Data separation via a finite number of discriminant functions

A global optimization approach

Kwangsoo Kim, Hong Seo Ryoo

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This paper presents a mixed 0-1 integer and linear programming (MILP) model for separation of data via a finite number of non-linear and non-convex discriminant functions. The MILP model concurrently optimizes the parameters of the user-provided individual discriminant functions to implement a decision boundary for an optimal separation of data under analysis. The performance of the MILP-based classification of data is illustrated on randomly generated two dimensional datasets and extensively tested on six well-studied datasets in data mining research, in comparison with three well-established supervised learning methodologies, namely, the multisurface method, the logical analysis of data and the support vector machines. Numerical results from these experiments show that the new MILP-based classification of data is an effective and useful methodology for supervised learning.

Original languageEnglish
Pages (from-to)476-489
Number of pages14
JournalApplied Mathematics and Computation
Volume190
Issue number1
DOIs
Publication statusPublished - 2007 Jul 1

Fingerprint

Discriminant Function
0-1 Integer Programming
Integer programming
Global optimization
Linear programming
Global Optimization
Mixed Integer Programming
Supervised learning
Supervised Learning
Programming Model
Linear Model
Methodology
Support vector machines
Data mining
Support Vector Machine
Data Mining
Optimise
Numerical Results
Experiments
Experiment

Keywords

  • Data classification
  • Global optimization
  • Mixed 0-1 and linear programming
  • Supervised learning

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Data separation via a finite number of discriminant functions : A global optimization approach. / Kim, Kwangsoo; Ryoo, Hong Seo.

In: Applied Mathematics and Computation, Vol. 190, No. 1, 01.07.2007, p. 476-489.

Research output: Contribution to journalArticle

@article{63d50a5c1e8b43d39af9af17247f66ad,
title = "Data separation via a finite number of discriminant functions: A global optimization approach",
abstract = "This paper presents a mixed 0-1 integer and linear programming (MILP) model for separation of data via a finite number of non-linear and non-convex discriminant functions. The MILP model concurrently optimizes the parameters of the user-provided individual discriminant functions to implement a decision boundary for an optimal separation of data under analysis. The performance of the MILP-based classification of data is illustrated on randomly generated two dimensional datasets and extensively tested on six well-studied datasets in data mining research, in comparison with three well-established supervised learning methodologies, namely, the multisurface method, the logical analysis of data and the support vector machines. Numerical results from these experiments show that the new MILP-based classification of data is an effective and useful methodology for supervised learning.",
keywords = "Data classification, Global optimization, Mixed 0-1 and linear programming, Supervised learning",
author = "Kwangsoo Kim and Ryoo, {Hong Seo}",
year = "2007",
month = "7",
day = "1",
doi = "10.1016/j.amc.2007.01.051",
language = "English",
volume = "190",
pages = "476--489",
journal = "Applied Mathematics and Computation",
issn = "0096-3003",
publisher = "Elsevier Inc.",
number = "1",

}

TY - JOUR

T1 - Data separation via a finite number of discriminant functions

T2 - A global optimization approach

AU - Kim, Kwangsoo

AU - Ryoo, Hong Seo

PY - 2007/7/1

Y1 - 2007/7/1

N2 - This paper presents a mixed 0-1 integer and linear programming (MILP) model for separation of data via a finite number of non-linear and non-convex discriminant functions. The MILP model concurrently optimizes the parameters of the user-provided individual discriminant functions to implement a decision boundary for an optimal separation of data under analysis. The performance of the MILP-based classification of data is illustrated on randomly generated two dimensional datasets and extensively tested on six well-studied datasets in data mining research, in comparison with three well-established supervised learning methodologies, namely, the multisurface method, the logical analysis of data and the support vector machines. Numerical results from these experiments show that the new MILP-based classification of data is an effective and useful methodology for supervised learning.

AB - This paper presents a mixed 0-1 integer and linear programming (MILP) model for separation of data via a finite number of non-linear and non-convex discriminant functions. The MILP model concurrently optimizes the parameters of the user-provided individual discriminant functions to implement a decision boundary for an optimal separation of data under analysis. The performance of the MILP-based classification of data is illustrated on randomly generated two dimensional datasets and extensively tested on six well-studied datasets in data mining research, in comparison with three well-established supervised learning methodologies, namely, the multisurface method, the logical analysis of data and the support vector machines. Numerical results from these experiments show that the new MILP-based classification of data is an effective and useful methodology for supervised learning.

KW - Data classification

KW - Global optimization

KW - Mixed 0-1 and linear programming

KW - Supervised learning

UR - http://www.scopus.com/inward/record.url?scp=34249866594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249866594&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2007.01.051

DO - 10.1016/j.amc.2007.01.051

M3 - Article

VL - 190

SP - 476

EP - 489

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 1

ER -