Related papers: Cauchy Principal Component Analysis
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…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
Accurate predictions of pollutant concentrations at new locations are often of interest in air pollution studies on fine particulate matters (PM$_{2.5}$), in which data is usually not measured at all study locations. PM$_{2.5}$ is also a…
Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…
Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches…
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…
In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…
Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…
Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…
Natural scene character recognition is challenging due to the cluttered background, which is hard to separate from text. In this paper, we propose a novel method for robust scene character recognition. Specifically, we first use robust…
Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…
Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…
Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
We provide a new robust convergence analysis of the well-known power method for computing the dominant singular vectors of a matrix that we call the noisy power method. Our result characterizes the convergence behavior of the algorithm when…
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…
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…
Fair Principal Component Analysis (PCA) is a problem setting where we aim to perform PCA while making the resulting representation fair in that the projected distributions, conditional on the sensitive attributes, match one another.…