Learning representations for classification problems in reproducing kernel Hilbert spaces

• Autor(a) principal: Murilo Vale Ferreira Menezes
• Data de Publicação: 2020
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/37927; https://orcid.org/0000-0002-7675-6432
• topic: Kernel methods; Representation learning; Classification; Engenharia elétrica; Classificação; Kernel, Funções de

The performance of a machine learning method, regardless of the task it is trying to solve, is dependent on the quality of the representations it receives. Not surprisingly, there is a wide class of methods that aim to leverage statistical properties of a dataset, either with raw or handcrafted features, to build more useful representations, from Principal Component Analysis to recent deep learning techniques. Kernel methods are a very powerful family of models, which have the ability to map the input data into a space where otherwise hard tasks become easier to solve, such as linear classification. These methods have the ability to express their learning process only in terms of kernels, which are similarity functions between samples and can be interpreted as inner products in this mapped space, dismissing the need to explicitly map the data. However, these kernel functions often have a set of parameters that have to be chosen according to each task and have a great influence on the mapping, and, therefore, on the final task. This work proposes two objective functions which can be used to learn these kernel parameters and achieve good classification results. Experiments with Gaussian, Laplacian, and sigmoid kernels are conducted. An interpretation of neural networks inside the kernel framework is also proposed, enabling these networks to be trained to learn representations using the proposed functions. Based on empirical results and the analysis of each kernel function used in the experiments, properties of the proposed functions are discussed, along with how they can successfully be used in practice.