Related papers: Complex Principle Kurtosis Analysis
The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…
Background: Independent Component Analysis (ICA) is a widespread tool for exploration and denoising of electroencephalography (EEG) or magnetoencephalography (MEG) signals. In its most common formulation, ICA assumes that the signal matrix…
Tensor, also known as multi-dimensional array, arises from many applications in signal processing, manufacturing processes, healthcare, among others. As one of the most popular methods in tensor literature, Robust tensor principal component…
Nonlinear independent component analysis (ICA) aims to recover the underlying independent latent sources from their observable nonlinear mixtures. How to make the nonlinear ICA model identifiable up to certain trivial indeterminacies is a…
Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…
We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a…
Tensor robust principal component analysis (RPCA), which seeks to separate a low-rank tensor from its sparse corruptions, has been crucial in data science and machine learning where tensor structures are becoming more prevalent. While…
As tensors become widespread in modern data analysis, Tucker low-rank Principal Component Analysis (PCA) has become essential for dimensionality reduction and structural discovery in tensor datasets. Motivated by the common scenario where…
Independent Mechanism Analysis (IMA) seeks to address non-identifiability in nonlinear Independent Component Analysis (ICA) by assuming that the Jacobian of the mixing function has orthogonal columns. As typical in ICA, previous work…
Reliable measures of statistical dependence could be useful tools for learning independent features and performing tasks like source separation using Independent Component Analysis (ICA). Unfortunately, many of such measures, like 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 many daily-life scenarios, acoustic sources recorded in an enclosure can only be observed with other interfering sources. Hence, convolutive Blind Source Separation (BSS) is a central problem in audio signal processing. Methods based on…
We deal with a model where a set of observations is obtained by a linear superposition of unknown components called sources. The problem consists in recovering the sources without knowing the linear transform. We extend the well-known…
Independent component analysis (ICA) is a powerful computational tool for separating independent source signals from their linear mixtures. ICA has been widely applied in neuroimaging studies to identify and characterize underlying brain…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
Independent component analysis (ICA) is now a widely used solution for the analysis of multi-subject functional magnetic resonance imaging (fMRI) data. Independent vector analysis (IVA) generalizes ICA to multiple datasets, i.e., to…
Independent Component Analysis (ICA) aims to find a coordinate system in which the components of the data are independent. In this paper we construct a new nonlinear ICA model, called WICA, which obtains better and more stable results than…
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…
In this paper, we consider the statistical inference for several low-rank tensor models. Specifically, in the Tucker low-rank tensor PCA or regression model, provided with any estimates achieving some attainable error rate, we develop the…
Independent Component Analysis (ICA) offers interpretable semantic components of embeddings. While ICA theory assumes that embeddings can be linearly decomposed into independent components, real-world data often do not satisfy this…