Related papers: Functional Data Analysis by Matrix Completion
We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial,…
In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as…
Data-fusion involves the integration of multiple related datasets. The statistical file-matching problem is a canonical data-fusion problem in multivariate analysis, where the objective is to characterise the joint distribution of a set of…
A software analysis is a computer program that takes some representation of a software product as input and produces some useful information about that product as output. A software product line encompasses \emph{many} software product…
The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, a majority of the reconstruction methods rely on estimating the covariance matrix or the components of its…
Functional data analysis on nonlinear manifolds has drawn recent interest. Sphere-valued functional data, which are encountered for example as movement trajectories on the surface of the earth, are an important special case. We consider an…
Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…
Slow feature analysis (SFA) is a method for extracting slowly varying features from a quickly varying multidimensional signal. An open source Matlab-implementation sfa-tk makes SFA easily useable. We show here that under certain…
Functional data is a powerful tool for capturing and analyzing complex patterns and relationships in a variety of fields, allowing for more precise modeling, visualization, and decision-making. For example, in healthcare, functional data…
The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One…
Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
Functional Principal Components Analysis (FPCA) provides a parsimonious, semi-parametric model for multivariate, sparsely-observed functional data. Frequentist FPCA approaches estimate principal components (PCs) from the data, then…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…
In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…
Factor analysis (FA) or principal component analysis (PCA) models the covariance matrix of the observed data as R = SS' + {\Sigma}, where SS' is the low-rank covariance matrix of the factors (aka latent variables) and {\Sigma} is the…
Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set.…
Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…