Strongly agree or strongly disagree? Rating features in support vector machines

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 statement, we propose the Discrete Level Support Vector Machine (DILSVM) where the feature scores can only take on a discrete number of values, de fined by the so-called feature rating levels. The DILSVM classifier benefits from interpretability as it can be seen as a collection of Likert scales, one for each feature, where we rate the level of agreement with the positive class. To build the DILSVM classifier, we propose a Mixed Integer Linear Programming approach, as well as a collection of strategies to reduce the building times. Our computational experience shows that the 3-point and the 5-point DILSVM classifiers have comparable accuracy to the SVM with a substantial gain in interpretability and sparsity, thanks to the appropriate choice of the feature rating levels.Ministerio de Economía y CompetitividadJunta de AndalucíaFondo Europeo de Desarrollo Regiona

Differential Evolution Algorithm in the Construction of Interpretable Classification Models

In this chapter, the application of a differential evolution-based approach to induce oblique decision trees (DTs) is described. This type of decision trees uses a linear combination of attributes to build oblique hyperplanes dividing the instance space. Oblique decision trees are more compact and accurate than the traditional univariate decision trees. On the other hand, as differential evolution (DE) is an efficient evolutionary algorithm (EA) designed to solve optimization problems with real-valued parameters, and since finding an optimal hyperplane is a hard computing task, this metaheuristic (MH) is chosen to conduct an intelligent search of a near-optimal solution. Two methods are described in this chapter: one implementing a recursive partitioning strategy to find the most suitable oblique hyperplane of each internal node of a decision tree, and the other conducting a global search of a near-optimal oblique decision tree. A statistical analysis of the experimental results suggests that these methods show better performance as decision tree induction procedures in comparison with other supervised learning approaches

Supervised Classification and Mathematical Optimization

Data Mining techniques often ask for the resolution of optimization problems. Supervised Classification, and, in particular, Support Vector Machines, can be seen as a paradigmatic instance. In this paper, some links between Mathematical Optimization methods and Supervised Classification are emphasized. It is shown that many different areas of Mathematical Optimization play a central role in off-the-shelf Supervised Classification methods. Moreover, Mathematical Optimization turns out to be extremely useful to address important issues in Classification, such as identifying relevant variables, improving the interpretability of classifiers or dealing with vagueness/noise in the data

Discrete support vector decision trees via tabu-search

An algorithm is proposed for generating decision trees in which multivariate splitting rules are based on the new concept of discrete support vector machines. By this term a discrete version of SVMs is denoted in which the error is properly expressed as the count of misclassified instances, in place of a proxy of the misclassification distance considered by traditional SVMs. The resulting mixed integer programming problem formulated at each node of the decision tree is then efficiently solved by a tabu search heuristic. Computational tests performed on both well-known benchmark and large marketing datasets indicate that the proposed algorithm consistently outperforms other classification approaches in terms of accuracy, and is therefore capable of good generalization on validation sets