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Olp: An R package for optimal linear partitions of finite sets of points on the plane
Author(s) -
Burigana Luigi,
Martino Francesco,
Vicovaro Michele
Publication year - 2014
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/bmsp.12022
Subject(s) - mathematics , set (abstract data type) , plane (geometry) , linear regression , line (geometry) , linear discriminant analysis , finite set , computation , partition (number theory) , function (biology) , algorithm , linear model , combinatorics , statistics , mathematical analysis , computer science , geometry , evolutionary biology , biology , programming language
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.