Binary Independent Component Analysis with OR Mixtures

Independent component analysis (ICA) is a computational method for separating a multivariate signal into subcomponents assuming the mutual statistical independence of the non-Gaussian source signals. The classical Independent Components Analysis (ICA) framework usually assumes linear combinations of independent sources over the field of realvalued numbers R. In this paper, we investigate binary ICA for OR mixtures (bICA), which can find applications in many domains including medical diagnosis, multi-cluster assignment, Internet tomography and network resource management. We prove that bICA is uniquely identifiable under the disjunctive generation model, and propose a deterministic iterative algorithm to determine the distribution of the latent random variables and the mixing matrix. The inverse problem concerning inferring the values of latent variables are also considered along with noisy measurements. We conduct an extensive simulation study to verify the effectiveness of the propose algorithm and present examples of real-world applications where bICA can be applied.Comment: Manuscript submitted to IEEE Transactions on Signal Processin

New Guarantees for Blind Compressed Sensing

Blind Compressed Sensing (BCS) is an extension of Compressed Sensing (CS) where the optimal sparsifying dictionary is assumed to be unknown and subject to estimation (in addition to the CS sparse coefficients). Since the emergence of BCS, dictionary learning, a.k.a. sparse coding, has been studied as a matrix factorization problem where its sample complexity, uniqueness and identifiability have been addressed thoroughly. However, in spite of the strong connections between BCS and sparse coding, recent results from the sparse coding problem area have not been exploited within the context of BCS. In particular, prior BCS efforts have focused on learning constrained and complete dictionaries that limit the scope and utility of these efforts. In this paper, we develop new theoretical bounds for perfect recovery for the general unconstrained BCS problem. These unconstrained BCS bounds cover the case of overcomplete dictionaries, and hence, they go well beyond the existing BCS theory. Our perfect recovery results integrate the combinatorial theories of sparse coding with some of the recent results from low-rank matrix recovery. In particular, we propose an efficient CS measurement scheme that results in practical recovery bounds for BCS. Moreover, we discuss the performance of BCS under polynomial-time sparse coding algorithms.Comment: To appear in the 53rd Annual Allerton Conference on Communication, Control and Computing, University of Illinois at Urbana-Champaign, IL, USA, 201

A decomposition approach for the Frequency Assignment Problem

The Frequency Assignment Problem (FAP) is an important optimization problem that arises in operational cellular wireless networks. Solution techniques based on meta-heuristic algorithms have been shown to be successful for some test problems but they have not been usually demonstrated on large scale problems that occur in practice. This thesis applies a problem decomposition approach in order to solve FAP in stances with standard meta-heuristics. Three different formulations of the problem are considered in order of difficulty: Minimum Span (MS-FAP), Fixed Spectrum (MS-FAP), and Minimum Interference FAP (MI-FAP). We propose a decomposed assignment technique which aims to divide the initial problem into a number of subproblems and then solves them either independently or in sequence respecting the constraints between them. Finally, partial subproblem solutions are recomposed into a solution of the original problem. Standard implementations of meta-heuristics may require considerable run times to produce good quality results whenever a problem is very large or complex. Our results, obtained by applying the decomposed approach to a Simulated Annealing and a Genetic Algorithm with two different assignment representations (direct and order-based), show that the decomposed assignment approach proposed can improve their outcomes, both in terms of solution quality and runtime. A number of partitioning methods are presented and compared for each FAP, such as clique detection partitioning based on sequential orderings and novel applications of existing graph partitioning and clustering methods adapted for this problem