SVM-Based Multiple Instance Classification via DC Optimization
1
Istituto di Calcolo e Reti ad Alte Prestazioni-C.N.R., 87036 Rende (CS), Italy
2
Dipartimento di Matematica e Informatica, Università della Calabria, 87036 Rende (CS), Italy
3
Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, Università della Calabria, 87036 Rende (CS), Italy
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Algorithms 2019, 12(12), 249; https://doi.org/10.3390/a12120249
Received: 31 October 2019
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Revised: 19 November 2019
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Accepted: 20 November 2019
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Published: 23 November 2019
(This article belongs to the Special Issue Nonsmooth Optimization in Honor of the 60th Birthday of Adil M. Bagirov)
A multiple instance learning problem consists of categorizing objects, each represented as a set (bag) of points. Unlike the supervised classification paradigm, where each point of the training set is labeled, the labels are only associated with bags, while the labels of the points inside the bags are unknown. We focus on the binary classification case, where the objective is to discriminate between positive and negative bags using a separating surface. Adopting a support vector machine setting at the training level, the problem of minimizing the classification-error function can be formulated as a nonconvex nonsmooth unconstrained program. We propose a difference-of-convex (DC) decomposition of the nonconvex function, which we face using an appropriate nonsmooth DC algorithm. Some of the numerical results on benchmark data sets are reported.
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Keywords:
multiple instance learning; support vector machine; DC optimization; nonsmooth optimization
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MDPI and ACS Style
Astorino, A.; Fuduli, A.; Giallombardo, G.; Miglionico, G. SVM-Based Multiple Instance Classification via DC Optimization. Algorithms 2019, 12, 249. https://doi.org/10.3390/a12120249
AMA Style
Astorino A, Fuduli A, Giallombardo G, Miglionico G. SVM-Based Multiple Instance Classification via DC Optimization. Algorithms. 2019; 12(12):249. https://doi.org/10.3390/a12120249
Chicago/Turabian StyleAstorino, Annabella, Antonio Fuduli, Giovanni Giallombardo, and Giovanna Miglionico. 2019. "SVM-Based Multiple Instance Classification via DC Optimization" Algorithms 12, no. 12: 249. https://doi.org/10.3390/a12120249
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