Related papers: Functional Data Analysis by Matrix Completion
Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected with measurement errors on discretized grids. In order to accurately smooth noisy functional…
Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
Most high-dimensional matrix recovery problems are studied under the assumption that the target matrix has certain intrinsic structures. For image data related matrix recovery problems, approximate low-rankness and smoothness are the two…
Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by…
Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role…
Constructing generative models for functional observations is an important task in statistical functional analysis. In general, functional data contains both phase (or x or horizontal) and amplitude (or y or vertical) variability. Tradi-…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression…
Smoothing of noisy sample covariances is an important component in functional data analysis. We propose a novel covariance smoothing method based on penalized splines and associated software. The proposed method is a bivariate spline…
Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or…
This paper proposes a new factor rotation for the context of functional principal components analysis. This rotation seeks to re-represent a functional subspace in terms of directions of decreasing smoothness as represented by a generalized…
We introduce Adaptive Functional Principal Component Analysis, a novel method to capture directions of variation in functional data that exhibit sharp changes in smoothness. We first propose a new adaptive scatterplot smoothing technique…
In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…
We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…
Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well in…
We introduce a novel framework for an approxi- mate recovery of data matrices which are low-rank on graphs, from sampled measurements. The rows and columns of such matrices belong to the span of the first few eigenvectors of the graphs…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
This paper focuses on the analysis of spatially correlated functional data. The between-curve correlation is modeled by correlating functional principal component scores of the functional data. We propose a Spatial Principal Analysis by…
In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to…
When considering functional principal component analysis for sparsely observed longitudinal data that take values on a nonlinear manifold, a major challenge is how to handle the sparse and irregular observations that are commonly…