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Many applications in data analysis rely on the decomposition of a data matrix into a low-rank and a sparse component. Existing methods that tackle this task use the nuclear norm and L1-cost functions as convex relaxations of the rank…

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…

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

Most of machine learning deals with vector parameters. Ideally we would like to take higher order information into account and make use of matrix or even tensor parameters. However the resulting algorithms are usually inefficient. Here we…

Kernel Principal Component Analysis (KPCA) is a popular dimensionality reduction technique with a wide range of applications. However, it suffers from the problem of poor scalability. Various approximation methods have been proposed in the…

We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…

This paper presents a remarkably simple, yet powerful, algorithm termed Coherence Pursuit (CoP) to robust Principal Component Analysis (PCA). As inliers lie in a low dimensional subspace and are mostly correlated, an inlier is likely to…

Robust principal component analysis (RPCA) has been widely used for recovering low-rank matrices in many data mining and machine learning problems. It separates a data matrix into a low-rank part and a sparse part. The convex approach has…

The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…

Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from…

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…

Robust Principal Component Analysis (PCA) has received massive attention in recent years. It aims to recover a low-rank matrix and a sparse matrix from their sum. This paper proposes a novel nonconvex Robust PCA algorithm, coined Riemannian…

Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…

Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…

Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose a novel non-convex algorithm, coined Iterated Robust CUR (IRCUR), for solving RPCA problems, which dramatically improves the…

Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning,…

Recent research on problem formulations based on decomposition into low-rank plus sparse matrices shows a suitable framework to separate moving objects from the background. The most representative problem formulation is the Robust Principal…

Probabilistic Component Latent Analysis (PLCA) is a statistical modeling method for feature extraction from non-negative data. It has been fruitfully applied to various research fields of information retrieval. However, the EM-solved…