Regularized fuzzy clusterwise ridge regression

Advances in Data Analysis and Classification

Volumn 4, Issue 1, 2010, Pages 35-51

  Suk, Hye Won ^a   Hwang, Heungsun ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Clusterwise regression; Regularized fuzzy clustering; Ridge regression

Indexed keywords

AUTOMOBILES; FUZZY CLUSTERING; FUZZY SYSTEMS; OPTIMIZATION;

CLUSTERWISE REGRESSION; FUZZY CLUSTERS; LEAST SQUARES REGRESSION; MULTICOLLINEARITY; PARAMETER RECOVERY; PREDICTOR VARIABLES; REGRESSION COEFFICIENT; RIDGE REGRESSION; SIMULATION STUDIES; UNIFIED FRAMEWORK;

REGRESSION ANALYSIS;

EID: 77955091544     PISSN: 18625347     EISSN: 18625355     Source Type: Journal    
DOI: 10.1007/s11634-009-0056-5     Document Type: Article

References (42)

1. Aurifeille J-M, Quester PG (2003) Predicting business ethical tolerance in international markets: a concomitant clusterwise regression analysis. Int Bus Rev 12: 253-272.
2. Belsley DA, Kuh E, Welsch RE (1980) Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New York.
3. Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York.
4. Brusco MJ, Cradit JD, Steinley D, Fox GL (2008) Cautionary remarks on the use of clusterwise regression. Multivar Behav Res 43: 29-49.
5. DeSarbo WS, Cron WL (1988) A maximum likelihood methodology for clusterwise linear regression. J Classif 5: 249-282.
6. DeSarbo WS, Oliver RL, Rangaswamy A (1989) A simulated annealing methodology for clusterwise linear regression. Psychometrika 54: 707-736.
7. DeVeaux RD (1989) Mixtures of linear regressions. Comput Stat Data Anal 8: 227-245.
8. D'Urso P (2003) Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data. Comput Stat Data Anal 42: 47-72.
9. D'Urso P, Santoro A (2006) Fuzzy clusterwise linear regression analysis with symmetrical fuzzy output variable. Comput Stat Data Anal 51: 287-313.
10. Efron B (1982) The jackknife, the bootstrap, and other resampling plans. Society of Industrial and Applied Mathematics CBMS-NSF Monographs 38.
11. Falk TH, Shatkay H, Chan W-Y (2006) Breast cancer prognosis via Gaussian mixture regression. Canadian conference on electrical and computer engineering, Queen's University, Canada, pp 987-990.
12. Gordon AD (1999) Classification. Chapman and Hall/CRC, Boca Raton.
13. Hathaway RJ, Bezdek JC (1993) Switching regression models and fuzzy clustering. IEEE Trans Fuzzy Syst 1: 195-204.
14. Heiser WJ, Groenen PJF (1997) Cluster differences scaling with a within-cluster loss component and a fuzzy successive approximation strategy to avoid local minima. Psychometrika 62: 63-83.
15. Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12: 55-67.
16. Hoerl AE, Kennard RW (1970) Ridge regression: applications to nonorthogonal problems. Technometrics 12: 69-82.
17. Hosmer DW (1974) Maximum likelihood estimates of the parameters of a mixture of two regression lines. Commun Stat 3: 995-1006.
18. Hruschka H (1986) Market definition and segmentation using fuzzy clustering methods. Int J Res Mark 3: 117-134.
19. Kuiper S (2008) Introduction to multiple regression: how much is your car worth? J Stat Educ 16. Available via http://www. amstat. org/publications/jse/v16n3/datasets. kuiper. html. Accessed 25 May 2009.
20. Kutner MH, Nachtsheim C, Neter J (2004) Applied linear regression models. McGraw-Hill/Irwin, Boston.
21. Laviolette M, Seaman JW (1992) Evaluating fuzzy representations of uncertainty. Math Sci 17: 26-41.
22. Laviolette M, Seaman JW (1994) Unity and diversity of fuzziness-from a probability viewpoint. IEEE Trans Fuzzy Syst 2: 38-42.
23. Laviolette M, Seaman JW, Barrett JD, Woodall WH (1995) A probabilistic and statistical view of fuzzy methods. Technometrics 37: 249-261.
24. Li R-P, Mukaidono M (1995) A maximum entropy approach to fuzzy clustering. Proceedings of the 4th IEEE international conference on fuzzy systems, Yokohama, Japan, pp 2227-2232.
25. McBratney AB, Moore AW (1985) Application of fuzzy sets to climatic classification. Agric For Meteorol 35: 165-185.
26. Miyamoto S (1998) An overview and new methods in fuzzy clustering. In: Jain LC, Jain RK (eds) Second international conference on knowledge-based intelligent electronic systems, Adelaide, Australia, pp 21-23.
27. Miyamoto S, Mukaidono M (1997) Fuzzy c-means as a regularization and maximum entropy approach. 7th international fuzzy systems association world congress, Prague, Czech Republic, pp 86-92.
28. Miyamoto S, Ichihashi H, Honda K (2008) Algorithms for fuzzy clustering: methods in c-means clustering with applications. Springer, Berlin.
29. Quandt RE (1958) The estimation of the parameters of a linear regression system obeying two separate regimes. J Am Stat Assoc 53: 873-880.
30. Quandt RE (1972) A new approach to estimating switching regressions. J Am Stat Assoc 67: 306-310.
31. Quandt RE, Ramsey JB (1978) Estimating mixtures of normal distributions and switching regressions. J Am Stat Assoc 73: 730-738.
32. Späth H (1979) Algorithm 39: clusterwise linear regression. Computing 22: 367-373.
33. Späth H (1981) Correction to algorithm 39: clusterwise linear regression. Computing 26: 275.
34. Späth H (1982) Algorithm 48: a fast algorithm for clusterwise linear regression. Computing 29: 175-181.
35. Späth H (1985) Cluster dissection and analysis. Wiley, New York.
36. Takane Y, Hwang H (2007) Regularized linear and kernel redundancy analysis. Comput Stat Data Anal 52: 394-405.
37. Tran D, Wagner M (2000) Fuzzy entropy clustering. The 9th IEEE international conference on fuzzy systems, San Antonio, pp 152-157.
38. Wedel M, DeSarbo WS (1995) A mixture likelihood approach for generalized linear models. J Classif 12: 21-55.
39. Wedel M, Kistemaker C (1989) Consumer benefit segmentation using clusterwise linear regression. Int J Res Mark 6: 45-49.
40. Wedel M, Steenkamp J-BEM (1989) A fuzzy clusterwise regression approach to benefit segmentation. Int J Res Mark 6: 241-258.
41. Wedel M, Steenkamp J-BEM (1991) A clusterwise regression method for simultaneous fuzzy market structuring and benefit segmentation. J Mark Res 28: 385-396.
42. Yang M-S, Ko C-H (1997) On cluster-wise fuzzy regression analysis. IEEE Trans Syst Man Cybern B 27: 1-13.