Learning Polyhedral Classifiers Using Logistic Function

Naresh Manwani, P. S. Sastry
Proceedings of 2nd Asian Conference on Machine Learning, PMLR 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 (Astorino and Gaudioso, 2002).

Cite this Paper

BibTeX
@InProceedings{pmlr-v13-manwani10a, title = {Learning Polyhedral Classifiers Using Logistic Function}, author = {Manwani, Naresh and Sastry, P. S.}, booktitle = {Proceedings of 2nd Asian Conference on Machine Learning}, pages = {17--30}, year = {2010}, editor = {Sugiyama, Masashi and Yang, Qiang}, volume = {13}, series = {Proceedings of Machine Learning Research}, address = {Tokyo, Japan}, month = {08--10 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v13/manwani10a/manwani10a.pdf}, url = {https://proceedings.mlr.press/v13/manwani10a.html}, 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 (Astorino and Gaudioso, 2002).} }
Endnote
%0 Conference Paper %T Learning Polyhedral Classifiers Using Logistic Function %A Naresh Manwani %A P. S. Sastry %B Proceedings of 2nd Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2010 %E Masashi Sugiyama %E Qiang Yang %F pmlr-v13-manwani10a %I PMLR %P 17--30 %U https://proceedings.mlr.press/v13/manwani10a.html %V 13 %X 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 (Astorino and Gaudioso, 2002).
RIS
TY - CPAPER TI - Learning Polyhedral Classifiers Using Logistic Function AU - Naresh Manwani AU - P. S. Sastry BT - Proceedings of 2nd Asian Conference on Machine Learning DA - 2010/10/31 ED - Masashi Sugiyama ED - Qiang Yang ID - pmlr-v13-manwani10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 13 SP - 17 EP - 30 L1 - http://proceedings.mlr.press/v13/manwani10a/manwani10a.pdf UR - https://proceedings.mlr.press/v13/manwani10a.html AB - 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 (Astorino and Gaudioso, 2002). ER -
APA
Manwani, N. & Sastry, P.S.. (2010). Learning Polyhedral Classifiers Using Logistic Function. Proceedings of 2nd Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 13:17-30 Available from https://proceedings.mlr.press/v13/manwani10a.html.

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