Identification of overcomplete dictionaries and their application in distributed classification problems

OF THE THESIS Identification of overcomplete dictionaries and their application in distributed classification problems by Zahra Shakeri Thesis Director: Prof. Waheed U. Bajwa The work presented in this thesis aims to study the conditions essential for reliable dictionary recovery based on the maximal response criterion and exploit the application of dictionary learning in classification of distributed data. The first part of this thesis revisits the problem of recovery of an overcomplete dictionary in a local neighborhood from training samples using the so-called maximal response criterion. While it is known in the literature that the maximal response criterion can be used for asymptotic exact recovery of a dictionary in a local neighborhood, those results do not allow for linear (in the ambient dimension) scaling of sparsity levels in signal representations. The first contribution in this work is introducing a new condition for the sparse representation of signals and leveraging a new proof technique to establish that maximal response criterion can in fact handle linear sparsity (modulo a logarithmic factor) of signal representations. While the focus of this work is on asymptotic exact recovery, the same ideas can be used in a straightforward manner to strengthen the original maximal response criterion-based results involving noisy observations and finite number of training samples. The second part of this thesis addresses the problem of collaborative training of nonlinear classifiers using big, distributed training data. The proposed supervised learning