Fast Conical Hull Algorithms for Near-separable Non-negative Matrix Factorization

The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem as that of finding the extreme rays of the conical hull of a finite set of vectors. From this geometric perspective, we derive new separable NMF algorithms that are highly scalable and empirically noise robust, and have several other favorable properties in relation to existing methods. A parallel implementation of our algorithm demonstrates high scalability on shared- and distributed-memory machines.Comment: 15 pages, 6 figure

Effects of duct source and termination impedance on the acoustic response characteristics of duct elements

The objective of the thesis is to study the effects of termination of an air duct on the acoustic response characteristics of the elements in the duct system. The end reflections due to the mis-match of the acoustic impedance at the termination affect the acoustic characteristics of the duct elements; The ducts of the duct system, terminating into atmosphere abruptly, like the HVAC ducts with diffusers, provide reflective termination. With this type of termination much of the sound energy in lower frequencies is reflected. This sets up standing sound waves inside the duct. The analytical methods to calculate the insertion-loss, noise reduction consider single reflection only inside the duct. Because of that, the analytical values of the insertion-loss and noise reduction do not match the experimental values well. When an anechoic termination is provided there will not be any reflections from the termination. This reduces the formation of standing sound waves on the downstream side of the acoustic element. This improves the agreement between the analytical and experimental values; The effect of termination on the acoustic characteristics of the duct elements was studied using a simple expansion chamber. (Abstract shortened by UMI.)