An ensemble-based method for linear feature extraction for two-class problems

In this paper we propose three variants of a linear feature extraction technique based on Adaboost for two-class classification problems. Unlike other feature extraction techniques, we do not make any assumptions about the distribution of the data. At each boosting step we select from a pool of linear projections the one that minimizes the weighted error. We propose three different variants of the feature extraction algorithm, depending on the way the pool of individual projections is constructed. Using nine real and two artificial data sets of different original dimensionality and sample size we compare the performance of the three proposed techniques with three classical techniques for linear feature extraction: Fisher linear discriminant analysis (FLD), Nonparametric discriminant analysis (NDA) and a recently proposed feature extraction method for heteroscedastic data based on the Chernoff criterion. Our results show that for data sets of relatively low-original dimensionality FLD appears to be both the most accurate and the most economical feature extraction method (giving just one-dimension in the case of two classes). The techniques based on Adaboost fare better than the classical techniques for data sets of large original dimensionality.