## Margin Optimal Classification Trees

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Article Download View Margin Optimal Classification Trees

In this work we study binary classification problems where we assume that our training data is subject to uncertainty, i.e. the precise data points are not known. To tackle this issue in the field of robust machine learning the aim is to develop models which are robust against small perturbations in the training data. We … Read more

Support vector machines (SVMs) are successful modeling and prediction tools with a variety of applications. Previous work has demonstrated the superiority of the SVMs in dealing with the high dimensional, low sample size problems. However, the numerical difficulties of the SVMs will become severe with the increase of the sample size. Although there exist many … Read more

In 1963, Polyak proposed a simple condition that is sufficient to show a global linear convergence rate for gradient descent. This condition is a special case of the Lojasiewicz inequality proposed in the same year, and it does not require strong convexity (or even convexity). In this work, we show that this much-older Polyak-Lojasiewicz (PL) … Read more

In this work we present a new feasible direction algorithm for solving smooth nonlinear second-order cone programs. These problems consist of minimizing a nonlinear dierentiable objective function subject to some nonlinear second-order cone constraints. Given a point interior to the feasible set denfined by the nonlinear constraints, the proposed approach computes a feasible and descent … Read more

Support Vector Machines (SVM) is the state-of-the-art in Supervised Classification. In this paper the Cluster Support Vector Machines (CLSVM) methodology is proposed with the aim to reduce the complexity of the SVM classifier in the presence of categorical features. The CLSVM methodology lets categories cluster around their peers and builds an SVM classifier using the … Read more

In linear classifiers, such as the Support Vector Machine (SVM), a score is associated with each feature and objects are assigned to classes based on the linear combination of the scores and the values of the features. Inspired by discrete psychometric scales, which measure the extent to which a factor is in agreement with a … Read more

We investigate constrained first order techniques for training Support Vector Machines (SVM) for online classification tasks. The methods exploit the structure of the SVM training problem and combine ideas of incremental gradient technique, gradient acceleration and successive simple calculations of Lagrange multipliers. Both primal and dual formulations are studied and compared. Experiments show that the … Read more

As in most Data Mining procedures, how to tune the parameters of a Support Vector Machine (SVM) is a critical, though not sufficiently explored, issue. The default approach is a grid search in the parameter space, which becomes prohibitively time-consuming even when just a few parameters are to be tuned. For this reason, for models … Read more

Recently, the so-called $\psi$-learning approach, the Support Vector Machine (SVM) classifier obtained with the ramp loss, has attracted attention from the computational point of view. A Mixed Integer Nonlinear Programming (MINLP) formulation has been proposed for $\psi$-learning, but solving this MINLP formulation to optimality is only possible for datasets of small size. For datasets of … Read more