Access the full text.
Sign up today, get DeepDyve free for 14 days.
L. Breiman, J. Friedman, R. Olshen, C. Stone (1984)
Classification and Regression TreesBiometrics, 40
H. Mannila, Hannu Toivonen (1996)
Multiple Uses of Frequent Sets and Condensed Representations (Extended Abstract)
H. Mannila, Hannu Toivonen, A. Verkamo (1994)
Efficient Algorithms for Discovering Association Rules
M.R. Garey, D.S. Johnson (1979)
Computers and Intractability
R. Caruana, D. Freitag (1994)
Machine Learning: Proceedings of the Eleventh International Conference
M. Boddy, T. Dean (1994)
Deliberation Scheduling for Problem Solving in Time-Constrained EnvironmentsArtif. Intell., 67
J. Quinlan (1992)
C4.5: Programs for Machine Learning
K. Kira, L. Rendell (1992)
Proceedings of the Tenth National Conference on Artificial Intelligence
(1990)
David M
L. Lovász (1975)
On the ratio of optimal integral and fractional coversDiscret. Math., 13
O.L. Mangasarian, R. Setiono, W.H. Wolberg (1990)
Large-Scale Numerical Optimization
Y. Crama, P. Hammer, T. Ibaraki (1988)
Cause-effect relationships and partially defined Boolean functionsAnnals of Operations Research, 16
U. Feige (1996)
A threshold of ln n for approximating set cover (preliminary version)
V. Chvátal (1979)
A Greedy Heuristic for the Set-Covering ProblemMath. Oper. Res., 4
D. Koller, M. Sahami (1996)
Toward Optimal Feature Selection
E. Boros, T. Horiyama, T. Ibaraki, K. Makino, M. Yagiura (2000)
Finding Essential Attributes in Binary Data
M. Conforti, G. Cornuéjols (1984)
Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some generalizations of the Rado-Edmonds theoremDiscret. Appl. Math., 7
P. Bradley, O. Mangasarian, W. Street (1997)
Feature Selection via Mathematical ProgrammingINFORMS J. Comput., 10
R. Fourer, B. Kernighan (1993)
AMPL: A Modeling Language for Mathematical Programming
D. Angluin (1988)
Queries and concept learningMachine Learning, 2
G. Nemhauser, L. Wolsey (1981)
Maximizing Submodular Set Functions: Formulations and Analysis of Algorithms*North-holland Mathematics Studies, 59
David Johnson, W. Freeman
The Np-completeness Column: an Ongoing Guide Garey and Myself in Our Book ''computers and Intractability: a Guide to the Theory of Np-completeness,''
D.S. Hochbaum, A. Pathria (1998)
Analysis of the greedy approach in covering problemsNaval Research Quarterly, 45
(1961)
Boolean functions realizable with single threshold devices
D. Harman (1995)
Overview of the Third Text REtrieval Conference (TREC-3)
S. Khuller, A. Moss, J. Naor (1999)
The Budgeted Maximum Coverage ProblemInf. Process. Lett., 70
S. Goldman (1997)
Computational Learning TheoryAn Introduction to Machine Learning
H. Almuallim, Thomas Dietterich (1994)
Learning Boolean Concepts in the Presence of Many Irrelevant FeaturesArtif. Intell., 69
Marek Karpinski, A. Zelikovsky (1996)
Approximating dense cases of covering problemsElectron. Colloquium Comput. Complex., TR97
D. Hampel, R. Winder (1971)
Threshold logicIEEE Spectrum, 8
L. Shapley, M. Shubik (1954)
A Method for Evaluating the Distribution of Power in a Committee SystemAmerican Political Science Review, 48
Catherine Blake (1998)
UCI Repository of machine learning databases
M. Scherf, W. Brauer (1997)
Feature Selection by Means of a Feature Weighting Approach
U. Feige (1998)
A threshold of ln n for approximating set coverJ. ACM, 45
B. Endre, Horiyama Takashi, Ibaraki Toshihide, Makino Kazuhisa, Yagiura Mutsunori (2000)
Finding Small Sets of Essential Attributes in Binary Data
F.J. Banzaf (1965)
Weighted voting doesn't work: A mathematical analysisRutgers Law Review, 19
E. Boros, T. Ibaraki, K. Makino (1999)
Logical Analysis of Binary Data with Missing BitsArtif. Intell., 107
G.L. Nemhauser, L. Wolsey (1981)
Studies of Graphs and Discrete Programming
D. Bertsekas (1982)
Constrained Optimization and Lagrange Multiplier Methods
N. Bshouty, L. Hellerstein (1998)
Attribute-efficient learning in query and mistake-bound modelsJ. Comput. Syst. Sci., 56
E. Boros, P. Hammer, T. Ibaraki, A. Kogan (1997)
Logical analysis of numerical dataMathematical Programming, 79
