title: Multi-class HingeBoost. Method and application to the classification of cancer types using gene expression data.
abstract: BACKGROUND
  Multi-class molecular cancer classification has great potential clinical implications. Such applications require statistical methods to accurately classify cancer types with a small subset of genes from thousands of genes in the data.
  
  
  OBJECTIVE
  This paper presents a new functional gradient descent boosting algorithm that directly extends the HingeBoost algorithm from the binary case to the multi-class case without reducing the original problem to multiple binary problems.
  
  
  METHODS
  Minimizing a multi-class hinge loss with boosting technique, the proposed HingeBoost has good theoretical properties by implementing the Bayes decision rule and providing a unifying framework with either equal or unequal misclassification costs. Furthermore, we propose Twin HingeBoost which has better feature selection behavior than HingeBoost by reducing the number of ineffective covariates. Simulated data, benchmark data and two cancer gene expression data sets are utilized to evaluate the performance of the proposed approach.
  
  
  RESULTS
  Simulations and the benchmark data showed that the multi-class HingeBoost generated accurate predictions when compared with the alternative methods, especially with high-dimensional covariates. The multi-class HingeBoost also produced more accurate prediction or comparable prediction in two cancer classification problems using gene expression data.
  
  
  CONCLUSIONS
  This work has shown that the HingeBoost provides a powerful tool for multi-classification problems. In many applications, the classification accuracy and feature selection behavior can be further improved when using Twin HingeBoost.
authors.affiliation: Connecticut Children's Medical Center, Department of Pediatrics, University of Connecticut School of Medicine, 282 Washington Street, Hartford, CT 06106, USA. zwang@ccmckids.org
authors.forename: Z
authors.initials: Z
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D015870:Gene Expression / Q000235:genetics*; D005786:Gene Expression Regulation / Q000235:genetics*; D006801:Humans; D009369:Neoplasms / Q000145:classification* / Q000235:genetics; D011336:Probability; D012044:Regression Analysis