Random Neural Networks and Optimisation

In this thesis we introduce new models and learning algorithms for the Random Neural Network (RNN), and we develop RNN-based and other approaches for the solution of emergency management optimisation problems. With respect to RNN developments, two novel supervised learning algorithms are proposed. The first, is a gradient descent algorithm for an RNN extension model that we have introduced, the RNN with synchronised interactions (RNNSI), which was inspired from the synchronised firing activity observed in brain neural circuits. The second algorithm is based on modelling the signal-flow equations in RNN as a nonnegative least squares (NNLS) problem. NNLS is solved using a limited-memory quasi-Newton algorithm specifically designed for the RNN case. Regarding the investigation of emergency management optimisation problems, we examine combinatorial assignment problems that require fast, distributed and close to optimal solution, under information uncertainty. We consider three different problems with the above characteristics associated with the assignment of emergency units to incidents with injured civilians (AEUI), the assignment of assets to tasks under execution uncertainty (ATAU), and the deployment of a robotic network to establish communication with trapped civilians (DRNCTC). AEUI is solved by training an RNN tool with instances of the optimisation problem and then using the trained RNN for decision making; training is achieved using the developed learning algorithms. For the solution of ATAU problem, we introduce two different approaches. The first is based on mapping parameters of the optimisation problem to RNN parameters, and the second on solving a sequence of minimum cost flow problems on appropriately constructed networks with estimated arc costs. For the exact solution of DRNCTC problem, we develop a mixed-integer linear programming formulation, which is based on network flows. Finally, we design and implement distributed heuristic algorithms for the deployment of robots when the civilian locations are known or uncertain

Unsupervised learning of overlapping image components using divisive input modulation

This paper demonstrates that nonnegative matrix factorisation is mathematically related to a class of neural networks that employ negative feedback as a mechanism of competition. This observation inspires a novel learning algorithm which we call Divisive Input Modulation (DIM). The proposed algorithm provides a mathematically simple and computationally efficient method for the unsupervised learning of image components, even in conditions where these elementary features overlap considerably. To test the proposed algorithm, a novel artificial task is introduced which is similar to the frequently-used bars problem but employs squares rather than bars to increase the degree of overlap between components. Using this task, we investigate how the proposed method performs on the parsing of artificial images composed of overlapping features, given the correct representation of the individual components; and secondly, we investigate how well it can learn the elementary components from artificial training images. We compare the performance of the proposed algorithm with its predecessors including variations on these algorithms that have produced state-of-the-art performance on the bars problem. The proposed algorithm is more successful than its predecessors in dealing with overlap and occlusion in the artificial task that has been used to assess performance

Non-negative mixtures

This is the author's accepted pre-print of the article, first published as M. D. Plumbley, A. Cichocki and R. Bro. Non-negative mixtures. In P. Comon and C. Jutten (Ed), Handbook of Blind Source Separation: Independent Component Analysis and Applications. Chapter 13, pp. 515-547. Academic Press, Feb 2010. ISBN 978-0-12-374726-6 DOI: 10.1016/B978-0-12-374726-6.00018-7file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.2