Non-negative Independent Component Analysis Algorithm Based on 2D Givens Rotations and a Newton Optimization

ISBN 978-3-642-15994-7, SoftcoverInternational audienceIn this paper, we consider the Independent Component Analysis problem when the hidden sources are non-negative (Non-negative ICA). This problem is formulated as a non-linear cost function optimization over the special orthogonal matrix group SO(n). Using Givens rotations and Newton optimization, we developed an effective axis pair rotation method for Non-negative ICA. The performance of the proposed method is compared to those designed by Plumbley and simulations on synthetic data show the efficiency of the proposed algorithm

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

An Effective Way of J Wave Separation Based on Multilayer NMF

J wave is getting more and more important in the clinical diagnosis as a new index of the electrocardiogram (ECG) of ventricular bipolar, but its signal often mixed in normal ST segment, using the traditional electrocardiograph, and diagnosed by experience cannot meet the practical requirements. Therefore, a new method of multilayer nonnegative matrix factorization (NMF) in this paper is put forward, taking the hump shape J wave, for example, which can extract the original J wave signal from the ST segment and analyze the accuracy of extraction, showing the characteristics of hump shape J wave from the aspects of frequency domain, power spectrum, and spectral type, providing the basis for clinical diagnosis and increasing the reliability of the diagnosis of J wave

Automatic Analysis of Composite Physical Signals Using Non-Negative Factorization and Information Criterion

In time-resolved spectroscopy, composite signal sequences representing energy transfer in fluorescence materials are measured, and the physical characteristics of the materials are analyzed. Each signal sequence is represented by a sum of non-negative signal components, which are expressed by model functions. For analyzing the physical characteristics of a measured signal sequence, the parameters of the model functions are estimated. Furthermore, in order to quantitatively analyze real measurement data and to reduce the risk of improper decisions, it is necessary to obtain the statistical characteristics from several sequences rather than just a single sequence. In the present paper, we propose an automatic method by which to analyze composite signals using non-negative factorization and an information criterion. The proposed method decomposes the composite signal sequences using non-negative factorization subjected to parametric base functions. The number of components (i.e., rank) is also estimated using Akaike's information criterion. Experiments using simulated and real data reveal that the proposed method automatically estimates the acceptable ranks and parameters

Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

Nowe metody analizy danych a teoria ekonomii

In this paper, we present relations between actual trends in economic research and novel methods in data analysis. As the representation of the new data analysis approach we choose the blind signal separation methods. Blind separation methods is a rapidly developed branch of data analysis. It started from some neurophysiological problem and grew to wide range analytical approaches which currently are considered in term of data separation, representation and transformation. The main techniques in this area are: independent component analysis, nonnegative matrix factorization or AMUSE and SOBI algorithms. In the second part of paper we consider knowledge discovery differences in inductive-exploration approach what is typical for blind signal separation methods and apriori-deductive approach what is typical for orthodox economy theories. Against often opposite treatments we suggest complementary interpretation. In our meaning the natural methodological choice is associated with relation data to expert knowledge about given phenomena. In the small data case we need to compensate it by some theorethical assumptions.(original abstract)W niniejszym opracowaniu przedstawiliśmy związki między współczesnymi trendami w badaniach ekonomicznych a nowymi metodami analizy danych. Jako reprezentanta nowego nurtu analizy danych wybraliśmy metody ślepej separacji. Jest to dynamicznie rozwijająca się gałąź analizy danych, która zapoczątkowana pewnymi badaniami neurofizjologicznymi, przekształciła się w szerokie spektrum podejść rozważanych w kategoriach metod separacji, reprezentacji oraz transformacji danych. Do zasadniczych technik w tym obszarze należą przede wszystkim: analiza składowych niezależnych, nieujemna faktoryzacja macierzy oraz algorytmy AMUSE oraz SOBI. W drugiej części opracowania rozważamy różnice pozyskiwania wiedzy w podejściu indukcyjno-eksploracyjnym, którego reprezentantem mogą być metody separacji, a podejściem aprioryczno-dedukcyjnym typowym dla ortodoksyjnych nurtów ekonomii. Wykazujemy, że wbrew często opozycyjnemu ich przedstawieniu są to zasadniczo podejścia komplementarne. W naszej interpretacji wybór podejścia jest związany z relacją ilości danych do wielkości wiedzy eksperckiej o zjawisku.(abstrakt oryginalny