Mapeamento explícito como Kernel em aprendizado de máquinas de vetores de suporte

Abstract

The problems that can be solved through the machine learning approach also have influence on particularities of the implemented algorithms, they are divided in three large groups: regression, classification and clustering. This dissertation deals with pattern classification problems, which aim to create separating surfaces along the pattern space dividing it in regions according to the pattern classes. Classification problems are quite similar to clustering problems, however the latter does not have access to the expected class for each pattern, and therefore its methods use structural characteristics of the data distribution in the space. The margin maximization approach for machine learning problems is appropriated, since the capability of generalization of any classification method is related to its margin. Therefore, it is possible to assert that large margin classifiers are more robust when classifying unknown data. Among large margin classifiers methods, the support vectors machines, SVM, use a Lagrangian based algorithm to determine support vectors, which constructs a separating surface whose distance, or margin, to every class patterns is the largest as possible. The SVM use kernels with the purpose of mapping the input space into a feature space that allows the data separation, allowing not only the pattern classification but also the function regression. Nowadays the SVM are still one of the best and most used methods in the academia. Explicit mapping approach became popular recently with the proposal of the extreme learning machines, ELM. These machines have a rather simple implementation that allows the creation of a classifier that uses only analytical calculations, discarding any iterations. The ELM uses a random explicit mapping of the input space into a feature space of higher dimensionality, allowing the linear separability of the data in the mapped space. For the ELM, the mapping is construed as the hidden layer of a feedforward neural network whose weights are assigned randomly, and the single parameter to be tuned in it is the quantity of neurons. The output layer, in the ELM, has its weights tuned according to an analytical calculation, which makes this method simple, fast and very elegant. The explicit mapping can also be interpreted as a complex kernel, whose parameters are only the mapping dimension and the variance of the random distribution that generated the weights. Since the number of neurons, in other words the mapping dimension, is not sensible by the methods performance, when it is big enough, and the variance has no effect either, this method can be considered non parametrical. The need of using large margin methods is widely accepted, hence it is possible to improve SVMs by using non parametric kernels. Thus the classifier becomes simpler to be implemented and used, since it is exempt of using a complicated methodology for a fine parameter tuning. With this motivation it was implemented a method that uses explicit mapping as kernel, therefore the great dimensionality of the feature space allows the linear separability of the data at the same time that the margin is maximized. Meanwhile, the use of the non-parametric explicit mapping and a linear support vectors machine allows a virtually non-parametric at all