Skip to main content

Gene Clustering: A Novel Decomposition-Based Clustering Approach: Global Optimum Search with Enhanced Positioning

  • Reference work entry
Encyclopedia of Optimization

Article Outline

Introduction

Formulations

  Notation and Pre-Clustering

  Proposed Algorithm

Case Study

  Experimental Data

  Description of Comparative Study

  Results and Discussion

References

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 2,499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Adams WP, Sherali HD (1990) Linearization Strategies for a Class of Zero-One Mixed Integer Programming Problems. Oper Res 38(2):217–226

    Article  MathSciNet  MATH  Google Scholar 

  2. Beer M, Tavazoie S (2004) Predicting Gene Expression from Sequence. Cell 117:185–198

    Article  Google Scholar 

  3. Bezdek JC (1981) Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York

    MATH  Google Scholar 

  4. Carpenter G, Grossberg S (1990) ART3: Hierarchical Search using Chemical Transmitters in Self‐Organizing Patterns Recognition Architectures. Neural Netw 3:129–152

    Article  Google Scholar 

  5. Claverie J (1999) Computational Methods for the Identification of Differential and Coordinated Gene Expression. Hum Mol Genet 8:1821–1832

    Article  Google Scholar 

  6. Davis DL, Bouldin DW (1979) A Cluster Separation Measure. IEEE Trans Pattern Anal Mach Intell 1(4):224–227

    Article  Google Scholar 

  7. 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

    MATH  Google Scholar 

  8. 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

    Google Scholar 

  9. Dunn JC (1973) A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well‐Separated Clusters. J Cybern 3:32–57

    Article  MathSciNet  MATH  Google Scholar 

  10. Dunn JC (1974) Well Separated Clusters and Optimal Fuzzy Partitions. J Cybern 4:95–104

    Article  MathSciNet  Google Scholar 

  11. Duran MA, Odell PL (1974) Cluster Analysis: A Survey. Springer, New York

    MATH  Google Scholar 

  12. Floudas CA (1995) Nonlinear and Mixed‐Integer Optimization: Fundamentals and Applications. Oxford University Press, Oxford

    MATH  Google Scholar 

  13. Floudas CA (2000) Deterministic Global Optimization: Theory, Algorithms, and Applications. Kluwer, Dordrecht

    Google Scholar 

  14. Floudas CA, Aggarwal A, Ciric AR (1989) Global Optimum Search for Non Convex NLP and MINLP Problems. Comp Chem Eng 13(10):1117–1132

    Article  Google Scholar 

  15. 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

    Article  Google Scholar 

  16. Goodman L, Kruskal W (1954) Measures of Associations for Cross‐Validations. J Am Stat Assoc 49:732–764

    Article  MATH  Google Scholar 

  17. Gower JC, Ross GJS (1969) Minimum Spanning Trees and Single‐Linkage Cluster Analysis. Appl Stat 18:54–64

    Article  MathSciNet  Google Scholar 

  18. Halkidi M, Batistakis Y, Vazirgiannis M (2002) Cluster Validity Methods: Part 1. SIGMOD Rec 31(2):40–45

    Article  Google Scholar 

  19. Hansen P, Jaumard B (1997) Cluster Analysis and Mathematical Programming. Math Program 79:191–215

    MathSciNet  Google Scholar 

  20. Hartigan JA (1975) Clustering Algorithms. Wiley, New York

    MATH  Google Scholar 

  21. Hartigan JA, Wong MA (1979) Algorithm AS 136: A K‑Means Clustering Algorithm. Appl Stat-J Roy St C 28:100–108

    Google Scholar 

  22. Herrero J, Valencia A, Dopazo J (2001) A Hierarchical Unsupervised Growing Neural Network for Clustering Gene Expression Patterns. Bioinformatics 17(2):126–136

    Article  Google Scholar 

  23. Heyer LJ, Kruglyak S, Yooseph S (1999) Exploring Expression Data: Identification and Analysis of Co‐Expressed Genes. Genome Res 9:1106–1115

    Article  Google Scholar 

  24. Hubert L, Schultz J (1976) Quadratic Assignment as a General Data‐Analysis Strategy. Br J Math Stat Psychol 29:190–241

    MathSciNet  MATH  Google Scholar 

  25. Jaccard P (1912) The Distribution of Flora in the Alpine Zone. New Phytol 11:37–50

    Article  Google Scholar 

  26. Jain AK, Murty MN, Flynn PJ (1999) Data Clustering: A Review. ACM Comput Surv 31(3):264–323

    Article  Google Scholar 

  27. Jain AK, Dubes RC (1988) Algorithms for Clustering Data. In: Prentice-Hall Advanced Reference Series. Prentice, New Jersey.

