Supervised classification and mathematical optimization

Abstract

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.

Biometric Gait Recognition Based on Machine Learning Algorithms

“…For a given set of ndimensional feature vectors, the SVM classifier can find the hyperplane with the highest margin that categorizes these vectors. Note that SVM is a powerful tool for solving classification problems in specific as a two-class classifier (Carrizosa and Morales, 2013). The k-NN classifier uses directly closest training samples from the feature vectors to classify a new test example.…”

“…There are many other techniques similar to artificial neural networks including Convolutional Neural Network (CNN), simple and oblique decision trees and Support Vector Machines (SVM) methods (Carrizosa and Morales, 2013). All of these techniques are founded on a similar principle that consists of choosing a structure (for example: MLP for neural networks, leaves representing class labels and branches representing conjunction of features for decision tree and core function for the SVM method).…”

Visualizing proportions and dissimilarities by Space-filling maps: A Large Neighborhood Search approach

“…In all the cases, we use the usual techniques to linearize the product of binary variables proposed in [22] and the absolute values both in the objective function and constraint (7). Thus, we consider the following reformulations R1, R2 and R3 stated as follows:…”

“…The box-connectivity of P r (x) is enforced by imposing that the box generated by each pair of non-adjacent cells belonging to P r (x) (two cells that do not share a common boundary) must contain also cells of P r (x), namely the intersection between such box (excluding its two generator cells) and the portion must be nonempty. Finally, the error incurred by approximating the statistical values ω by the area of the portions is modeled through constraint (7).…”

“…Visualizing data with complex underlying structures has become a crucial task to help analysts to draw conclusions by detecting patterns and behaviours which remain hidden when classic techniques are applied, [9,10,23]. Mathematical Optimization plays an important role in the field of Information Visualization, both developing new tools to adapt existent visualization techniques and creating new ones, [7,24,28,42]. In this paper, Mathematical Optimization is used to build a planar space-filling visualization map, in the sense that the whole region in which the data are visualized is covered.…”