In fuzzy clustering, the fuzzy c-means (FCM) algorithm is the most commonly used clustering method. Various extensions of FCM had been proposed in the literature. However, the FCM algorithm and its extensions are usually affected by initializations and parameter selection with a number of clusters to be given a priori. Although there were some works to solve these problems in FCM, there is no work for FCM to be simultaneously robust to initializations and parameter selection under free of the fuzziness index without a given number of clusters. In this paper, we construct a robust learning-based FCM framework, called a robust-learning FCM (RL-FCM) algorithm, so that it becomes free of the fuzziness index m and initializations without parameter selection, and can also automatically find the best number of clusters. We first use entropy-type penalty terms for adjusting bias with free of the fuzziness index, and then create a robust learning-based schema for finding the best number of clusters. The computational complexity of the proposed RL-FCM algorithm is also analyzed. Comparisons between RL-FCM and other existing methods are made. Experimental results and comparisons actually demonstrate these good aspects of the proposed RL-FCM where it exhibits three robust characteristics: 1) robust to initializations with free of the fuzziness index, 2) robust to (without) parameter selection, and 3) robust to number of clusters (with unknown number of clusters). (C) 2017 Elsevier Ltd. All rights reserved.
This paper extends earlier work C. Borgelt, R. Kruse. Speeding up fuzzy clustering with neural network techniques, in: Proceedings of the 12th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE'03, St. Louis, MO, USA), IEEE Press, Piscataway, NJ, USA, 2003] on an approach to accelerate fuzzy clustering by transferring methods that were originally developed to speed up the training process of (artificial) neural networks. The core idea is to consider the difference between two consecutive steps of the alternating optimization scheme of fuzzy clustering as providing a gradient. This "gradient" may then be modified in the same way as a gradient is modified in error backpropagation in order to enhance the training. Even though these modifications are, in principle, directly applicable, carefully checking and bounding the update steps can improve the performance and can make the procedure more robust. In addition, this paper provides a new and much more detailed experimental evaluation that is based on fuzzy cluster comparison measures C. Borgelt, Resampling for fuzzy clustering, Int. J. Uncertainty, Fuzziness Knowledge-based Syst. 15 (5) (2007), 595-614], which can be used nicely to study the convergence speed.
Triplet Markov fields (TMF) model proposed recently is suitable for nonstationary image segmentation. For synthetic aperture radar (SAR) image segmentation, TMF model can adopt diverse statistical models for SAR data related to diverse radar backscattering sources. However, TMF model does not take into account the inherent imprecision associated with SAR images. In this paper, we propose a statistical fuzzy TMF (FTMF) model, which is a fuzzy clustering type treatment of TMF model, for unsupervised multi-class segmentation of SAR images. This paper contributes to SAR image segmentation in four aspects: (1) Nonstationarity of the statistical distribution of SAR intensity/amplitude data is taken into account to improve the spatial modeling capability of fuzzy TMF model. (2) Mean field theory is generalized to deal with planar variables to derive prior probability in fuzzy TMF model, which resolves the problem in Gibbs sampler in terms of computation cost. (3) A fuzzy objective function with regularization by Kullback-Leibler information of fuzzy TMF model is constructed for SAR image segmentation. The introduction of fuzziness for the belongingness of SAR image pixel makes fuzzy TMF model be able to retain more information from SAR image. (4) Fuzzy iterative conditional estimation (ICE) method, as an extension of the general ICE method is proposed to perform the model parameters estimation. The effectiveness of the proposed algorithm is demonstrated by application to simulated data and real SAR images.
Fuzzy C-means clustering (FCM) is proposed as a promising method for the clustering of chromatographic fingerprints of complex samples, such as essential oils. As an example, secondary metabolites of 14 citrus leaves samples are extracted and analyzed by gas chromatography-mass spectrometry (GC-MS). The obtained chromatographic fingerprints are divided to desired number of chromatographic regions. Owing to the fact that chromatographic problems, such as elution time shift and peak overlap can significantly affect the clustering results, therefore, each chromatographic region is analyzed using multivariate curve resolution-alternating least squares (MCR-ALS) to address these problems. Then, the resolved elution profiles are used to make a new data matrix based on peak areas of pure components to cluster by FCM. The FCM clustering parameters (i.e., fuzziness coefficient and number of cluster) are optimized by two different methods of partial least squares (PLS) as a conventional method and minimization of FCM objective function as our new idea. The results showed that minimization of FCM objective function is an easier and better way to optimize FCM clustering parameters. Then, the optimized FCM clustering algorithm is used to cluster samples and variables to figure out the similarities and dissimilarities among samples and to find discriminant secondary metabolites in each cluster (chemotype). Finally, the FCM clustering results are compared with those of principal component analysis (PCA), hierarchical cluster analysis (HCA) and Kohonon maps. The results confirmed the outperformance of FCM over the frequently used clustering algorithms. (C) 2016 Elsevier B.V. All rights reserved.