Related papers: Provable Dynamic Robust PCA or Robust Subspace Tra…
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…
Due to its efficiency and stability, Robust Principal Component Analysis (RPCA) has been emerging as a promising tool for moving object detection. Unfortunately, existing RPCA based methods assume static or quasi-static background, and…
We study the problem of subspace tracking in the presence of missing data (ST-miss). In recent work, we studied a related problem called robust ST. In this work, we show that a simple modification of our robust ST solution also provably…
For many modern applications in science and engineering, data are collected in a streaming fashion carrying time-varying information, and practitioners need to process them with a limited amount of memory and computational resources in a…
This paper presents a novel robust predictive controller for constrained nonlinear systems that is able to track piece-wise constant setpoint signals. The tracking model predictive controller presented in this paper extends the nonlinear…
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…
We study the tensor robust principal component analysis (TRPCA) problem, a tensorial extension of matrix robust principal component analysis (RPCA), that aims to split the given tensor into an underlying low-rank component and a sparse…
Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…
Data Enabled Predictive Control (DeePC) is an established model free approach to predictive control, but it faces two open challenges: computational complexity that scales cubically with dataset size and performance degradation when data…
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…
We explore the connection between outlier-robust high-dimensional statistics and non-convex optimization in the presence of sparsity constraints, with a focus on the fundamental tasks of robust sparse mean estimation and robust sparse PCA.…
Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data popularized as Robust PCA (Candes et al., 2011; Chandrasekaran et al., 2009). Compressed sensing,…
Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…
Model Predictive Control (MPC) is a powerful control strategy; however, its reliance on online optimization poses significant challenges for implementation on systems with limited computational resources. One possible approach to address…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…
Foreground detection in a given video sequence is a pivotal step in many computer vision applications such as video surveillance system. Robust Principal Component Analysis (RPCA) performs low-rank and sparse decomposition and accomplishes…
Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…
Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its…
Principal component analysis (PCA) is a well-established method commonly used to explore and visualise data. A classical PCA model is the fixed effect model where data are generated as a fixed structure of low rank corrupted by noise. Under…