Abstract
We consider a multiple instance learning problem where the objective is the binary classifications of bags of instances, instead of single ones. We adopt spherical separation as a classification tool and come out with an optimization model which is of difference-of-convex type. We tackle the model by resorting to a specialized nonsmooth optimization algorithm, recently proposed in the literature which is based on objective function linearization and bundling. The results obtained by applying the proposed approach to some benchmark test problems are also reported.
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References
Amores J (2013) Multiple instance classification: review, taxonomy and comparative study. Artif Intell 201:81–105
Andrews S, Tsochantaridis I, Hofmann T (2003) Support vector machines for multiple-instance learning. In: Becker S, Thrun S, Obermayer K (eds) Advances in neural information processing systems. MIT Press, Cambridge, pp 561–568
Astorino A, Gaudioso M (2009) A fixed-center spherical separation algorithm with kernel transformation for classification problems. Comput Manag Sci 6:357–373
Astorino A, Miglionico G (2016) Optimizing sensor cover energy via DC programming. Optim Lett 10:355–368
Astorino A, Fuduli A, Gaudioso M (2010) DC models in spherical separation. J Glob Optim 48:657–669
Astorino A, Fuduli A, Gaudioso M (2012) Margin maximization in spherical separation. Comput Optim Appl 53:301–322
Astorino A, Fuduli A, Gaudioso M (2019) A Lagrangian relaxation approach for binary multiple instance classification. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2018.2885852
Bergeron C, Moore G, Zaretzki J, Breneman CM, Bennett KP (2012) Fast bundle algorithm for multiple-instance learning. IEEE Trans Pattern Anal Mach Intell 34:1068–1079
Carbonneau M-A, Cheplygina V, Granger E, Gagnon G (2018) Multiple instance learning: a survey of problem characteristics and applications. Pattern Recognit 77:329–353
de Oliveira W (2019) Proximal bundle methods for nonsmooth DC programming. J Glob Optim. https://doi.org/10.1007/s10898-019-00755-4
de Oliveira W, Tcheou Michel P (2018) An inertial algorithm for DC programming. Set Valued Var Anal. https://doi.org/10.1007/s11228-018-0497-0
Gaudioso M, Giallombardo G, Miglionico G (2018a) Minimizing piecewise-concave functions over polytopes. Math Oper Res 43:580–597
Gaudioso M, Giallombardo G, Miglionico G, Bagirov AM (2018b) Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations. J Glob Optim 71:37–55
Hiriart-Urruty J-B (1986) Generalized differentiability/duality and optimization for problems dealing with differences of convex functions. Lecture notes in economic and mathematical systems, vol 256. Springer, Berlin, pp 37–70
Hiriart-Urruty J-B (1989) From convex optimization to nonconvex optimization. Necessary and sufficient conditions for global optimality. In: Clarke FH, Demyanov VF, Giannessi F (eds) Nonsmooth optimization and related topics. Springer, New York
Hiriart-Urruty J-B, Lemaréchal C (1993) Convex analysis and minimization algorithms, vol I–II. Springer, New York
Joki K, Bagirov AM, Karmitsa N, Mäkelä MM (2017) A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes. J Glob Optim 68:501–535
Joki K, Bagirov AM, Karmitsa N, Mäkelä MM, Taheri S (2018) Double bundle method for finding clarke stationary points in nonsmooth DC programming. SIAM J Optim 28(2):1892–1919
Kelley JE (1960) The cutting-plane method for solving convex programs. J SIAM 8:703–712
Khalaf W, Astorino A, D’Alessandro P, Gaudioso M (2017) A DC optimization-based clustering technique for edge detection. Optim Lett 11:627–640
Le Thi HA, Pham Dinh T (2005) The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. J Glob Optim 133:23–46
Mangasarian O, Wild E (2008) Multiple instance classification via successive linear programming. J Optim Theory Appl 137:555–568
Plastria F, Carrizosa E, Gordillo J (2014) Multi-instance classification through spherical separation and VNS. Comput Oper Res 52:326–333
Strekalovsky AS (1997) On global optimality conditions for D.C. programming problems. Irkutsk State University, Russia
Vapnik V (1995) The nature of statistical learning theory. Springer, New York
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Gaudioso, M., Giallombardo, G., Miglionico, G. et al. Classification in the multiple instance learning framework via spherical separation. Soft Comput 24, 5071–5077 (2020). https://doi.org/10.1007/s00500-019-04255-1
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DOI: https://doi.org/10.1007/s00500-019-04255-1