Article Outline
Introduction
Formulations
Notation and Pre-Clustering
Proposed Algorithm
Case Study
Experimental Data
Description of Comparative Study
Results and Discussion
References
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Adams WP, Sherali HD (1990) Linearization Strategies for a Class of Zero-One Mixed Integer Programming Problems. Oper Res 38(2):217–226
Beer M, Tavazoie S (2004) Predicting Gene Expression from Sequence. Cell 117:185–198
Bezdek JC (1981) Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York
Carpenter G, Grossberg S (1990) ART3: Hierarchical Search using Chemical Transmitters in Self‐Organizing Patterns Recognition Architectures. Neural Netw 3:129–152
Claverie J (1999) Computational Methods for the Identification of Differential and Coordinated Gene Expression. Hum Mol Genet 8:1821–1832
Davis DL, Bouldin DW (1979) A Cluster Separation Measure. IEEE Trans Pattern Anal Mach Intell 1(4):224–227
Dempster AP, Laird NM, Rudin DB (1977) Maximum Likelihood from Incomplete Data via the EM Algorithm. J Royal Stat Soc B 39(1):1–38
Dhillon IS, Guan Y (2003) Information Theoretic Clustering of Sparse Co‐Occurrence Data. In: Proceedings of the Third IEEE International Conference on Data Mining (ICDM), Melbourbe, November 2003
Dunn JC (1973) A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well‐Separated Clusters. J Cybern 3:32–57
Dunn JC (1974) Well Separated Clusters and Optimal Fuzzy Partitions. J Cybern 4:95–104
Duran MA, Odell PL (1974) Cluster Analysis: A Survey. Springer, New York
Floudas CA (1995) Nonlinear and Mixed‐Integer Optimization: Fundamentals and Applications. Oxford University Press, Oxford
Floudas CA (2000) Deterministic Global Optimization: Theory, Algorithms, and Applications. Kluwer, Dordrecht
Floudas CA, Aggarwal A, Ciric AR (1989) Global Optimum Search for Non Convex NLP and MINLP Problems. Comp Chem Eng 13(10):1117–1132
Floudas CA, Akrotirianakis IG, Caratzoulas S, Meyer CA, Kallrath J (2005) Global Optimization in the 21st Century: Advances and Challenges. Comput Chem Eng 29:1185–2002
Goodman L, Kruskal W (1954) Measures of Associations for Cross‐Validations. J Am Stat Assoc 49:732–764
Gower JC, Ross GJS (1969) Minimum Spanning Trees and Single‐Linkage Cluster Analysis. Appl Stat 18:54–64
Halkidi M, Batistakis Y, Vazirgiannis M (2002) Cluster Validity Methods: Part 1. SIGMOD Rec 31(2):40–45
Hansen P, Jaumard B (1997) Cluster Analysis and Mathematical Programming. Math Program 79:191–215
Hartigan JA (1975) Clustering Algorithms. Wiley, New York
Hartigan JA, Wong MA (1979) Algorithm AS 136: A K‑Means Clustering Algorithm. Appl Stat-J Roy St C 28:100–108
Herrero J, Valencia A, Dopazo J (2001) A Hierarchical Unsupervised Growing Neural Network for Clustering Gene Expression Patterns. Bioinformatics 17(2):126–136
Heyer LJ, Kruglyak S, Yooseph S (1999) Exploring Expression Data: Identification and Analysis of Co‐Expressed Genes. Genome Res 9:1106–1115
Hubert L, Schultz J (1976) Quadratic Assignment as a General Data‐Analysis Strategy. Br J Math Stat Psychol 29:190–241
Jaccard P (1912) The Distribution of Flora in the Alpine Zone. New Phytol 11:37–50
Jain AK, Murty MN, Flynn PJ (1999) Data Clustering: A Review. ACM Comput Surv 31(3):264–323
Jain AK, Dubes RC (1988) Algorithms for Clustering Data. In: Prentice-Hall Advanced Reference Series. Prentice, New Jersey.
