ICA and Sparse ICA for Biomedical Signals

Biomedical signs or bio signals are a wide range of signals obtained from the human body that can be at the cell organ or sub-atomic level Electromyogram refers to electrical activity from muscle sound signals electroencephalogram refers to electrical activity from the encephalon electrocardiogram refers to electrical activity from the heart electroretinogram refers to electrical activity from the eye and so on Monitoring and observing changes in these signals assist physicians whose work is related to this branch of medicine in covering predicting and curing various diseases It can also assist physicians in examining prognosticating and curing numerous condition

Score Function Features for Discriminative Learning: Matrix and Tensor Framework

Feature learning forms the cornerstone for tackling challenging learning problems in domains such as speech, computer vision and natural language processing. In this paper, we consider a novel class of matrix and tensor-valued features, which can be pre-trained using unlabeled samples. We present efficient algorithms for extracting discriminative information, given these pre-trained features and labeled samples for any related task. Our class of features are based on higher-order score functions, which capture local variations in the probability density function of the input. We establish a theoretical framework to characterize the nature of discriminative information that can be extracted from score-function features, when used in conjunction with labeled samples. We employ efficient spectral decomposition algorithms (on matrices and tensors) for extracting discriminative components. The advantage of employing tensor-valued features is that we can extract richer discriminative information in the form of an overcomplete representations. Thus, we present a novel framework for employing generative models of the input for discriminative learning.Comment: 29 page

Sparse Linear Identifiable Multivariate Modeling

In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, and model comparison. It consists of a fully Bayesian hierarchy for sparse models using slab and spike priors (two-component delta-function and continuous mixtures), non-Gaussian latent factors and a stochastic search over the ordering of the variables. The framework, which we call SLIM (Sparse Linear Identifiable Multivariate modeling), is validated and bench-marked on artificial and real biological data sets. SLIM is closest in spirit to LiNGAM (Shimizu et al., 2006), but differs substantially in inference, Bayesian network structure learning and model comparison. Experimentally, SLIM performs equally well or better than LiNGAM with comparable computational complexity. We attribute this mainly to the stochastic search strategy used, and to parsimony (sparsity and identifiability), which is an explicit part of the model. We propose two extensions to the basic i.i.d. linear framework: non-linear dependence on observed variables, called SNIM (Sparse Non-linear Identifiable Multivariate modeling) and allowing for correlations between latent variables, called CSLIM (Correlated SLIM), for the temporal and/or spatial data. The source code and scripts are available from http://cogsys.imm.dtu.dk/slim/.Comment: 45 pages, 17 figure

Adaptive methods for score function modeling in blind source separation

In signal processing and related fields, multichannel measurements are often encountered. Depending on the application, for instance, multiple antennas, multiple microphones or multiple biomedical sensors are used for the data acquisition. Such systems can be described using Multiple-Input Multiple-Output (MIMO) system models. In many cases, several source signals are present at the same time and there is only limited knowledge of their properties and how they contribute to each sensor output. If the source signals and the physical system are unknown and only the sensor outputs are observed, the processing methods developed for recovering the original signals are called blind. In Blind Source Separation (BSS) the goal is to recover the source signals from the observed mixed signals (mixtures). Blindness means that neither the sources nor the mixing system is known. Separation can be based on the theoretically limiting but practically feasible assumption that the sources are statistically independent. This assumption connects BSS and Independent Component Analysis (ICA). The usage of mutual information as a measure of independence leads to iterative estimation of the score functions of the mixtures. The purpose of this thesis is to develop BSS methods that can adapt to different source distributions. Adaptation makes it possible to separate sources without knowing the source distributions or even the characteristics of source distributions. Special attention is paid to methods that allow also asymmetric source distributions. Asymmetric distributions occur in important applications such as communications and biomedical signal processing. Adaptive techniques are proposed for the modeling of score functions or estimating functions. Three approaches based on the Pearson system, the Extended Generalized Lambda Distribution (EGLD) and adaptively combined fixed estimating functions are proposed. The Pearson system and the EGLD are parametric families of distributions and they are used to model the distributions of the mixtures. The strength of these parametric families is that they contain a wide class of distributions, including asymmetric distributions with positive and negative kurtosis, while the estimation of the parameters is still a relatively simple procedure. The methods may be implemented using existing ICA algorithms. The reliable performance of the proposed methods is demonstrated in extensive simulations. In addition to symmetric source distributions, asymmetric distributions, such as Rayleigh and lognormal distribution, are utilized in simulations. The score adaptive methods outperform commonly used methods due to their ability to adapt to asymmetric distributions.reviewe

Robust variational Bayesian clustering for underdetermined speech separation

The main focus of this thesis is the enhancement of the statistical framework employed for underdetermined T-F masking blind separation of speech. While humans are capable of extracting a speech signal of interest in the presence of other interference and noise; actual speech recognition systems and hearing aids cannot match this psychoacoustic ability. They perform well in noise and reverberant free environments but suffer in realistic environments. Time-frequency masking algorithms based on computational auditory scene analysis attempt to separate multiple sound sources from only two reverberant stereo mixtures. They essentially rely on the sparsity that binaural cues exhibit in the time-frequency domain to generate masks which extract individual sources from their corresponding spectrogram points to solve the problem of underdetermined convolutive speech separation. Statistically, this can be interpreted as a classical clustering problem. Due to analytical simplicity, a finite mixture of Gaussian distributions is commonly used in T-F masking algorithms for modelling interaural cues. Such a model is however sensitive to outliers, therefore, a robust probabilistic model based on the Student's t-distribution is first proposed to improve the robustness of the statistical framework. This heavy tailed distribution, as compared to the Gaussian distribution, can potentially better capture outlier values and thereby lead to more accurate probabilistic masks for source separation. This non-Gaussian approach is applied to the state-of the-art MESSL algorithm and comparative studies are undertaken to confirm the improved separation quality. A Bayesian clustering framework that can better model uncertainties in reverberant environments is then exploited to replace the conventional expectation-maximization (EM) algorithm within a maximum likelihood estimation (MLE) framework. A variational Bayesian (VB) approach is then applied to the MESSL algorithm to cluster interaural phase differences thereby avoiding the drawbacks of MLE; specifically the probable presence of singularities and experimental results confirm an improvement in the separation performance. Finally, the joint modelling of the interaural phase and level differences and the integration of their non-Gaussian modelling within a variational Bayesian framework, is proposed. This approach combines the advantages of the robust estimation provided by the Student's t-distribution and the robust clustering inherent in the Bayesian approach. In other words, this general framework avoids the difficulties associated with MLE and makes use of the heavy tailed Student's t-distribution to improve the estimation of the soft probabilistic masks at various reverberation times particularly for sources in close proximity. Through an extensive set of simulation studies which compares the proposed approach with other T-F masking algorithms under different scenarios, a significant improvement in terms of objective and subjective performance measures is achieved