On Piecewise-Linear Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
The nature of statistical learning theory
The nature of statistical learning theory
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Polyhedral separability through successive LP
Journal of Optimization Theory and Applications
Mathematical Programming in Data Mining
Data Mining and Knowledge Discovery
Regularization and statistical learning theory for data analysis
Computational Statistics & Data Analysis - Nonlinear methods and data mining
Mathematical Programming for Data Mining: Formulations and Challenges
INFORMS Journal on Computing
On data classification by iterative linear partitioning
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
A study of cross-validation and bootstrap for accuracy estimation and model selection
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Evaluating Membership Functions for Fuzzy Discrete SVM
WILF '07 Proceedings of the 7th international workshop on Fuzzy Logic and Applications: Applications of Fuzzy Sets Theory
Non-smoothness in classification problems
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
Softening the margin in discrete SVM
ICDM'07 Proceedings of the 7th industrial conference on Advances in data mining: theoretical aspects and applications
Gene selection and cancer microarray data classification via mixed-integer optimization
EvoBIO'08 Proceedings of the 6th European conference on Evolutionary computation, machine learning and data mining in bioinformatics
Regularization through fuzzy discrete SVM with applications to customer ranking
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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In the context of learning theory many efforts have been devoted to developing classification algorithms able to scale up with massive data problems. In this paper the complementary issue is addressed, aimed at deriving powerful classification rules by accurately learning from few data. This task is accomplished by solving a new mixed integer programming model that extends the notion of discrete support vector machines, in order to derive an optimal set of separating hyperplanes for binary classification problems. According to the cardinality of the set of hyperplanes, the classification region may take the form of a convex polyhedron or a polytope in the original space where the examples are defined. Computational tests on benchmark datasets highlight the effectiveness of the proposed model, that yields the greatest accuracy when compared to other classification approaches.