A novel piecewise linear classifier based on polyhedral conic and max-min separabilities
- Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean , Ozturk, Gurkan , Kasimbeyli, Refail
- Date: 2011
- Type: Text , Journal article
- Relation: TOP Vol.21, no.1 (2011), p. 1-22
- Full Text: false
- Reviewed:
- Description: In this paper, an algorithm for finding piecewise linear boundaries between pattern classes is developed. This algorithm consists of two main stages. In the first stage, a polyhedral conic set is used to identify data points which lie inside their classes, and in the second stage we exclude those points to compute a piecewise linear boundary using the remaining data points. Piecewise linear boundaries are computed incrementally starting with one hyperplane. Such an approach allows one to significantly reduce the computational effort in many large data sets. Results of numerical experiments are reported. These results demonstrate that the new algorithm consistently produces a good test set accuracy on most data sets comparing with a number of other mainstream classifiers. © 2011 Sociedad de EstadÃstica e Investigación Operativa.
Piecewise linear classifiers based on nonsmooth optimization approaches
- Authors: Bagirov, Adil , Kasimbeyli, Refail , Ozturk, Gurkan , Ugon, Julien
- Date: 2014
- Type: Text , Book chapter
- Relation: Optimization in Science and Engineering p. 1-32
- Full Text: false
- Reviewed:
- Description: Nonsmooth optimization provides efficient algorithms for solving many machine learning problems. In particular, nonsmooth optimization approaches to supervised data classification problems lead to the design of very efficient algorithms for their solution. In this chapter, we demonstrate how nonsmooth optimization algorithms can be applied to design efficient piecewise linear classifiers for supervised data classification problems. Such classifiers are developed using a max–min and a polyhedral conic separabilities as well as an incremental approach. We report results of numerical experiments and compare the piecewise linear classifiers with a number of other mainstream classifiers.