R. Motwani, P. Raghavan (1995)
Randomized AlgorithmsSIGACT News, 26
R. Caruana, Dayne Freitag (1994)
Greedy Attribute Selection
M. Anthony, N. Biggs (1992)
Computational learning theory: an introduction
N. Littlestone (1987)
Learning Quickly When Irrelevant Attributes Abound: A New Linear-Threshold AlgorithmMachine Learning, 2
D. Hochbaum, A. Pathria (1998)
Analysis of the greedy approach in problems of maximum k‐coverageNaval Research Logistics, 45
K. Kira, L. Rendell (1992)
The Feature Selection Problem: Traditional Methods and a New Algorithm
D. Bell, Hui Wang (2000)
A Formalism for Relevance and Its Application in Feature Subset SelectionMachine Learning, 41
Avrim Blum, P. Langley (1997)
Selection of Relevant Features and Examples in Machine LearningArtif. Intell., 97
George John, Ron Kohavi, Karl Pfleger (1994)
Irrelevant Features and the Subset Selection Problem
Temple Smith (1980)
Occam's razorNature, 285
E. Boros, P. Hammer, T. Ibaraki, A. Kogan, E. Mayoraz, I. Muchnik (2000)
An Implementation of Logical Analysis of DataIEEE Trans. Knowl. Data Eng., 12
Huan Liu, H. Motoda, M. Dash (1998)
A Monotonic Measure for Optimal Feature Selection
W. Wolberg, O. Mangasarian, R. Setiono (1989)
Pattern Recognition Via Linear Programming: Theory and Application to Medical Diagnosis
P. Narendra, K. Fukunaga (1977)
A Branch and Bound Algorithm for Feature Subset SelectionIEEE Transactions on Computers, C-26
(1991)
FORTRAN 77 Optimization Programming (in Japanese), Iwanami
L.G. Valiant (1984)
A theory of the learnableCommunications of the ACM, 27
R. Winder (1971)
Chow Parameters in Threshold LogicJ. ACM, 18
(2004)
Advances in Knowledge Discovery and Data Mining, 3056
E. Boros, T. Ibaraki, K. Makino (1998)
Error-Free and Best-Fit Extensions of Partially Defined Boolean FunctionsInf. Comput., 140
Avrim Blum, L. Hellerstein, N. Littlestone (1991)
Learning in the presence of finitely or infinitely many irrelevant attributesJ. Comput. Syst. Sci., 50
M. Hall, L. Smith (1998)
Practical feature subset selection for machine learning
H. Almuallim, Thomas Dietterich (1992)
Efficient Algorithms for Identifying Relevant Features
R. Agrawal, T. Imielinski, A. Swami (1993)
Mining association rules between sets of items in large databasesProceedings of the 1993 ACM SIGMOD international conference on Management of data
J. Quinlan (1986)
Induction of Decision TreesMachine Learning, 1
(1992)
Banzaf III , Weighted voting doesn ’ t work : A mathematical analysis
David Editor
Artificial Intelligence and Language Processing a Theory of the Learnable
S. Salzberg, Alberto Segre (1994)
Programs for Machine Learning
Y. Nesterov, A. Nemirovski (1994)
Interior-point polynomial algorithms in convex programming, 13
We consider data sets that consist of n-dimensional binary vectors representing positive and negative examples for some (possibly unknown) phenomenon. A subset S of the attributes (or variables) of such a data set is called a support set if the positive and negative examples can be distinguished by using only the attributes in S. In this paper we study the problem of finding small support sets, a frequently arising task in various fields, including knowledge discovery, data mining, learning theory, logical analysis of data, etc. We study the distribution of support sets in randomly generated data, and discuss why finding small support sets is important. We propose several measures of separation (real valued set functions over the subsets of attributes), formulate optimization models for finding the smallest subsets maximizing these measures, and devise efficient heuristic algorithms to solve these (typically NP-hard) optimization problems. We prove that several of the proposed heuristics have a guaranteed constant approximation ratio, and we report on computational experience comparing these heuristics with some others from the literature both on randomly generated and on real world data sets.
Annals of Mathematics and Artificial Intelligence – Springer Journals
Published: Oct 10, 2004
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.