Simple and flexible classification of gene expression microarrays via Swirls and Ripples

Stuart G Baker

doi:10.1186/1471-2105-11-452

Abstract

BackgroundA simple classification rule with few genes and parameters is desirable when applying a classification rule to new data. One popular simple classification rule, diagonal discriminant analysis, yields linear or curved classification boundaries, called Ripples, that are optimal when gene expression levels are normally distributed with the appropriate variance, but may yield poor classification in other situations.ResultsA simple modification of diagonal discriminant analysis yields smooth highly nonlinear classification boundaries, called Swirls, that sometimes outperforms Ripples. In particular, if the data are normally distributed with different variances in each class, Swirls substantially outperforms Ripples when using a pooled variance to reduce the number of parameters. The proposed classification rule for two classes selects either Swirls or Ripples after parsimoniously selecting the number of genes and distance measures. Applications to five cancer microarray data sets identified predictive genes related to the tissue organization theory of carcinogenesis.ConclusionThe parsimonious selection of classifiers coupled with the selection of either Swirls or Ripples provides a good basis for formulating a simple, yet flexible, classification rule. Open source software is available for download.

Highlights

A simple classification rule with few genes and parameters is desirable when applying a classification rule to new data
The threshold increase in AUC to add a gene to the classification rule of 0.02 for the greedy algorithm and 0.01 for the wrapper algorithm represents a small improvement in performance relative to the range of AUC from 0.5 to 1.00
The specified threshold increase in AUC is smaller with the wrapper than with the greedy algorithm because splitting of the training sample into a training-training sample and training-test sample with the wrapper avoids overfitting, unlike the case with the greedy algorithm in which the entire training sample is used both gene selection and evaluation

Summary

Introduction

A simple classification rule with few genes and parameters is desirable when applying a classification rule to new data. One popular simple classification rule, diagonal discriminant analysis, yields linear or curved classification boundaries, called Ripples, that are optimal when gene expression levels are normally distributed with the appropriate variance, but may yield poor classification in other situations. Classification performance is primarily a function of the first few variables selected, with only slight improvements when additional variables are included Only those variables that strongly predict class in the study data, namely the first few selected, are likely to moderately or strongly predict class in new data. A simple modification of diagonal discriminant analysis with two classes yields a smooth highly nonlinear classification boundary, given the name Swirls. The proposed simple, yet flexible, classification rule for two classes selects either Swirls or Ripples after parsimoniously selecting the number of genes and the distance measure

Methods

Results

Conclusion