzy Non-Metric Model for Data with Tolerance and its Application to Incomplete Data Clustering

Yasunori Endo*1, Tomoyuki Suzuki*2, Naohiko Kinoshita*3, and Yukihiro Hamasuna*4

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

*2Graduate School of Systems and Information Engineering, University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

*3Department of Risk Engineering, University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

*4Department of Informatics, Kindai University
3-4-1 Kowakae, Higashiosaka, Osaka 577-8502, Japan

Received:
January 28, 2016
Accepted:
April 13, 2016
Published:
July 19, 2016
Keywords:
clustering, incomplete data, non-metric model, data with tolerance
Abstract

The fuzzy non-metric model (FNM) is a representative non-hierarchical clustering method, which is very useful because the belongingness or the membership degree of each datum to each cluster can be calculated directly from the dissimilarities between data and the cluster centers are not used. However, the original FNM cannot handle data with uncertainty. In this study, we refer to the data with uncertainty as “uncertain data,” e.g., incomplete data or data that have errors. Previously, a methods was proposed based on the concept of a tolerance vector for handling uncertain data and some clustering methods were constructed according to this concept, e.g. fuzzy c-means for data with tolerance. These methods can handle uncertain data in the framework of optimization. Thus, in the present study, we apply the concept to FNM. First, we propose a new clustering algorithm based on FNM using the concept of tolerance, which we refer to as the fuzzy non-metric model for data with tolerance. Second, we show that the proposed algorithm can handle incomplete data sets. Third, we verify the effectiveness of the proposed algorithm based on comparisons with conventional methods for incomplete data sets in some numerical examples.

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Last updated on Aug. 21, 2017