0-1 multilinear programming as a unifying theory for LAD pattern generation

Kedong Yan; Hong Seo Ryoo

doi:10.1016/j.dam.2016.08.007

0-1 multilinear programming as a unifying theory for LAD pattern generation

Kedong Yan, Hong Seo Ryoo

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

This paper revisits the Boolean logical requirement of a pattern and develops 0-1 multilinear programming (MP) models for (Pareto-)optimal patterns for logical analysis of data (LAD). We show that all existing and also new pattern generation models can naturally be obtained from the MP models via linearization techniques for 0-1 multilinear functions. Furthermore, 0-1 MP provides an insight for understanding how different and independently developed models for a particular type of pattern are inter-related. These show that 0-1 MP presents a unifying theory for pattern generation in LAD.

Original language	English
Pages (from-to)	21-39
Number of pages	19
Journal	Discrete Applied Mathematics
Volume	218
DOIs	https://doi.org/10.1016/j.dam.2016.08.007
Publication status	Published - 2017 Feb 19

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant Number: NRF-2013R1A1A2011784 ).

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

0-1 linearization
Boolean logic
Logical analysis of data
Multilinear programming
Pattern generation

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1016/j.dam.2016.08.007

Cite this

@article{0d40b1a1dff341c18f63409bbab6b288,

title = "0-1 multilinear programming as a unifying theory for LAD pattern generation",

abstract = "This paper revisits the Boolean logical requirement of a pattern and develops 0-1 multilinear programming (MP) models for (Pareto-)optimal patterns for logical analysis of data (LAD). We show that all existing and also new pattern generation models can naturally be obtained from the MP models via linearization techniques for 0-1 multilinear functions. Furthermore, 0-1 MP provides an insight for understanding how different and independently developed models for a particular type of pattern are inter-related. These show that 0-1 MP presents a unifying theory for pattern generation in LAD.",

keywords = "0-1 linearization, Boolean logic, Logical analysis of data, Multilinear programming, Pattern generation",

author = "Kedong Yan and Ryoo, {Hong Seo}",

note = "Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant Number: NRF-2013R1A1A2011784 ). Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2017",

month = feb,

day = "19",

doi = "10.1016/j.dam.2016.08.007",

language = "English",

volume = "218",

pages = "21--39",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - 0-1 multilinear programming as a unifying theory for LAD pattern generation

AU - Yan, Kedong

AU - Ryoo, Hong Seo

N1 - Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant Number: NRF-2013R1A1A2011784 ). Publisher Copyright: © 2016 Elsevier B.V.

PY - 2017/2/19

Y1 - 2017/2/19

N2 - This paper revisits the Boolean logical requirement of a pattern and develops 0-1 multilinear programming (MP) models for (Pareto-)optimal patterns for logical analysis of data (LAD). We show that all existing and also new pattern generation models can naturally be obtained from the MP models via linearization techniques for 0-1 multilinear functions. Furthermore, 0-1 MP provides an insight for understanding how different and independently developed models for a particular type of pattern are inter-related. These show that 0-1 MP presents a unifying theory for pattern generation in LAD.

AB - This paper revisits the Boolean logical requirement of a pattern and develops 0-1 multilinear programming (MP) models for (Pareto-)optimal patterns for logical analysis of data (LAD). We show that all existing and also new pattern generation models can naturally be obtained from the MP models via linearization techniques for 0-1 multilinear functions. Furthermore, 0-1 MP provides an insight for understanding how different and independently developed models for a particular type of pattern are inter-related. These show that 0-1 MP presents a unifying theory for pattern generation in LAD.

KW - 0-1 linearization

KW - Boolean logic

KW - Logical analysis of data

KW - Multilinear programming

KW - Pattern generation

UR - http://www.scopus.com/inward/record.url?scp=84995753084&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2016.08.007

DO - 10.1016/j.dam.2016.08.007

M3 - Article

AN - SCOPUS:84995753084

SN - 0166-218X

VL - 218

SP - 21

EP - 39

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

0-1 multilinear programming as a unifying theory for LAD pattern generation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this