Related papers: Robust Principal Component Analysis: A Constructio…
Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank…
Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the…
This work proposes a causal and recursive algorithm for solving the "robust" principal components' analysis (PCA) problem. We primarily focus on robustness to correlated outliers. In recent work, we proposed a new way to look at this…
Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called…
In this paper we analyze different ways of performing principal component analysis throughout three different approaches: robust covariance and correlation matrix estimation, projection pursuit approach and non-parametric maximum entropy…
Principal component analysis (PCA) is known to be sensitive to outliers, so that various robust PCA variants were proposed in the literature. A recent model, called REAPER, aims to find the principal components by solving a convex…
Robust principal component analysis seeks to recover a low-rank matrix from fully observed data with sparse corruptions. A scalable approach fits a low-rank factorization by minimizing the sum of entrywise absolute residuals, leading to a…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
Many machine learning systems are vulnerable to small perturbations made to inputs either at test time or at training time. This has received much recent interest on the empirical front due to applications where reliability and security are…
Privacy-preserving data mining has become an important topic. People have built several multi-party-computation (MPC)-based frameworks to provide theoretically guaranteed privacy, the poor performance of real-world algorithms have always…
Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…
We consider principal component analysis for contaminated data-set in the high dimensional regime, where the dimensionality of each observation is comparable or even more than the number of observations. We propose a deterministic…
Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…
Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…
In this paper, we propose a novel robust Principal Component Analysis (PCA) for high-dimensional data in the presence of various heterogeneities, especially the heavy-tailedness and outliers. A transformation motivated by the characteristic…
We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables…
Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…
Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…
Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…