Related papers: Independent component analysis for multivariate fu…
Dimension reduction is crucial in functional data analysis (FDA). The key tool to reduce the dimension of the data is functional principal component analysis. Existing approaches for functional principal component analysis usually involve…
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is…
The independent component model is a latent variable model where the components of the observed random vector are linear combinations of latent independent variables. The aim is to find an estimate for a transformation matrix back to…
Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal…
The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not…
Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in…
Traditional Functional Principal Component Analysis typically focuses on densely observed univariate functional data, yet many applications, particularly in longitudinal studies, involve multivariate functional data observed sparsely and…
Multivariate functional principal component analysis (MFPCA) is a powerful dimension reduction technique for analyzing multiple functional variables simultaneously. However, existing MFPCA methods assume that all functional observations are…
Many fMRI analyses examine functional connectivity, or statistical dependencies among remote brain regions. Yet popular methods for studying whole-brain functional connectivity often yield results that are difficult to interpret. Factor…
In preprocessing tensor-valued data, e.g. images and videos, a common procedure is to vectorize the observations and subject the resulting vectors to one of the many methods used for independent component analysis (ICA). However, the tensor…
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…
We develop a theory for functional independent component analysis in an infinite-dimensional framework using Sobolev spaces that accommodate smoother functions. The notion of penalized kurtosis is introduced motivated by Silverman's method…
Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…
Independent component analysis is a standard tool in modern data analysis and numerous different techniques for applying it exist. The standard methods however quickly lose their effectiveness when the data are made up of structures of…
Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof.…
The power of multivariate functions is their ability to model a wide variety of phenomena, but have the disadvantages that they lack an intuitive or interpretable representation, and often require a (very) large number of parameters. We…
This paper introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating and testing the existence of mutually independent components for a given dataset, and a…
Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. In this paper we present Multiple-weighted Independent Component Analysis…
Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on…
In this article, we introduce the mean independent component analysis for multivariate time series to reduce the parameter space. In particular, we seek for a contemporaneous linear transformation that detects univariate mean independent…