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Comparação Sistemática do Desempenho de Classificadores Binários Supervisionados
Matheus Avellar de Barros, Carlos Eduardo Pedreira, Laura de Oliveira Fernandes Moraes
Programa de Engenharia de Sistemas e Computação·2025
Classification algorithms, or classifiers, categorize data into distinct classes, and play a fundamental role in machine learning. Classifiers are used in various areas, from detecting spam and financial fraud, to recognizing objects in images (such as people, animals and gestures) and even detecting cancer cells. Because the classification task isn't trivial, or even deterministic, implementing heuristics to aid in the decision-making process for ambiguous cases is necessary – and that's the algorithms' function. However, faced with a plethora of options, pragmatic differences between the many classifiers are not always clear. In this dissertation, we show that it is possible to group certain supervised binary classifiers widely used in the literature (SVM, GBDT, kNN, RF and NB) according to their resistance to noise and/or unbalanced data, or to their running time. These results indicate that, even if there is a great deal of similarity in the general performance of well known algorithms, they have differences in execution that may have a significant impact depending on the dataset being used. Therefore, the results may assist in the choice for a more adequate classifier.
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View paper →Flat tori in three-dimensional space and convex integration
Vincent Borrelli, Saïd Jabrane, Francis Lazarus, Boris Thibert
Proceedings of the National Academy of Sciences·2012·31 citations
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It is well-known that the curvature tensor is an isometric invariant of
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Riemannian manifolds. This invariant is at the origin of the rigidity observed in Riemannian geometry. In the mid 1950s, Nash amazed the world mathematical community by showing that this rigidity breaks down in regularity
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. This unexpected flexibility has many paradoxical consequences, one of them is the existence of
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isometric embeddings of flat tori into Euclidean three-dimensional space. In the 1970s and 1980s, M. Gromov, revisiting Nash’s results introduced convex integration theory offering a general framework to solve this type of geometric problems. In this research, we convert convex integration theory into an algorithm that produces isometric maps of flat tori. We provide an implementation of a convex integration process leading to images of an embedding of a flat torus. The resulting surface reveals a
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fractal structure: Although the tangent plane is defined everywhere, the normal vector exhibits a fractal behavior. Isometric embeddings of flat tori may thus appear as a geometric occurrence of a structure that is simultaneously
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and fractal. Beyond these results, our implementation demonstrates that convex integration, a theory still confined to specialists, can produce computationally tractable solutions of partial differential relations.
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