Simple Pattern Minimality Problems: Integer Linear Programming Formulations and Covering-Based Heuristic Solving Approaches
Published Online:4 May 2020https://doi.org/10.1287/ijoc.2019.0940
References
- (2005) Spanned patterns for the logical analysis of data. Discrete Appl. Math. 154(7):1039–1049.Google Scholar
- (2006) Pattern-based clustering and attribute analysis. Soft Comput. 10(5):442–452.Crossref, Google Scholar
- (2007) Logical analysis of data—the vision of Peter L. Hammer. Ann. Math. Artificial Intelligence 49(1–4):265–312.Crossref, Google Scholar
- (2008) Comprehensive vs. comprehensible classifiers in logical analysis of data. Discrete Appl. Math. 156(6):870–882.Crossref, Google Scholar
- (2015) Heuristic and criteria for constructing logical pattern in data. IOP Conf. Ser. Materials Sci. Engrg. (IOP Publishing, Bristol, UK), 1–7.Google Scholar
- I (2005) A decomposition approach for a very large scale optimal diversity management problem. 4OR 3(1):23–37.Google Scholar
- (2017) A partitioning based heuristic for a variant of the simple pattern minimality problem. Sforza A, Sterle C, eds. Optim. Decision Sci.: Methodologies Appl. (Springer, New York), 93–102.Crossref, Google Scholar
- (2007) Optimization in logical analysis of data. PhD thesis, Rutgers University, New Brunswick, NJ.Google Scholar
- (2008) Maximum patterns in datasets. Discrete Appl. Math. 156(6):846–861.Crossref, Google Scholar
- (1997) Logical analysis of numerical data. Math. Programming 79(1–3):163–190.Crossref, Google Scholar
- (2011) Logical analysis of data: Classification with justification. Ann. Oper. Res. 188(2):33–61.Crossref, Google Scholar
- (2000) An implementation of logical analysis of data. IEEE Trans. Knowledge Data Engrg. 12(2):292–306.Crossref, Google Scholar
- (2016) A pool-based pattern generation algorithm for logical analysis of data with automatic fine-tuning. Eur. J. Oper. Res. 248(2):593–606.Crossref, Google Scholar
- (2013) Logical analysis of data: Theory, methodology and applications. Three Approaches to Data Analysis (Springer, New York), 147–192.Google Scholar
- (2017) Multi-pattern generation framework for logical analysis of data. Ann. Oper. Res. 249(1):329–349.Crossref, Google Scholar
- (2014) Column generation framework of nonlinear similarity model for reconstructing sibling groups. INFORMS J. Comput. 27(1):35–47.Link, Google Scholar
- (2002) Two-level logic minimization. Hassoun S, Sasao T, eds. Logic Synthesis and Verification (Springer, New York), 1–27.Crossref, Google Scholar
- (1988) Cause-effect relationships and partially defined Boolean functions. Ann. Oper. Res. 16(1):299–326.Crossref, Google Scholar
- (1996) From data mining to knowledge discovery: An overview. Fayyad U, Piatetsky-Shapiro G, Smyth P, Uthurusamy R, eds. Advances in Knowledge Discovery and Data Mining (American Association for Artificial Intelligence, Menlo Park, CA), 1–34.Google Scholar
- (2002) A MINSAT approach for learning in logic domains. INFORMS J. Comput. 14(1):20–36.Link, Google Scholar
- (1999) Separate-and-conquer rule learning. Artificial Intelligence Rev. 13(1):3–54.Google Scholar
- (2005) Roc ‘n’ rule learning toward a better understanding of covering algorithms. Machine Learn. 58(1):39–77.Crossref, Google Scholar
- (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness (W. H. Freeman and Company, San Francisco).Google Scholar
- (2012) Compact MILP models for optimal and Pareto-optimal LAD patterns. Discrete Appl. Math. 160(16–17):2339–2348.Crossref, Google Scholar
