Melanoma Detection by Means of Multiple Instance Learning.

We present an application to melanoma detection of a multiple instance learning (MIL) approach, whose objective, in the binary case, is to discriminate between positive and negative sets of items. In the MIL terminology these sets are called bags and the items inside the bags are called instances. Under the hypothesis that a bag is positive if at least one of its instances is positive and it is negative if all its instances are negative, the MIL paradigm fits very well with images classification, since an image (bag) is in general classified on the basis of some its subregions (instances). In this work we have applied a MIL algorithm on some clinical data constituted by color dermoscopic images, with the aim to discriminate between melanomas (positive images) and common nevi (negative images). In comparison with standard classification approaches, such as the well known support vector machine, our method performs very well in terms both of accuracy and sensitivity. In particular, using a leave-one-out validation on a data set constituted by 80 melanomas and 80 common nevi, we have obtained the following results: accuracy = 92.50%, sensitivity = 97.50% and specificity = 87.50%. Since the results appear promising, we conclude that a MIL technique could be at the basis of more sophisticated tools useful to physicians in melanoma detection.

A Lagrangian Relaxation Approach for Binary Multiple Instance Classification.

In the standard classification problems, the objective is to categorize points into different classes. Multiple instance learning (MIL), instead, is aimed at classifying bags of points, each point being an instance. The main peculiarity of a MIL problem is that, in the learning phase, only the label of each bag is known whereas the labels of the instances are unknown. We discuss an instance-level learning approach for a binary MIL classification problem characterized by two classes of instances, positive and negative, respectively. In such a problem, a negative bag is constituted only by negative instances, while a bag is positive if it contains at least one positive instance. We start from a mixed integer nonlinear optimization model drawn from the literature and the main result we obtain is to prove that a Lagrangian relaxation approach, equipped with a dual ascent scheme, allows us to obtain an optimal solution of the original problem. The relaxed problem is tackled by means of a block coordinate descent (BCD) algorithm. We provide, finally, the results of our implementation on some benchmark data sets.

The Proximal Trajectory Algorithm in SVM Cross Validation.

We propose a bilevel cross-validation scheme for support vector machine (SVM) model selection based on the construction of the entire regularization path. Since such path is a particular case of the more general proximal trajectory concept from nonsmooth optimization, we propose for its construction an algorithm based on solving a finite number of structured linear programs. Our methodology, differently from other approaches, works directly on the primal form of SVM. Numerical results are presented on binary data sets drawn from literature.

Scaling up support vector machines using nearest neighbor condensation.

In this brief, we describe the FCNN-SVM classifier, which combines the support vector machine (SVM) approach and the fast nearest neighbor condensation classification rule (FCNN) in order to make SVMs practical on large collections of data. As a main contribution, it is experimentally shown that, on very large and multidimensional data sets, the FCNN-SVM is one or two orders of magnitude faster than SVM, and that the number of support vectors (SVs) is more than halved with respect to SVM. Thus, a drastic reduction of both training and testing time is achieved by using the FCNN-SVM. This result is obtained at the expense of a little loss of accuracy. The FCNN-SVM is proposed as a viable alternative to the standard SVM in applications where a fast response time is a fundamental requirement.

Nonsmooth optimization techniques for semisupervised classification.

We apply nonsmooth optimization techniques to classification problems, with particular reference to the TSVM (Transductive Support Vector Machine) approach, where the considered decision function is nonconvex and nondifferentiable and then difficult to minimize. We present some numerical results obtained by running the proposed method on some standard test problems drawn from the binary classification literature.