Silhouettes: a graphical aid to the interpretation and validation of cluster analysis
Journal of Computational and Applied Mathematics
Algorithms for clustering data
Algorithms for clustering data
A Validity Measure for Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Clustering Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
Journal of Global Optimization
Performance Evaluation of Some Clustering Algorithms and Validity Indices
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the algorithmic implementation of multiclass kernel-based vector machines
The Journal of Machine Learning Research
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Analysis of Biological Data: A Soft Computing Approach - Vol. 3
Analysis of Biological Data: A Soft Computing Approach - Vol. 3
Integrating clustering and supervised learning for categorical data analysis
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA
IEEE Transactions on Evolutionary Computation
On cluster validity for the fuzzy c-means model
IEEE Transactions on Fuzzy Systems
A comparison of methods for multiclass support vector machines
IEEE Transactions on Neural Networks
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In this article, a novel concept is introduced by using both unsupervised and supervised learning. For unsupervised learning, the problem of fuzzy clustering in microarray data as a multiobjective optimization is used, which simultaneously optimizes two internal fuzzy cluster validity indices to yield a set of Pareto-optimal clustering solutions. In this regards, a new multiobjective differential evolution based fuzzy clustering technique has been proposed. Subsequently, for supervised learning, a fuzzy majority voting scheme along with support vector machine is used to integrate the clustering information from all the solutions in the resultant Pareto-optimal set. The performances of the proposed clustering techniques have been demonstrated on five publicly available benchmark microarray data sets. A detail comparison has been carried out with multiobjective genetic algorithm based fuzzy clustering, multiobjective differential evolution based fuzzy clustering, single objective versions of differential evolution and genetic algorithm based fuzzy clustering as well as well known fuzzy c-means algorithm. While using support vector machine, comparative studies of the use of four different kernel functions are also reported. Statistical significance test has been done to establish the statistical superiority of the proposed multiobjective clustering approach. Finally, biological significance test has been carried out using a web based gene annotation tool to show that the proposed integrated technique is able to produce biologically relevant clusters of coexpressed genes.