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B1663
**Title: **Optimization approaches for multiple instance classification
**Authors: **Annabella Astorino - Consiglio Nazionale delle Ricerche (CNR) (Italy) **[presenting]**

Antonio Fuduli - University of Calabria (Italy)

Giovanni Giallombardo - University of Calabria (Italy)

Giovanna Miglionico - University of Calabria (Italy)

**Abstract: **Multiple Instance Learning (MIL) problems are tackled, where the objective is to categorize bags of points (instances). Differently from supervised classification problems, where the label of each point in the training set is known, in a MIL problem only the labels of the bags are known, whereas the labels of the instances are unknown. Examples of application are in image classification, text categorization, drug prediction. We focus on a binary MIL classification problem, where the objective is to discriminate between positive and negative bags by means of an appropriate hyperplane. Moreover, we assume that a bag is negative if all its instances are negative and positive whenever at least one instance is positive, then only the labels of the instances of the positive bags are to be predicted. Different mathematical programming models have been proposed. We analyze two optimization models: a mixed integer nonlinear programming model and a nonconvex nonsmooth unconstrained optimization one. In particular for the first model we propose to use a Lagrangian Relaxation technique, while for the second we construct a DC (Difference of Convex) formulation and we propose to use appropriate DC methods. We also provide some numerical results on benchmark datasets.

Antonio Fuduli - University of Calabria (Italy)

Giovanni Giallombardo - University of Calabria (Italy)

Giovanna Miglionico - University of Calabria (Italy)