Independent Component Analysis Scheme Research Articles

Compressive independent component analysis: theory and algorithms

Abstract Compressive learning forms the exciting intersection between compressed sensing and statistical learning where one exploits sparsity of the learning model to reduce the memory and/or computational complexity of the algorithms used to solve the learning task. In this paper, we look at the independent component analysis (ICA) model through the compressive learning lens. In particular, we show that solutions to the cumulant-based ICA model have a particular structure that induces a low-dimensional model set that resides in the cumulant tensor space. By showing that a restricted isometry property holds for random cumulants e.g. Gaussian ensembles, we prove the existence of a compressive ICA scheme. Thereafter, we propose two algorithms of the form of an iterative projection gradient and an alternating steepest descent algorithm for compressive ICA, where the order of compression asserted from the restricted isometry property is realized through empirical results. We provide analysis of the CICA algorithms including the effects of finite samples. The effects of compression are characterized by a trade-off between the sketch size and the statistical efficiency of the ICA estimates. By considering synthetic and real datasets, we show the substantial memory gains achieved over well-known ICA algorithms by using one of the proposed CICA algorithms.

Iterative spectral independent component analysis

Abstract Linear independent component analysis (ICA) is a fundamental problem in signal processing. In this work we study the Spectral ICA approach introduced by Singer that is based on the Diffusion Framework. We analyze its asymptotic optimality condition, related to the discretization error of the Graph Laplacian with respect to the continuous backward Fokker–Planck operator. Thus, we derive an iterative Diffusion Framework-based spectral ICA formulation, that is rigorously shown to reduce the discretization error of the Graph Laplacian by iteratively estimating and canceling-out ICA components. The proposed scheme is shown to compare favourably with contemporary state-of-the-art linear ICA schemes, when applied to the demixing of signals and images.

Application and Evaluation of Independent Component Analysis Methods to Generalized Seizure Disorder Activities Exhibited in the Brain

EEG records the spontaneous electrical activity of the brain using multiple electrodes placed on the scalp, and it provides a wealth of information related to the functions of brain. Nevertheless, the signals from the electrodes cannot be directly applied to a diagnostic tool like brain mapping as they undergo a "mixing" process because of the volume conduction effect in the scalp. A pervasive problem in neuroscience is determining which regions of the brain are active, given voltage measurements at the scalp. Because of which, there has been a surge of interest among the biosignal processing community to investigate the process of mixing and unmixing to identify the underlying active sources. According to the assumptions of independent component analysis (ICA) algorithms, the resultant mixture obtained from the scalp can be closely approximated by a linear combination of the "actual" EEG signals emanating from the underlying sources of electrical activity in the brain. As a consequence, using these well-known ICA techniques in preprocessing of the EEG signals prior to clinical applications could result in development of diagnostic tool like quantitative EEG which in turn can assist the neurologists to gain noninvasive access to patient-specific cortical activity, which helps in treating neuropathologies like seizure disorders. The popular and proven ICA schemes mentioned in various literature and applications were selected (which includes Infomax, JADE, and SOBI) and applied on generalized seizure disorder samples using EEGLAB toolbox in MATLAB environment to see their usefulness in source separations; and they were validated by the expert neurologist for clinical relevance in terms of pathologies on brain functionalities. The performance of Infomax method was found to be superior when compared with other ICA schemes applied on EEG and it has been established based on the validations carried by expert neurologist for generalized seizure and its clinical correlation. The results are encouraging for furthering the studies in the direction of developing useful brain mapping tools using ICA methods.

A process monitoring method based on noisy independent component analysis

Independent component analysis (ICA) is an effective feature extraction tool for process monitoring. However, the conventional ICA-based process monitoring methods usually adopt noise-free ICA models and thus may perform unsatisfactorily under the adverse effects of the measurement noise. In this paper, a process monitoring method using a new noisy independent component analysis, referred to as NoisyICAn, is proposed. Using the noisy ICA model which considers the measurement noise explicitly, a NoisyICAn algorithm is developed to estimate the mixing matrix by setting up a series of the fourth-order cumulant matrices of the measured data and performing the joint diagonalization of these matrices. The kurtosis relationships of the independent components and measured variables are subsequently obtained based on the estimated mixing matrix, for recursively estimating the kurtosis of independent components. Two monitoring statistics are then built to detect process faults using the obtained recursive estimate of the independent components' kurtosis. The simulation studies are carried out on a simple three-variable system and a continuous stirred tank reactor system, and the results obtained demonstrate that the proposed NoisyICAn-based monitoring method outperforms the conventional noise-free ICA-based monitoring methods as well as the benchmark monitoring methods based on the existing noisy ICA schemes adopted from blind source separation, in terms of the fault detection time and local fault detection rate.

TDOA Estimation for Multiple Sound Sources in Noisy and Reverberant Environments Using Broadband Independent Component Analysis

In this paper, we show that minimization of the statistical dependence using broadband independent component analysis (ICA) can be successfully exploited for acoustic source localization. As the ICA signal model inherently accounts for the presence of several sources and multiple sound propagation paths, the ICA criterion offers a theoretically more rigorous framework than conventional techniques based on an idealized single-path and single-source signal model. This leads to algorithms which outperform other localization methods, especially in the presence of multiple simultaneously active sound sources and under adverse conditions, notably in reverberant environments. Three methods are investigated to extract the time difference of arrival (TDOA) information contained in the filters of a two-channel broadband ICA scheme. While for the first, the blind system identification (BSI) approach, the number of sources should be restricted to the number of sensors, the other methods, the averaged directivity pattern (ADP) and composite mapped filter (CMF) approaches can be used even when the number of sources exceeds the number of sensors. To allow fast tracking of moving sources, the ICA algorithm operates in block-wise batch mode, with a proportionate weighting of the natural gradient to speed up the convergence of the algorithm. The TDOA estimation accuracy of the proposed schemes is assessed in highly noisy and reverberant environments for two, three, and four stationary noise sources with speech-weighted spectral envelopes as well as for moving real speech sources.

Quantized based image watermarking in an independent domain

This paper presents a performance study for two well known quantized based watermarking schemes Scalar Costa Scheme (SCS), and Trellis Coded Quantization scheme (TCQ) in an independent domain. For our study, the independent domain is obtained by the combination of the cited schemes with Independent Component Analysis (ICA). The Independent Component Analysis is used while inserting and extracting the message. Thus a performance compromise improvement of the original SCS and TCQ schemes in terms of robustness, capacity, and security is shown. Then the obtained schemes performances are compared to the Spread Transform (ST) based scheme well known for its proven good robustness properties. Our results show that, using watermarking with side information in independent domain permits to improve the global SCS and TCQ schemes performances. For example, in the case of SCS, by studying the Bit Error Rate (BER) in function of the watermark to noise ratio (WNR), the robustness has been improved by 20 dB (1 decade) when WNR is equal to 0 dB. Moreover, the capacity study shows for the same WNR=0 dB, the amount of information to be transmitted without error for a given noise level of the proposed SCS combined with ICA scheme (SCS–ICA) is much higher than that of the existing schemes. Finally, the study of the probability density functions (PDF) of the original and marked signals has shown that the Cachin-security level of the TCQ in an independent domain scheme (TCQ–ICA) is the best one compared to the other known schemes.