Related papers: Distributed Banach-Picard Iteration: Application t…

We present a methodology to automatically compute worst-case performance bounds for a large class of first-order decentralized optimization algorithms. These algorithms aim at minimizing the average of local functions that are distributed…

Traditionally, a regional dispatch center uses the equivalent method to deal with external grids, which fails to reflect the interactions among regions. This paper proposes a distributed N-1 contingency analysis (DCA) solution, where…

Missing data is a commonly occurring problem in practice. Many imputation methods have been developed to fill in the missing entries. However, not all of them can scale to high-dimensional data, especially the multiple imputation…

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal…

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

In this brief note, we formulate Principal Component Analysis (PCA) over datasets consisting not of points but of distributions, characterized by their location and covariance. Just like the usual PCA on points can be equivalently derived…

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…

This paper derives sufficient conditions for bounded distributed connectivity-preserving coordination of Euler-Lagrange systems with only position measurements and with system uncertainties, respectively. The paper proposes two strategies…

Image perceptual hashing finds applications in content indexing, large-scale image database management, certification and authentication and digital watermarking. We propose a Block-DCT and PCA based image perceptual hash in this article…

Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…

We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph. In particular, we consider the following setting: given a directed acyclic graph $G$ on $p$ vertices corresponding to variables, the…

Distributed optimization utilizes local computation and communication to realize a global aim of optimizing the sum of local objective functions. This article addresses a class of constrained distributed nonconvex optimization problems…

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

Decentralized optimization, particularly the class of decentralized composite convex optimization (DCCO) problems, has found many applications. Due to ubiquitous communication congestion and random dropouts in practice, it is highly…

Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…

This paper addresses distributed parameter estimation in randomized one-hidden-layer neural networks. A group of agents sequentially receive measurements of an unknown parameter that is only partially observable to them. In this paper, we…

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…

Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the…

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

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…