L/sub 1/-Norm based Fuzzy Clustering for Data with Tolerance
L/sub 1/-Norm based Fuzzy Clustering for Data with Tolerance
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DOI：
10.1109/fuzzy.2006.1681797
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发表时间：
2006-09
期刊：
影响因子：
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通讯作者：
Y. Endo;Ryuichi Murata;H. Toyoda;S. Miyamoto
中科院分区：
文献类型：
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作者：
Y. Endo;Ryuichi Murata;H. Toyoda;S. Miyamoto
本文构建了基于L1范数的容差数据聚类算法，并通过数值算例验证了算法的有效性。首先，定义了分别基于SFCM-T和EFCM-T的两个目标函数。理论上在L1范数空间中计算这些函数的精确解比在L1范数空间（欧几里德空间）中更复杂，因此提出了两种获得解的方法。接下来，提出两种基于L1范数的聚类算法，利用这两种方法获得精确解。最后，通过人工数据集和Iris数据集的数值例子验证了所提出算法的有效性。
In this paper, the clustering algorithms for data with tolerance are constructed based on L1-norm and the effectiveness is verified through numerical examples. First, two objective functions, which are based on SFCM-T and EFCM-T respectively, is defined. It is more complex to calculate exact solutions of these functions theoretically in the L1-norm space than the L1-norm space (Euclidean space) so that two methods to obtain the solutions are proposed. Next, two kinds of clustering algorithms based on L1-norm are proposed using the two methods to obtain the exact solutions. Last, the effectiveness of the proposed algorithms is verified through the numerical examples of an artificial data set and the Iris data set.