q-Gaussians for pattern recognition

Abstract

Pattern recognition plays an important role for solving many problems in our everyday lives: from simple tasks such as reading texts to more complex ones like driving cars. Subconsciously, the recognition of patterns is instantaneous and an innate ability to every human. However, programming (or “teaching”) a machine how to do the same can present an incredibly difficult task. There are many situations where irrelevant or misleading patterns, poorly represented classes, and complex decision boundaries make recognition very hard, or even impossible by current standards. Important contributions to the field of pattern recognition have been attained through the adoption of methods of statistical mechanics, which has paved the road for much of the research done in academia and industry, ranging from the revival of connectionism to modern day deep learning. Yet traditional statistical mechanics is not universal and has a limited domain of applicability - outside this domain it can make wrong predictions. Non-extensive statistical mechanics has recently emerged to cover a variety of anomalous situations that cannot be described within standard Boltzmann-Gibbs theory, such as non-ergodic systems characterized by long-range interactions, or long-term memories. The literature on pattern recognition is vast, and scattered with applications of non-extensive statistical mechanics. However, most of this work has been done using non-extensive entropy, and little can be found on practical applications of other non-extensive constructs. In particular, non-extensive entropy is widely used to improve segmentation of images that possess strongly correlated patterns, while only a small number of works employ concepts other than entropy for solving similar recognition tasks. The main goal of this dissertation is to expand applications of non-extensive distributions, namely the q-Gaussian, in pattern recognition. We present ourcontributions in the form of two (published) articles where practical uses of q-Gaussians are explored in neural networks. The first paper introduces q Gaussian transfer functions to improve classification of random neural networks, and the second paper extends this work to ensembles which involves combining a set of such classifiers via majority voting.