Piece-wise quasi-linear modeling in QSAR and analytical calibration based on linear substructures detected by genetic algorithm

This paper introduces an alternative approach called piece-wise quasi-linear modeling methodology to split the data set into linear subsets when single linear calibration model failed to describe the whole data with desired residuals. The paper treats the linear models describing the sought-for subsets as hyperplanes in the data space. A modified genetic algorithm splits the data set into linear subsets according to a given maximum error. The proposed algorithm has successfully split a real QSAR data set into three chemically homogeneous linear subsets with very small residuals comparing with those obtained when a single linear model used to describe the data.