Learning Polyhedral Classifiers Using Logistic Function
Naresh Manwani (Indian Institute of Science) and P. S. Sastry (Indian
Institute of Science);
JMLR W&P 13:17-30, 2010.
Abstract
In this paper we propose a new algorithm for learning polyhedral classifiers.
In contrast to existing methods for learning polyhedral classifier
which solve a constrained optimization problem, our method solves
an unconstrained optimization problem. Our method is based on a
logistic function based model for the posterior probability function.
We propose an alternating optimization algorithm, namely, SPLA1
(Single Polyhedral Learning Algorithm1) which maximizes the loglikelihood
of the training data to learn the parameters. We also extend
our method to make it independent of any user specified parameter
(e.g., number of hyperplanes required to form a polyhedral set) in
SPLA2. We show the effectiveness of our approach with experiments
on various synthetic and real world datasets and compare our approach
with a standard decision tree method (OC1) and a constrained
optimization based method for learning polyhedral sets.
