Beyond one-against-all (OAA) and one-against-one (OAO): An exhaustive and parallel half-against-half (HAH) strategy for multi-class classification and applications to metabolomics

Abstract

Urinary metabolomics coupled with GC-MS has become a leading technology in newborn screening. Because of non-specificity, complexity and high-variety in clinical characteristics and metabolomic profiling, the simultaneous detection of multiple inherited metabolic diseases (IMDs) is often challenging. As a substantial health problem, a competent chemometrics multi-class classification system for the early detection and diagnosis of IMDs would be advantageous. Beyond the commonly used binarization techniques of one-against-all (OAA) and one-against-one (OAO), an exhaustive and parallel half-against-half (EPHAH) decomposition is described in this study to deal with multi-class classification. For a K-class problem, EPHAH employs uniform class binary partition strategy to induce the binary classifier evaluating a half of K classes against the other half. With K-class problem exhaustively decomposed into all uniform binary partitions of K classes, EPHAH parallelly arranges the corresponding binary classifiers and aggregates their outputs to obtain the multi-class prediction using max-wins voting strategy. Based on orthogonal partial least squares discriminant analysis (OPLS-DA) with feature selection using particle swarm optimization (PSO) algorithm, EPHAH is investigated by GC-MS urinary metabolomics data among healthy controls and 9 most common IMDs. The results show that EPHAH enables a complete learning of the complex multi-class decision boundaries of 10 classes, exhibiting significant superiority in classification accuracies over OAA, OAO and traditional HAH. Meanwhile, compared with OAO using the same max-wins voting strategy, EPHAH gives an effective break of the tie problem in classification and enhanced resolution in votes.