改进模糊划分的FCM聚类算法的一般化研究

Research on Generalized Fuzzy C-Means Clustering Algorithm with Improved Fuzzy Partitions

聚类分析是无监督模式识别中的一种重要方法,已广泛应用于数据挖掘、图像处理、计算机视觉、生物信息和文本分析中.在聚类算法中,模糊指数m对聚类结果有十分重要的影响.针对IFP-FCM算法模糊指数m被限定为2的问题,提出了一般化的改进模糊划分的FCM聚类算法GIFP-FCM.通过引入新的隶属度约束,解决了IFP-FCM算法模糊指数m的一般化问题;同时GIFP-FCM算法从Voronoi距离和竞争学习的角度对其鲁棒性和快速收敛性进行了合理解释;其次,通过引入模糊程度系数α,使得FCM算法和IFP-FCM算法分别表示为GIFP-FCM算法在α等于0和α趋于1时的特例.实验结果表明,GIFP-FCM算法较之于IFP-FCM和FCM算法具有更好的鲁棒性和参数适应性;在纹理图像分割中,GIFP-FCM也明显优于IFP-FCM和FCM算法.

Cluster analysis is an important tool of unsupervised pattern recognition. It has been used in diverse fields such as data mining, biology, computer vision, and document analysis. The fuzziness index m has important influence on the clustering result of fuzzy clustering algorithms and it should not be forced to fix at the usual value m=2. In view of its distinctive features in applications and its limitation of having m =2 only, a recent advance of fuzzy clustering called fuzzy e-means elustering with improved fuzzy partitions （IFP-FCM） is extended in this paper and a generalized algorithm ealled GIFP-FCM for more effective clustering is proposed. By introducing a novel membership constraint function, a new objective function is constructed and GIFP-FCM clustering is derived. Me.anwhile, from the viewpoints of Voronoi distance and competitive learning, the robustness and convergence of the proposed algorithm are analyzed. The proposed GIFP-FCM algorithm not only inherits the merits of IFP-FCM, but also generalizes it so that the original limitation on the fuzziness index m can be removed. Furthermore, the classical fuzzy e-means algorithm （FCM） and IFP-FCM can be taken as two special cases of the proposed algorithm, and GIFP-FCM provides a reasonable link between FCM and IFP-FCM. Several experimental results including its application to noisy image texture segmentation demonstrate its average advantage over FCM and IFP-FCM in both clustering and robustness capability.