Jacobi iterations for canonical dependence analysis

International audienceIn this manuscript we will study the advantages of Jacobi iterations to solve the problem of Canonical Dependence Analysis. Canonical Dependence Analysis can be seen as an extension of the Canonical Correlation Analysis where correlation measures are replaced by measures of higher order statistical dependencies. We will show the benefits of choosing an algorithm that exploits the manifold structure on which the optimisation problem can be formulated and contrast our results with the joint blind source separation algorithm that optimises the criterion in its ambient space. A major advantage of the proposed algorithm is the capability of identifying a linear mixture when multiple observation sets are available containing variables that are linearly dependent between the sets, independent within the sets and contaminated with non-Gaussian independent noise. Performance analysis reveals at least linear convergence speed as a function of the number of sweeps

Extraction of the atrial activity from the ECG based on independent component analysis with prior knowledge of the source kurtosis signs

In this work it will be shown that a contrast for independent component analysis based on prior knowledge of the source kurtosis signs (ica-sks) is able to extract atrial activity from the electrocardiogram when a constrained updating is introduced. A spectral concentration measure is used, only allowing signal pair updates when spectral concentration augments. This strategy proves to be valid for independent source extraction with priors on the spectral concentration. Moreover, the method is computationally attractive with a very low complexity compared to the recently proposed methods based on spatiotemporal extraction of the atrial fibrillation signal

Atrial signal extraction in atrial fibrillation ECGs exploiting spatial constraints

International audienceThe accuracy in the extraction of the atrial activity (AA) from electrocardiogram (ECG) signals recorded during atrial fibrillation (AF) episodes plays an important role in the analysis and characterization of atrial arrhhythmias. The present contribution puts forward a new method for AA signal automatic extraction based on a blind source separation (BSS) formulation that exploits spatial information about the AA during the T-Q segments. This prior knowledge is used to optimize the spectral content of the AA signal estimated by BSS on the full ECG recording. The comparative performance of the method is evaluated on real data recorded from AF sufferers. The AA extraction quality of the proposed technique is comparable to that of previous algorithms, but is achieved at a reduced cost and without manual selection of parameters

A Fixed-Point Algorithm for Estimating Power Means of Positive Definite Matrices

International audienceThe estimation of means of data points lying on the Riemannian manifold of symmetric positive-definite (SPD) matrices is of great utility in classification problems and is currently heavily studied. The power means of SPD matrices with exponent p in the interval [-1, 1] interpolate in between the Harmonic (p =-1) and the Arithmetic mean (p = 1), while the Geometric (Karcher) mean corresponds to their limit evaluated at 0. In this article we present a simple fixed point algorithm for estimating means along this whole continuum. The convergence rate of the proposed algorithm for p = ±0.5 deteriorates very little with the number and dimension of points given as input. Along the whole continuum it is also robust with respect to the dispersion of the points on the manifold. Thus, the proposed algorithm allows the efficient estimation of the whole family of power means, including the geometric mean

Less is More -- Towards parsimonious multi-task models using structured sparsity

Model sparsification in deep learning promotes simpler, more interpretable models with fewer parameters. This not only reduces the model's memory footprint and computational needs but also shortens inference time. This work focuses on creating sparse models optimized for multiple tasks with fewer parameters. These parsimonious models also possess the potential to match or outperform dense models in terms of performance. In this work, we introduce channel-wise l1/l2 group sparsity in the shared convolutional layers parameters (or weights) of the multi-task learning model. This approach facilitates the removal of extraneous groups i.e., channels (due to l1 regularization) and also imposes a penalty on the weights, further enhancing the learning efficiency for all tasks (due to l2 regularization). We analyzed the results of group sparsity in both single-task and multi-task settings on two widely-used Multi-Task Learning (MTL) datasets: NYU-v2 and CelebAMask-HQ. On both datasets, which consist of three different computer vision tasks each, multi-task models with approximately 70% sparsity outperform their dense equivalents. We also investigate how changing the degree of sparsification influences the model's performance, the overall sparsity percentage, the patterns of sparsity, and the inference time.Comment: Under revie

Removing Ocular Movement Artefacts by a Joint Smoothened Subspace Estimator

To cope with the severe masking of background cerebral activity in the electroencephalogram (EEG) by ocular movement artefacts, we present a method which combines lower-order, short-term and higher-order, long-term statistics. The joint smoothened subspace estimator (JSSE) calculates the joint information in both statistical models, subject to the constraint that the resulting estimated source should be sufficiently smooth in the time domain (i.e., has a large autocorrelation or self predictive power). It is shown that the JSSE is able to estimate a component from simulated data that is superior with respect to methodological artefact suppression to those of FastICA, SOBI, pSVD, or JADE/COM1 algorithms used for blind source separation (BSS). Interference and distortion suppression are of comparable order when compared with the above-mentioned methods. Results on patient data demonstrate that the method is able to suppress blinking and saccade artefacts in a fully automated way

Blind hyperspectral unmixing using an Extended Linear Mixing Model to address spectral variability

International audienceSpectral Unmixing is one of the main research topics in hyperspectral imaging. It can be formulated as a source separation problem whose goal is to recover the spectral signatures of the materials present in the observed scene (called endmembers) as well as their relative proportions (called fractional abundances), and this for every pixel in the image. A Linear Mixture Model is often used for its simplicity and ease of use but it implicitly assumes that a single spectrum can be completely representative of a material. However, in many scenarios, this assumption does not hold since many factors, such as illumination conditions and intrinsic variability of the endmembers, induce modifications on the spectral signatures of the materials. In this paper, we propose an algorithm to unmix hyperspectral data using a recently proposed Extended Linear Mixing Model. The proposed approach allows a pixelwise spatially coherent local variation of the endmembers, leading to scaled versions of reference endmembers. We also show that the classic nonnegative least squares, as well as other approaches to tackle spectral variability can be interpreted in the framework of this model. The results of the proposed algorithm on two different synthetic datasets, including one simulating the effect of topography on the measured reflectance through physical modelling, and on two real datasets, show that the proposed technique outperforms other methods aimed at addressing spectral variability, and can provide an accurate estimation of endmember variability along the scene thanks to the scaling factors estimation