On Tolerant Fuzzy c-Means Clustering with L1-Regularization

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  • HAMASUNA Yukihiro
    Graduate School of Systems and Information Engineering, University of Tsukuba
  • ENDO Yasunori
    Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba

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Other Title
  • L1正則化によるトレラントファジィc-平均法
  • L ₁ セイソクカ ニ ヨル トレラントファジィ c-ヘイキンホウ

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Abstract

We have proposed L2 or L1-norm based tolerant fuzzy c-means clustering (TFCM) from the viewpoint of handling data more flexibly. This paper presents a new type of tolerant fuzzy c-means clustering with L1-regularization. The L1-regularization is well-known as the most successful technique to induce sparseness. The proposed algorithm induce the sparseness for tolerance vector. First, tolerant fuzzy c-means clustering is introduced. Second, the optimization problems with L1-regularization are solved. Third, a new clustering algorithm is constructed based on the explicit optimal solutions. Finally, the effectiveness of the proposed algorithm is verified through numerical examples.

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