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Robust PCA methods are typically batch algorithms which requires loading all observations into memory before processing. This makes them inefficient to process big data. In this paper, we develop an efficient online robust principal…
In recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from their sum, $\mathbf{M}:= \mathbf{L} + \mathbf{S}$ and a provably exact…
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…
Particle Image Velocimetry (PIV) data processing procedures are adversely affected by light reflections and backgrounds as well as defects in the models and sticky particles that occlude the inner walls of the boundaries. In this paper, a…
This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…
Principal component analysis (PCA) has been widely used in analyzing high-dimensional data. It converts a set of observed data points of possibly correlated variables into a set of linearly uncorrelated variables via an orthogonal…
In this paper, we study the problem of sparse Principal Component Analysis (PCA) in the high-dimensional setting with missing observations. Our goal is to estimate the first principal component when we only have access to partial…
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…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Finding informative low-dimensional representations that can be computed efficiently in large datasets is an important problem in data analysis. Recently, contrastive Principal Component Analysis (cPCA) was proposed as a more informative…
In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…
Deep unfolded neural networks are designed by unrolling the iterations of optimization algorithms. They can be shown to achieve faster convergence and higher accuracy than their optimization counterparts. This paper proposes a new…
A basic algorithmic task in automated video surveillance is to separate background and foreground objects. Camera tampering, noisy videos, low frame rate, etc., pose difficulties in solving the problem. A general approach that classifies…
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…
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…
In this paper, we propose a non-convex formulation to recover the authentic structure from the corrupted real data. Typically, the specific structure is assumed to be low rank, which holds for a wide range of data, such as images and…
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…
Principal Component Analysis (PCA)-based techniques can separate data into different uncorrelated components and facilitate the statistical analysis as a pre-processing step. Independent Component Analysis (ICA) can separate statistically…
We introduce the notion of Principal Component Analysis (PCA) of image gradient orientations. As image data is typically noisy, but noise is substantially different from Gaussian, traditional PCA of pixel intensities very often fails to…