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

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that higher-order tensors (i.e., multiway arrays) enable such a fundamental paradigm shift towards models that are essentially polynomial and whose uniqueness, unlike the matrix methods, is guaranteed under verymild and natural conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical backbone, data analysis techniques using tensor decompositions are shown to have great flexibility in the choice of constraints that match data properties, and to find more general latent components in the data than matrix-based methods. A comprehensive introduction to tensor decompositions is provided from a signal processing perspective, starting from the algebraic foundations, via basic Canonical Polyadic and Tucker models, through to advanced cause-effect and multi-view data analysis schemes. We show that tensor decompositions enable natural generalizations of some commonly used signal processing paradigms, such as canonical correlation and subspace techniques, signal separation, linear regression, feature extraction and classification. We also cover computational aspects, and point out how ideas from compressed sensing and scientific computing may be used for addressing the otherwise unmanageable storage and manipulation problems associated with big datasets. The concepts are supported by illustrative real world case studies illuminating the benefits of the tensor framework, as efficient and promising tools for modern signal processing, data analysis and machine learning applications; these benefits also extend to vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker decomposition, HOSVD, tensor networks, Tensor Train

Surfactant-induced migration of a spherical drop in Stokes flow

In Stokes flows, symmetry considerations dictate that a neutrally-buoyant spherical particle will not migrate laterally with respect to the local flow direction. We show that a loss of symmetry due to flow-induced surfactant redistribution leads to cross-stream drift of a spherical drop in Poiseuille flow. We derive analytical expressions for the migration velocity in the limit of small non-uniformities in the surfactant distribution, corresponding to weak-flow conditions or a high-viscosity drop. The analysis predicts that the direction of migration is always towards the flow centerline.Comment: Significant extension with additional text, figures, equations, et

An analysis of the far-field response to external forcing of a suspension in Stokes flow in a parallel-wall channel

The leading-order far-field scattered flow produced by a particle in a parallel-wall channel under creeping flow conditions has a form of the parabolic velocity field driven by a 2D dipolar pressure distribution. We show that in a system of hydrodynamically interacting particles, the pressure dipoles contribute to the macroscopic suspension flow in a similar way as the induced electric dipoles contribute to the electrostatic displacement field. Using this result we derive macroscopic equations governing suspension transport under the action of a lateral force, a lateral torque or a macroscopic pressure gradient in the channel. The matrix of linear transport coefficients in the constitutive relations linking the external forcing to the particle and fluid fluxes satisfies the Onsager reciprocal relation. The transport coefficients are evaluated for square and hexagonal periodic arrays of fixed and freely suspended particles, and a simple approximation in a Clausius-Mossotti form is proposed for the channel permeability coefficient. We also find explicit expressions for evaluating the periodic Green's functions for Stokes flow between two parallel walls.Comment: 23 pages, 12 figure

Least Dependent Component Analysis Based on Mutual Information

We propose to use precise estimators of mutual information (MI) to find least dependent components in a linearly mixed signal. On the one hand this seems to lead to better blind source separation than with any other presently available algorithm. On the other hand it has the advantage, compared to other implementations of `independent' component analysis (ICA) some of which are based on crude approximations for MI, that the numerical values of the MI can be used for: (i) estimating residual dependencies between the output components; (ii) estimating the reliability of the output, by comparing the pairwise MIs with those of re-mixed components; (iii) clustering the output according to the residual interdependencies. For the MI estimator we use a recently proposed k-nearest neighbor based algorithm. For time sequences we combine this with delay embedding, in order to take into account non-trivial time correlations. After several tests with artificial data, we apply the resulting MILCA (Mutual Information based Least dependent Component Analysis) algorithm to a real-world dataset, the ECG of a pregnant woman. The software implementation of the MILCA algorithm is freely available at http://www.fz-juelich.de/nic/cs/softwareComment: 18 pages, 20 figures, Phys. Rev. E (in press

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Speech Denoising Using Non-Negative Matrix Factorization with Kullback-Leibler Divergence and Sparseness Constraints

Proceedings of: IberSPEECH 2012 Conference, Madrid, Spain, November 21-23, 2012.A speech denoising method based on Non-Negative Matrix Factorization (NMF) is presented in this paper. With respect to previous related works, this paper makes two contributions. First, our method does not assume a priori knowledge about the nature of the noise. Second, it combines the use of the Kullback-Leibler divergence with sparseness constraints on the activation matrix, improving the performance of similar techniques that minimize the Euclidean distance and/or do not consider any sparsification. We evaluate the proposed method for both, speech enhancement and automatic speech recognitions tasks, and compare it to conventional spectral subtraction, showing improvements in speech quality and recognition accuracy, respectively, for different noisy conditions.This work has been partially supported by the Spanish Government grants TSI-020110-2009-103 and TEC2011-26807.Publicad

Pushmepullyou: An efficient micro-swimmer

The swimming of a pair of spherical bladders that change their volumes and mutual distance is efficient at low Reynolds numbers and is superior to other models of artificial swimmers. The change of shape resembles the wriggling motion known as {\it metaboly} of certain protozoa.Comment: Minor rephrasing and changes in style; short explanations adde