Advances in subspace learning and its applications

Pattern-set matching refers to a class of problems where learning takes place through sets rather than elements. Much used in computer vision, this approach presents robustness to variations such as illumination, intrinsic parameters of the signal capture devices, and pose of the analyzed object. Inspired by applications of subspace analysis, three new collections of methods are presented in this thesis summary: (1) New representations for two-dimensional sets; (2) Shallow networks for image classification; and (3) Tensor data representation by subspaces. New representations are proposed to preserve the spatial structure and maintain a fast processing time. We also introduce a technique to keep temporal structure, even using the principal component analysis, which classically does not model sequences. In shallow networks, we present two convolutional neural networks that do not require backpropagation, employing only subspaces for their convolution filters. These networks present advantages when the training time and hardware resources are scarce. Finally, to handle tensor data, such as videos, we propose methods that employ subspaces for representation in a compact and discriminative way. Our proposed work has been applied in problems other than computer vision, such as representation and classification of bioacoustics and text patterns.