title: Olp: an R package for optimal linear partitions of finite sets of points on the plane.
abstract: Given a set of points on the plane and an assignment of values to them, an optimal linear partition is a division of the set into two subsets which are separated by a straight line and maximally contrast with each other in the values assigned to their points. We present a method for inspecting and rating all linear partitions of a finite set, and a package of three functions in the R language for executing the computations. One function is for finding the optimal linear partitions and corresponding separating lines, another for graphically representing the results, and a third for testing how well the data comply with the linear separability condition. We illustrate the method on possible data from a psychophysical experiment (concerning the size-weight illusion) and compare its performance with that of linear discriminant analysis and multiple logistic regression, adapted to dividing linearly a set of points on the plane.
authors.affiliation: Department of General Psychology, University of Padova, Italy.
authors.forename: Luigi
authors.initials: L
authors.lastname: Burigana
authors.forename: Francesco
authors.initials: F
authors.lastname: Martino
authors.forename: Michele
authors.initials: M
authors.lastname: Vicovaro
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004192:Discrimination, Psychological; D020342:Finite Element Analysis; D006801:Humans; D016014:Linear Models; D016015:Logistic Models; D008432:Mathematical Computing; D009903:Optical Illusions; D011594:Psychometrics / Q000706:statistics & numerical data*; D011601:Psychophysics / Q000706:statistics & numerical data*; D015203:Reproducibility of Results; D012858:Size Perception; D014892:Weight Perception