Multiple Instance Classification via Successive Linear Programming

The multiple instance classification problem (Dietterich et al., Artif. Intell. 89:31–71, [ 1998 ]; Auer, Proceedings of 14th International Conference on Machine Learning, pp. 21–29, Morgan Kaufmann, San Mateo, [ 1997 ]; Long et al., Mach. Learn. 30(1):7–22, [ 1998 ]) is formulated using a linear or...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 137; H. 3; S. 555 - 568
Hauptverfasser: Mangasarian, O. L., Wild, E. W.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.06.2008
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Applications of Mathematics
Applied sciences
Calculus of Variations and Optimal Control; Optimization
Classification
Classifiers
Engineering
Exact sciences and technology
Integer programming
Learning
Linear programming
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Minimization
Nonlinearity
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Optimization
Quadratic programming
Reduction
Studies
Support vector machines
Theory of Computation
Support vector machines
Successive linearization algorithm
Bilinear constraints
Multiple instance learning
Kernels
Integer programming
Learning (artificial intelligence)
Vector support machine
Minimization
Linear programming
Classifier
Complex programming
Multiple instance learning, Support vector machines, Successive linearization algorithm
Competitive algorithms
Linearization
ISSN:0022-3239, 1573-2878
Online-Zugang:Volltext
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Zusammenfassung:The multiple instance classification problem (Dietterich et al., Artif. Intell. 89:31–71, [ 1998 ]; Auer, Proceedings of 14th International Conference on Machine Learning, pp. 21–29, Morgan Kaufmann, San Mateo, [ 1997 ]; Long et al., Mach. Learn. 30(1):7–22, [ 1998 ]) is formulated using a linear or nonlinear kernel as the minimization of a linear function in a finite-dimensional (noninteger) real space subject to linear and bilinear constraints. A linearization algorithm is proposed that solves a succession of fast linear programs that converges in a few iterations to a local solution. Computational results on a number of datasets indicate that the proposed algorithm is competitive with the considerably more complex integer programming and other formulations. A distinguishing aspect of our linear classifier not shared by other multiple instance classifiers is the sparse number of features it utilizes. In some tasks, the reduction amounts to less than one percent of the original features.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-007-9343-5