- (1986) Partially defined Boolean functions and cause-effect relationships. Internat. Conf. Multi-Attribute Decision-Making OR-Based Expert Systems (University of Passau, Passau, Germany).Google Scholar
- (2006) Logical analysis of data—an overview: From combinatorial optimization to medical applications. Ann. Oper. Res. 148(1):203–225.Crossref, Google Scholar
- (2004) Pareto-optimal patterns in logical analysis of data. Discrete Appl. Math. 144(1–2):79–102.Crossref, Google Scholar
- (2011) Pattern selection approaches for the logical analysis of data considering the outliers and the coverage of a pattern. Expert Systems Appl. 38(11):13857–13862.Google Scholar
- (2011) A new column generation algorithm for logical analysis of data. Ann. Oper. Res. 188(1):215–249.Crossref, Google Scholar
- (2012) Set-cover heuristics for two-level logic minimization. IEEE 25th Internat. Conf. VLSI Design, Hyderabad, India, 197–202.Google Scholar
- (2015) Pattern generation for multi-class lad using iterative genetic algorithm with flexible chromosomes and multiple populations. Expert Systems Appl. 42(2):833–843.Crossref, Google Scholar
- (2014) Soft Computing and Its Applications: A Unified Engineering Concept (Apple Academic Press, Palm Bay, FL).Google Scholar
- (2009) A set covering approach with column generation for parsimony haplotyping. INFORMS J. Comput. 21(1):151–166.Link, Google Scholar
- (2016) The complexity of some pattern problems in the logical analysis of large genomic data sets. Ortuño F, Rojas I, eds. Bioinformatics Biomedical Engrg. 4th Internat. Conf., IWBBIO 2016, Grenada, Spain, April 20–22, 2016, Lecture Notes in Computer Science, vol. 9656 (Springer, New York), 3–12.Crossref, Google Scholar
- (2012) Version 1.1.4, released November 9, 2012. Accessed July 26, 2019, https://web.archive.org/web/20131022021257/http://www.sontrak.com/.Google Scholar
- (2015) Machine Learning: An Algorithmic Perspective, 2nd ed. (CRC Press, Boca Raton, FL).Google Scholar
- (1956) Minimization of Boolean function. Bell System Tech. J. 35(5):1417–1444.Crossref, Google Scholar
- (2012) Foundations of Machine Learning (MIP Press, Kalamazoo, MI).Google Scholar
- (2008) Operations research and data mining. Eur. J. Oper. Res. 187(3):1429–1448.Crossref, Google Scholar
- (2009) MILP approach to pattern generation in logical analysis of data. Discrete Appl. Math. 157(4):749–761.Crossref, Google Scholar
- SeattleSNPs Education Program (2008) SeattleSNPs. Accessed July 26, 2019, http://pga.gs.washington.edu.Google Scholar
- (2014) Classifying negative and positive points by optimal box clustering. Discrete Appl. Math. 165(March):270–282.Crossref, Google Scholar
- Simple Solver Logic (2017) Version 5.4.8, build on January 8, 2019. Accessed July 26, 2019, http://www.simplesolverlogic.com.Google Scholar
- (1998) Effective Logic Computation (Wiley-Interscience, New York).Google Scholar
- (2006) General symmetry breaking constraints. Benhamou F, ed. Internat. Conf. Principles Practice Constraint Programming (Springer, New York), 650–664.Google Scholar
- (2016) Data Mining: Practical Machine Learning Tools and Techniques, 4th ed. (Morgan Kaufman, San Francisco).Google Scholar
- (2017a) 0-1 multi-linear programming as a unifying theory for LAD pattern generation. Discrete Appl. Math. 218(February):21–39.Crossref, Google Scholar
- (2017b) Strong valid inequalities for Boolean logical pattern generation. J. Global Optim. 69(1):183–230.Crossref, Google Scholar
- (2003) Three perspectives of data mining. Artificial Intelligence 143(1):139–146.Crossref, Google Scholar

