Pattern-set Representations using Linear, Shallow and Tensor Subspaces

Abstract

Pattern-set matching belongs to a class of problems where learning takes place through sets rather than elements. Much used in computer vision, this approach has the advantage of having a low processing time and robustness to variations such as illumination, intrinsic parameters of the signal capture devices and pose of the analyzed object. Inspired by applications of subspace methods, three new collections of methods are presented in this thesis: (1) New representations for sets of two-dimensional images and videos; (2) Shallow networks for image classification; and (3) Subspaces for tensor representation and classification. New representations are proposed with the aim of preserving the spatial structure and maintaining a fast processing time. We also introduce a technique to maintain temporal structure, even using the principal component analysis, which classically does not preserve the data's order. In shallow networks, we present two convolutional neural networks that do not need backpropagation, employing only subspaces for its convolution filters. In addition to their competitive classification results, the proposed networks present an advantage when the time available for learning is limited. Finally, to handle multidimensional data, such as video data, we propose two methods that employ subspaces to represent this kind of data in a compact and discriminative way. In addition to the new methods introduced, our proposed work has been applied in problems other than computer vision, such as representation and classification of bioacoustics and text patterns.