A novel feature extraction algorithm for asymmetric classification

A linear feature extraction technique for asymmetric distributions is introduced, the asymmetric class projection (ACP). By asymmetric classification is understood discrimination among distributions with different covariance matrices. Two distributions with unequal covariance matrices do not, in general, have a symmetry plane, a fact that makes the analysis more difficult compared to the symmetric case. The ACP is similar to linear discriminant analysis (LDA) in the respect that both aim at extracting discriminating features (linear combinations or projections) from many variables. However, the drawback of the well-known LDA is the assumption of symmetric classes with separated centroids. The ACP, in contrast, works on (two) possibly concentric distributions with unequal covariance matrices. The ACP is tested on data from an array of semiconductor gas sensors with the purpose of distinguish bad grain from good.