Regularized fuzzy clusterwise ridge regression

Hye Won Suk, Heungsun Hwang

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Fuzzy clusterwise regression has been a useful method for investigating cluster-level heterogeneity of observations based on linear regression. This method integrates fuzzy clustering and ordinary least-squares regression, thereby enabling to estimate regression coefficients for each cluster and fuzzy cluster memberships of observations simultaneously. In practice, however, fuzzy clusterwise regression may suffer from multicollinearity as it builds on ordinary least-squares regression. To deal with this problem in fuzzy clusterwise regression, a new method, called regularized fuzzy clusterwise ridge regression, is proposed that combines ridge regression with regularized fuzzy clustering in a unified framework. In the proposed method, ridge regression is adopted to estimate clusterwise regression coefficients while handling potential multicollinearity among predictor variables. In addition, regularized fuzzy clustering based on maximizing entropy is utilized to systematically determine an optimal degree of fuzziness in memberships. A simulation study is conducted to evaluate parameter recovery of the proposed method as compared to the extant non-regularized counterpart. The usefulness of the proposed method is illustrated by an application concerning the relationship among the characteristics of used cars.

Original languageEnglish (US)
Pages (from-to)35-51
Number of pages17
JournalAdvances in Data Analysis and Classification
Issue number1
StatePublished - 2010
Externally publishedYes


  • Clusterwise regression
  • Regularized fuzzy clustering
  • Ridge regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Applied Mathematics


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