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
Self-organization and associative memory: 3rd edition
Self-organization and associative memory: 3rd edition
Self-organizing maps
Cluster analysis and mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Finding salient regions in images: nonparametric clustering for image segmentation and grouping
Computer Vision and Image Understanding - Special issue on content-based access for image and video libraries
ACM Computing Surveys (CSUR)
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Clustering Algorithms
Cluster validity methods: part I
ACM SIGMOD Record
A Decision Criterion for the Optimal Number of Clusters in Hierarchical Clustering
Journal of Global Optimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Information Theoretic Clustering of Sparse Co-Occurrence Data
ICDM '03 Proceedings of the Third IEEE International Conference on Data Mining
A Global Optimization RLT-based Approach for Solving the Hard Clustering Problem
Journal of Global Optimization
A Global Optimization RLT-based Approach for Solving the Fuzzy Clustering Problem
Journal of Global Optimization
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
Survey of clustering algorithms
IEEE Transactions on Neural Networks
Clustering of document collection - A weighting approach
Expert Systems with Applications: An International Journal
A review of recent advances in global optimization
Journal of Global Optimization
Journal of Global Optimization
Performance evaluation of density-based clustering methods
Information Sciences: an International Journal
A network flow model for biclustering via optimal re-ordering of data matrices
Journal of Global Optimization
Solving the Order-Preserving Submatrix Problem via Integer Programming
INFORMS Journal on Computing
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Cluster analysis of genome-wide expression data from DNA microarray hybridization studies is a useful tool for identifying biologically relevant gene groupings (DeRisi et al. 1997; Weiler et al. 1997). It is hence important to apply a rigorous yet intuitive clustering algorithm to uncover these genomic relationships. In this study, we describe a novel clustering algorithm framework based on a variant of the Generalized Benders Decomposition, denoted as the Global Optimum Search (Floudas et al. 1989; Floudas 1995), which includes a procedure to determine the optimal number of clusters to be used. The approach involves a pre-clustering of data points to define an initial number of clusters and the iterative solution of a Linear Programming problem (the primal problem) and a Mixed-Integer Linear Programming problem (the master problem), that are derived from a Mixed Integer Nonlinear Programming problem formulation. Badly placed data points are removed to form new clusters, thus ensuring tight groupings amongst the data points and incrementing the number of clusters until the optimum number is reached. We apply the proposed clustering algorithm to experimental DNA microarray data centered on the Ras signaling pathway in the yeast Saccharomyces cerevisiae and compare the results to that obtained with some commonly used clustering algorithms. Our algorithm compares favorably against these algorithms in the aspects of intra-cluster similarity and inter-cluster dissimilarity, often considered two key tenets of clustering. Furthermore, our algorithm can predict the optimal number of clusters, and the biological coherence of the predicted clusters is analyzed through gene ontology.