Robust Fuzzy C-means Clustering Algorithm Integrating Between-cluster Information
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摘要:
与经典的K均值聚类算法相比，模糊C均值(FCM)聚类算法通过引入模糊因子，考虑不同聚类数据簇之间的相互关系，得到可分性更好的聚类结果。但是模糊因子的引入，使得任意一个样本点都存在模糊性，造成FCM极易受到噪声和离群点的影响，聚类结果泛化性能较差。因此，该文提出一种簇间可分的鲁棒FCM算法(RBI-FCM)。RBI-FCM利用K均值算法对模糊隶属度的稀疏特征，降低不同数据簇之间的相互作用，突出不同数据簇相邻区域的可分性；另外，RBI-FCM在极小化数据簇内部散布度的条件下，考虑不同数据簇之间的可分性，可提高聚类模型的泛化性能。该文设计了有效的模型求解迭代算法。实验结果表明，RBI-FCM算法提高了FCM的鲁棒性，有效降低FCM对数据簇分布差异性和抽样不均衡的敏感性，得到理想的聚类结果。
Abstract:Comparing with K-means, Fuzzy logic is introduced in Fuzzy C-Means to handle the information between clusters. It can obtain better cluster results. However, fuzzy logic makes observations could belong to more than just one cluster, which results FCM is especially sensitivity to the noisy and outlier and has poor generalization performance. So a Rrobust Fuzzy C-Means clustering integrated Between-cluster Information algorithm (RBI-FCM) is proposed. Taking advantage of the sparsity of K-means, RBI-FCM helps to reduce the interactions among different clusters and improve the separability of sample points which locate in the adjacent domains of different clusters. Beside minimizing the inner-cluster scattering condition, RBI-FCM considers the between-cluster information. The generalization performance of RBI-FCM can be improved. An effective iterative algorithm for solving the model is designed in this paper. The experimental results show that the RBI-FCM improves the robustness of FCM and reduce effectively its sensitivity to size-imbalance and differences on the distribution of clusters of FCM. The great clustering result is obtained.
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Key words:
- Clustering /
- Fuzzy C-Means (FCM) /
- Sample distribution /
- Between-cluster information
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表 1 实验1：人造样本数据集主要参数
样本集 类中心 协方差矩阵 各类样本数 1 (5, 5), (15, 15) [1 0; 0 1], [1 0; 0 1] 50, 50 2 (5, 5), (15, 15) [1 0; 0 1], [2 0; 0 2] 50, 50 $\vdots $ $\vdots $ $\vdots $ $\vdots $ 10 (5, 5), (15, 15) [1 0; 0 1], [10 0; 0 10] 50, 50 
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表 2 实验2：人造样本数据集主要参数
样本集 样本随机分布的圆心 各类样本数 1 (5, 5), (15, 15) 50, 50 2 (5, 5), (15, 15) 50, 51 $\vdots $ $\vdots $ $\vdots $ $\vdots $ 151 (5, 5), (15, 15) 50, 200
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表 3 UCI数据集聚类实验的NMI正确率和RI正确率
UCI数据集 FCM PFCM GIFP-FCM RBI-FCM UCI数据集 FCM PFCM GIFP-FCM RBI-FCM Auto-mgp 0.5190 0.5167 0.5008 0.5443 Wine 0.4169 0.4168 0.3946 0.4911 0.7534 0.7537 0.7505 0.7895 0.7104 0.7105 0.6700 0.7287 Zoo 0.6760 0.6824 0.6284 0.6873 Balance Scale 0.1223 0.1232 0.1293 0.1326 0.8381 0.8400 0.8236 0.8464 0.5887 0.5900 0.5806 0.5947 Parkinsons 0.0926 0.0936 0.0526 0.1071 House Votes 0.4743 0.4743 0.2917 0.4948 0.5934 0.5934 0.5693 0.6266 0.7752 0.7752 0.6688 0.7890 Credit Approval 0.0304 0.0304 0.0365 0.1020 Vowel 0.3019 0.3127 0.3357 0.3737 0.5048 0.5048 0.5207 0.5448 0.7755 0.7988 0.8275 0.8153 Banknote Authentication 0.0292 0.0292 0.1145 0.5249 Mammographic Masses 0.1054 0.1065 0.1020 0.1130 0.5236 0.5236 0.5555 0.8053 0.5676 0.5683 0.5524 0.5746 注：每个数据集实验结果的第1行为NMI正确率，第2行为RI正确率
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