Related papers: Spatial Matrix Completion for Spatially-Misaligned…
Matrix completion refers to completing a low-rank matrix from a few observed elements of its entries and has been known as one of the significant and widely-used problems in recent years. The required number of observations for exact…
Air pollution, a pressing global problem, threatens public health, environmental sustainability, and climate stability. Achieving accurate and scalable forecasting across spatially distributed monitoring stations is challenging due to…
Multivariate binary data is becoming abundant in current biological research. Logistic principal component analysis (PCA) is one of the commonly used tools to explore the relationships inside a multivariate binary data set by exploiting the…
The recently established RPCA method provides us a convenient way to restore low-rank matrices from grossly corrupted observations. While elegant in theory and powerful in reality, RPCA may be not an ultimate solution to the low-rank matrix…
In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…
Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…
Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…
We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…
We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…
The health impact of long-term exposure to air pollution is now routinely estimated using spatial ecological studies, due to the recent widespread availability of spatial referenced pollution and disease data. However, this areal unit study…
This work studies two interrelated problems - online robust PCA (RPCA) and online low-rank matrix completion (MC). In recent work by Cand\`{e}s et al., RPCA has been defined as a problem of separating a low-rank matrix (true data),…
Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly…
Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice including collaborative filtering, prior information and special structures are usually…
The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically…
Low-rank matrix completion is the task of recovering unknown entries of a matrix by assuming that the true matrix admits a good low-rank approximation. Sometimes additional information about the variables is known, and incorporating this…
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization,…
We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of…
Imputation of missing data in large regions of satellite imagery is necessary when the acquired image has been damaged by shadows due to clouds, or information gaps produced by sensor failure. The general approach for imputation of missing…