Related papers: Faster ICA under orthogonal constraint
Independent component analysis is commonly applied to functional magnetic resonance imaging (fMRI) data to extract independent components (ICs) representing functional brain networks. While ICA produces reliable group-level estimates,…
The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the…
Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…
In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to…
Isogeometric Analysis (IgA) is a spline based approach to the numerical solution of partial differential equations. There are two major issues that IgA was designed to address. The first issue is the exact representation of domains stemming…
Group studies involving large cohorts of subjects are important to draw general conclusions about brain functional organization. However, the aggregation of data coming from multiple subjects is challenging, since it requires accounting for…
Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…
Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…
Linear principal component analysis (PCA) learns (semi-)orthogonal transformations by orienting the axes to maximize variance. Consequently, it can only identify orthogonal axes whose variances are clearly distinct, but it cannot identify…
The study of the atmospheres of transiting exoplanets requires a photometric precision, and repeatability, of one part in $\sim 10^4$. This is beyond the original calibration plans of current observatories, hence the necessity to…
Unsupervised feature learning algorithms based on convolutional formulations of independent components analysis (ICA) have been demonstrated to yield state-of-the-art results in several action recognition benchmarks. However, existing…
Dimensionality reduction techniques have found great success in a wide range of fields requiring analysis of high-dimensional datasets. Time-lagged independent components analysis (TICA), which finds independent components (TICs) with…
We address the convolutive blind source separation problem for the (over-)determined case where (i) the number of nonstationary target-sources $K$ is less than that of microphones $M$, and (ii) there are up to $M - K$ stationary Gaussian…
We analyze the dynamics of an online algorithm for independent component analysis in the high-dimensional scaling limit. As the ambient dimension tends to infinity, and with proper time scaling, we show that the time-varying joint empirical…
Nonlinear independent component analysis (nICA) aims at recovering statistically independent latent components that are mixed by unknown nonlinear functions. Central to nICA is the identifiability of the latent components, which had been…
Noise subtraction is a crucial process in gravitational wave (GW) data analysis to improve the sensitivity of interferometric detectors. While linear noise coupling has been extensively studied and successfully mitigated using methods such…
Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…
Canonical Correlation Analysis (CCA) is a statistical technique used to extract common information from multiple data sources or views. It has been used in various representation learning problems, such as dimensionality reduction, word…
Independent Component Analysis (ICA) is commonly-used in electroencephalogram (EEG) signal processing to remove non-cerebral artifacts from cerebral data. Despite the ubiquity of ICA, the effect of measurement uncertainty on the artifact…
We propose an ICA contrast based on the density estimation of the observed signal and its marginals by means of wavelets. The risk of the associated moment estimator is linked with approximation properties in Besov spaces. It is shown to…