687 research outputs found
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
Non-Euclidean principal component analysis by Hebbian learning
Principal component analysis based on Hebbian learning is originally designed for data processing inEuclidean spaces. We present in this contribution an extension of Oja's Hebbian learning approach fornon-Euclidean spaces. We show that for Banach spaces the Hebbian learning can be carried out using theunderlying semi-inner product. Prominent examples for such Banach spaces are the lp-spaces for p≠2.For kernels spaces, as applied in support vector machines or kernelized vector quantization, thisapproach can be formulated as an online learning scheme based on the differentiable kernel. Hence,principal component analysis can be explicitly carried out in the respective data spaces but nowequipped with a non-Euclidean metric. In the article we provide the theoretical framework and giveillustrative examples
Modelling and Contractivity of Neural-Synaptic Networks with Hebbian Learning
This paper is concerned with the modelling and analysis of two of the most
commonly used recurrent neural network models (i.e., Hopfield neural network
and firing-rate neural network) with dynamic recurrent connections undergoing
Hebbian learning rules. To capture the synaptic sparsity of neural circuits we
propose a low dimensional formulation. We then characterize certain key
dynamical properties. First, we give biologically-inspired forward invariance
results. Then, we give sufficient conditions for the non-Euclidean
contractivity of the models. Our contraction analysis leads to stability and
robustness of time-varying trajectories -- for networks with both excitatory
and inhibitory synapses governed by both Hebbian and anti-Hebbian rules. For
each model, we propose a contractivity test based upon biologically meaningful
quantities, e.g., neural and synaptic decay rate, maximum in-degree, and the
maximum synaptic strength. Then, we show that the models satisfy Dale's
Principle. Finally, we illustrate the effectiveness of our results via a
numerical example.Comment: 24 pages, 4 figure
Neural Relax
We present an algorithm for data preprocessing of an associative memory
inspired to an electrostatic problem that turns out to have intimate relations
with information maximization
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