Johnson RE (2001) The Role of Cluster Analysis in Assessing Comparability under the US Transfer Pricing Regulations. Bus Econ
Jung Y, Park H, Du D, Drake BL (2003) A Decision Criterion for the Optimal Number of Clusters in Hierarchical Clustering. J Glob Optim 25:91–111
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by Simulated Annealing. Science 220(4598):671–680
Kohonen T (1989) Self Organization and Associative Memory. In: Springer Information Science Series. Springer, New York
Kohonen T (1997) Self‐Organizing Maps. Springer, Berlin
Leisch F, Weingessel A, Dimitriadou E (1998) Competitive Learning for Binary Valued Data. In: Niklasson L, Bod'en M, Ziemke T (eds) Proceedings of the 8th International Conference on Artificial Neural Networks (ICANN 98) vol 2. Springer, Skövde, pp 779–784
Likas A, Vlassis N, Vebeek JL (2003) The Global K‑Means Clustering Algorithm. Pattern Recognit 36:451–461
Lin X, Floudas C, Wang Y, Broach JR (2003) Theoretical and Computational Studies of the Glucose Signaling Pathways in Yeast Using Global Gene Expression Data. Biotechnol Bioeng 84(7):864–886
Lukashin AV, Fuchs R (2001) Analysis of Temporal Gene Expression Profiles: Clustering by Simulated Annealing and Determining the Optimal Number of Clusters. Bioinform 17(5):405–414
McQueen J (1967) Some Methods for Classification and Analysis of Multivariate Observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, January 1966. University of California, Berkely, pp 281–297
Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller EJ (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087
Pardalos PM, Boginski V, Vazakopoulos A (Co-Ed.) (2007) Data Mining in Biomedicine. Springer, Berlin
Pauwels EJ, Fregerix G (1999) Finding Salient Regions in Images: Non‐parametric Clustering for Image Segmentation and Grouping. Comput Vis Image Underst 75:73–85
Pipenbacher P, Schliep A, Schneckener S, Schonhuth A, Schomburg D, Schrader R (2002) ProClust: Improved Clustering of Protein Sequences with an Extended Graph-Based Approach. Bioinform 18(Supplement 2):S182–191
Rand WM (1971) Objective Criteria for the Evaluation of Clustering Methods. J Am Stat Assoc 846–850
Rousseeuw PJ (1987) Silhouettes: A Graphical Aid to the Interpretation and Validation of Cluster Analysis. J Comp Appl Math 20:53–65
Ruspini EH (1969) A New Approach to Clustering. Inf Control 15:22–32
Schneper L, Düvel K, Broach JR (2004) Sense and Sensibility: Nutritional Response and Signal Integration in Yeast. Curr Opin Microbiol 7(6):624–630
Sherali HD, Desai J (2005) A Global Optimization RLT-Based Approach for Solving the Hard Clustering Problem. J Glob Optim 32(2):281–306
Sherali HD, Desai J (2005) A Global Optimization RLT-Based Approach for Solving the Fuzzy Clustering Approach. J Glob Optim 33(4):597–615
Slonim N, Atwal GS, Tkačik G, Bialek W (2005) Information Based Clustering. Proc Natl Acad Sci USA 102(51):18297–18302
Sokal RR, Michener CD (1958) A Statistical Method for Evaluating Systematic Relationships. Univ Kans Sci Bull 38:1409–1438
Sorlie T, Tibshirani R, Parker J, Hastie T, Marron JS, Nobel A, Deng S, Johnsen H, Pesich R, Geisler S, Demeter J, Perou CM, Lonning PE, Brown PO, Borresen-Dala AL, Botstein D (2003) Repeated Observations of Breast Tumor Subtypes in Independent Gene Expression Data Sets. Proc Natl Acad Sci USA 100:8418–8423
Tan MP, Broach JR, Floudas CA (2007) A Novel Clustering Approach and Prediction of Optimal Number of Clusters: Global Optimum Search with Enhanced Positioning. J Glob Optim 39:323–346
Tan MP, Broach JR, Floudas CA (2007) Evaluation of Normalization and Pre‐Clustering Issues in a Novel Clustering Approach: Global Optimum Search with Enhanced Positioning. J Bioinform Comput Biol 5(4):895–913
Tan MP, Broach JR, Floudas CA (2007) Microarray Data Mining: A Novel Optimization‐Based Iterative Clustering Approach to Uncover Biologically Coherent Structures. (submitted for publication)
Tishby N, Pereira F, Bialek W (1999) The Information Bottleneck Method. In: Proceedings of the 37th Annual Allerton Conference on Communication, Monticello, September 1999. Control and Computing, pp 368–377
Troyanskaya OG, Dolinski K, Owen AB, Altman RB, Botstein D (2003) A Bayesian Framework for Combining Heterogeneous Data Sources for Gene Function Prediction (in Saccharomyces Cerevisiae). Proc Natl Acad Sci USA 100:8348–8353
Wang Y, Pierce M, Schneper L, Guldal CG, Zhang X, Tavazoie S, Broach JR (2004) Ras and Gpa2 Mediate One Branch of a Redundant Glucose Signaling Pathway in Yeast. PLoS Biol 2(5):610–622
Wu Z, Leahy R (1993) An Optimal Graph Theoretic Approach to Data Clustering: Theory and Its Application to Image Segmentation. IEEE Trans Pattern Recognit Mach Intell 15(11):1101–1113
Xu R, Wunsch IID (2005) Survey of Clustering Algorithms. IEEE Trans Neural Netw 16(3):645–678
Zahn CT (1971) Graph Theoretical Methods for Detecting and Describing Gestalt Systems. IEEE Trans Comput C‑20:68–86
Zhang B, Hsu M, Dayal U (1999) K‑Harmonic Means – A Data Clustering Algorithm. Hewlett‐Packard Research Laboratory Technical Report HPL-1999-124
Zhang B (2000) Generalized K‐Harmonic Means: Boosting in Unsupervised Learning. Technical Report, Hewlett‐Packard Research Laboratory
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Tan, M.P., Floudas, C.A. (2008). Gene Clustering: A Novel Decomposition-Based Clustering Approach: Global Optimum Search with Enhanced Positioning . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_198
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DOI: https://doi.org/10.1007/978-0-387-74759-0_198
Publisher Name: Springer, Boston, MA
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