    Google Scholar 

  28. Johnson RE (2001) The Role of Cluster Analysis in Assessing Comparability under the US Transfer Pricing Regulations. Bus Econ

    Google Scholar 

  29. 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

    Article  MathSciNet  Google Scholar 

  30. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by Simulated Annealing. Science 220(4598):671–680

    Article  MathSciNet  Google Scholar 

  31. Kohonen T (1989) Self Organization and Associative Memory. In: Springer Information Science Series. Springer, New York

    Google Scholar 

  32. Kohonen T (1997) Self‐Organizing Maps. Springer, Berlin

    MATH  Google Scholar 

  33. 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

    Google Scholar 

  34. Likas A, Vlassis N, Vebeek JL (2003) The Global K‑Means Clustering Algorithm. Pattern Recognit 36:451–461

    Article  Google Scholar 

  35. 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

    Article  Google Scholar 

  36. 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

    Article  Google Scholar 

  37. 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

    Google Scholar 

  38. Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller EJ (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087

    Article  Google Scholar 

  39. Pardalos PM, Boginski V, Vazakopoulos A (Co-Ed.) (2007) Data Mining in Biomedicine. Springer, Berlin

    Book  MATH  Google Scholar 

  40. 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

    Article  Google Scholar 

  41. 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

    Google Scholar 

  42. Rand WM (1971) Objective Criteria for the Evaluation of Clustering Methods. J Am Stat Assoc 846–850

    Google Scholar 

  43. Rousseeuw PJ (1987) Silhouettes: A Graphical Aid to the Interpretation and Validation of Cluster Analysis. J Comp Appl Math 20:53–65

    Article  MATH  Google Scholar 

  44. Ruspini EH (1969) A New Approach to Clustering. Inf Control 15:22–32

    Article  MATH  Google Scholar 

  45. Schneper L, Düvel K, Broach JR (2004) Sense and Sensibility: Nutritional Response and Signal Integration in Yeast. Curr Opin Microbiol 7(6):624–630

    Article  Google Scholar 

  46. Sherali HD, Desai J (2005) A Global Optimization RLT-Based Approach for Solving the Hard Clustering Problem. J Glob Optim 32(2):281–306

    Article  MathSciNet  MATH  Google Scholar 

  47. Sherali HD, Desai J (2005) A Global Optimization RLT-Based Approach for Solving the Fuzzy Clustering Approach. J Glob Optim 33(4):597–615

    Article  MathSciNet  MATH  Google Scholar 

  48. Slonim N, Atwal GS, Tkačik G, Bialek W (2005) Information Based Clustering. Proc Natl Acad Sci USA 102(51):18297–18302

    Article  MathSciNet  MATH  Google Scholar 

  49. Sokal RR, Michener CD (1958) A Statistical Method for Evaluating Systematic Relationships. Univ Kans Sci Bull 38:1409–1438

    Google Scholar 

  50. 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

    Article  Google Scholar 

  51. 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

    Article  MathSciNet  MATH  Google Scholar 

  52. 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

    Article  Google Scholar 

  53. 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)

    Google Scholar 

  54. 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

    Google Scholar 

  55. 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

    Article  Google Scholar 

  56. 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

    Article  Google Scholar 

  57. 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

    Article  Google Scholar 

  58. Xu R, Wunsch IID (2005) Survey of Clustering Algorithms. IEEE Trans Neural Netw 16(3):645–678

    Article  Google Scholar 

  59. Zahn CT (1971) Graph Theoretical Methods for Detecting and Describing Gestalt Systems. IEEE Trans Comput C‑20:68–86

    Google Scholar 

  60. Zhang B, Hsu M, Dayal U (1999) K‑Harmonic Means – A Data Clustering Algorithm. Hewlett‐Packard Research Laboratory Technical Report HPL-1999-124

    Google Scholar 

  61. Zhang B (2000) Generalized K‐Harmonic Means: Boosting in Unsupervised Learning. Technical Report, Hewlett‐Packard Research Laboratory

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

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

Download citation

Publish with us

Policies and ethics