Bayesian source separation with mixture of Gaussians prior for sources and Gaussian prior for mixture coefficients

In this contribution, we present new algorithms to source separation for the case of noisy instantaneous linear mixture, within the Bayesian statistical framework. The source distribution prior is modeled by a mixture of Gaussians [Moulines97] and the mixing matrix elements distributions by a Gaussian [Djafari99a]. We model the mixture of Gaussians hierarchically by mean of hidden variables representing the labels of the mixture. Then, we consider the joint a posteriori distribution of sources, mixing matrix elements, labels of the mixture and other parameters of the mixture with appropriate prior probability laws to eliminate degeneracy of the likelihood function of variance parameters and we propose two iterative algorithms to estimate jointly sources, mixing matrix and hyperparameters: Joint MAP (Maximum a posteriori) algorithm and penalized EM algorithm. The illustrative example is taken in [Macchi99] to compare with other algorithms proposed in literature. Keywords: Source separation, Gaussian mixture, classification, JMAP algorithm, Penalized EM algorithm.Comment: Presented at MaxEnt00. Appeared in Bayesian Inference and Maximum Entropy Methods, Ali Mohammad-Djafari(Ed.), AIP Proceedings (http://proceedings.aip.org/proceedings/confproceed/568.jsp

MCMC joint separation and segmentation of hidden Markov fields

In this contribution, we consider the problem of the blind separation of noisy instantaneously mixed images. The images are modelized by hidden Markov fields with unknown parameters. Given the observed images, we give a Bayesian formulation and we propose to solve the resulting data augmentation problem by implementing a Monte Carlo Markov Chain (MCMC) procedure. We separate the unknown variables into two categories: 1. The parameters of interest which are the mixing matrix, the noise covariance and the parameters of the sources distributions. 2. The hidden variables which are the unobserved sources and the unobserved pixels classification labels. The proposed algorithm provides in the stationary regime samples drawn from the posterior distributions of all the variables involved in the problem leading to a flexibility in the cost function choice. We discuss and characterize some problems of non identifiability and degeneracies of the parameters likelihood and the behavior of the MCMC algorithm in this case. Finally, we show the results for both synthetic and real data to illustrate the feasibility of the proposed solution. keywords: MCMC, blind source separation, hidden Markov fields, segmentation, Bayesian approachComment: Presented at NNSP2002, IEEE workshop Neural Networks for Signal Processing XII, Sept. 2002, pp. 485--49

Penalized maximum likelihood for multivariate Gaussian mixture

In this paper, we first consider the parameter estimation of a multivariate random process distribution using multivariate Gaussian mixture law. The labels of the mixture are allowed to have a general probability law which gives the possibility to modelize a temporal structure of the process under study. We generalize the case of univariate Gaussian mixture in [Ridolfi99] to show that the likelihood is unbounded and goes to infinity when one of the covariance matrices approaches the boundary of singularity of the non negative definite matrices set. We characterize the parameter set of these singularities. As a solution to this degeneracy problem, we show that the penalization of the likelihood by an Inverse Wishart prior on covariance matrices results to a penalized or maximum a posteriori criterion which is bounded. Then, the existence of positive definite matrices optimizing this criterion can be guaranteed. We also show that with a modified EM procedure or with a Bayesian sampling scheme, we can constrain covariance matrices to belong to a particular subclass of covariance matrices. Finally, we study degeneracies in the source separation problem where the characterization of parameter singularity set is more complex. We show, however, that Inverse Wishart prior on covariance matrices eliminates the degeneracies in this case too.Comment: Presented at MaxEnt01. To appear in Bayesian Inference and Maximum Entropy Methods, B. Fry (Ed.), AIP Proceedings. 11pages, 3 Postscript figure

FABLE : Fabric Anomaly Detection Automation Process

Unsupervised anomaly in industry has been a concerning topic and a stepping stone for high performance industrial automation process. The vast majority of industry-oriented methods focus on learning from good samples to detect anomaly notwithstanding some specific industrial scenario requiring even less specific training and therefore a generalization for anomaly detection. The obvious use case is the fabric anomaly detection, where we have to deal with a really wide range of colors and types of textile and a stoppage of the production line for training could not be considered. In this paper, we propose an automation process for industrial fabric texture defect detection with a specificity-learning process during the domain-generalized anomaly detection. Combining the ability to generalize and the learning process offer a fast and precise anomaly detection and segmentation. The main contributions of this paper are the following: A domain-generalization texture anomaly detection method achieving the state-of-the-art performances, a fast specific training on good samples extracted by the proposed method, a self-evaluation method based on custom defect creation and an automatic detection of already seen fabric to prevent re-training.Comment: 7th International Conference on Control, Automation and Diagnosis (ICCAD'23), 6 page

Localization in sensor networks - a matrix regression approach

In this paper, we propose a new approach to sensor localization problems, based on recent developments in machine leaning. The main idea behind it is to consider a matrix regression method between the ranging matrix and the matrix of inner products between positions of sensors, in order to complete the latter. Once we have learnt this regression from information between sensors of known positions (beacons), we apply it to sensors of unknown positions. Retrieving the estimated positions of the latter can be done by solving a linear system. We propose a distributed algorithm, where each sensor positions itself with information available from its nearby beacons. The proposed method is validated by experimentations. 1

On the detection of elderly equilibrium degradation using multivariate-EMD

International audienceThe aim of this paper is to provide a new methodology for the detection of an increased risk of falling in community-dwelling elderly. A new extended method of the empirical mode decomposition (EMD) called multivariate-EMD is employed in the proposed solution. This method will be mainly used to analyze the stabilogram center of pressure (COP) time series. In this paper, we describe also the remote non-invasive assessment method, which is suitable for static and dynamic balance. Balance was assessed using a miniature force plate, while gait was assessed using wireless sensors placed in a corridor of the home. The experimental results show the effectiveness of this indicator to identify the differences in standing posture between different groups of population

Univariate and bivariate empirical mode decomposition for postural stability analysis

The aim of this paper was to compare empirical mode decomposition (EMD) and two new extended methods of Open image in new windowEMD named complex empirical mode decomposition (complex-EMD) and bivariate empirical mode decomposition (bivariate-EMD). All methods were used to analyze stabilogram center of pressure (COP) time series. The two new methods are suitable to be applied to complex time series to extract complex intrinsic mode functions (IMFs) before the Hilbert transform is subsequently applied on the IMFs. The trace of the analytic IMF in the complex plane has a circular form, with each IMF having its own rotation frequency. The area of the circle and the average rotation frequency of IMFs represent efficient indicators of the postural stability status of subjects. Experimental results show the effectiveness of these indicators to identify differences in standing posture between groups