Multi-Class Classification using Covariance among Binary Classifiers and its Application to the Analysis of Tumor Microarrays

Abstract

Many microarray datasets include samples from more than two types or conditions and call for models capable of multi-class classification. Prior work such as Dudoit et al. pioneered on comparative multi-class classification studies using simple classifiers in a one-versus-one (OVO) manner. Dietterich and Bakiri introduced a generic metaclassifier approach called the Error-Correcting-OutputCoding (ECOC). ECOC first generates ideal representative codes as „class codes‟ by each binary-class sub-problems. Then it generates an “output code” as the vector of outcomes from all binary-class sub-problems for the sample to be classified. A “decoding” step finds the class that produces the most similar code using a dissimilarity measure such as Hamming distance. Since the binary classification sub-problems have substantial overlap, the coordinates in the output code are correlated but this is not leveraged in ECOC or later revisions. The new MCAB (Multi-class classification using Covariance Among Binary Classifiers) algorithm uses the covariance matrix from the training dataset in decoding which captures the correlations among the classes. We compared MCAB with the best variant of ECOC (Escelera et al.) available in the latest (2010) ECOC library by external 10-fold cross validation on three published multi-class benchmark cancer gene expression microarray datasets. We found that MCAB generally outperforms ECOC in overall accuracy and class-specific precision values regardless of what binary classifiers was being used. MCAB using Support Vector Machine with Recursive Feature Elimination (SVM-RFE) as the binaryclass classifier had the best overall accuracy and betterbalanced class-specific precision and recall values in all three datasets. These results suggest that MCAB is robust and accurate for classifying multi-class microarray datasets, and can be readily used for other types of data.