Related papers: Provable Model-Parallel Distributed Principal Comp…

We describe a Lagrange-Newton framework for the derivation of learning rules with desirable convergence properties and apply it to the case of principal component analysis (PCA). In this framework, a Newton descent is applied to an extended…

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…

Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…

A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…

We study the fairness of dimensionality reduction methods for recommendations. We focus on the fundamental method of principal component analysis (PCA), which identifies latent components and produces a low-rank approximation via the…

In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…

Oja's algorithm of principal component analysis (PCA) has been one of the methods utilized in practice to reduce dimension. In this paper, we focus on the convergence property of the discrete algorithm. To realize that, we view the…

This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal…

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…

Principal component analysis (PCA) is a key statistical technique for multivariate data analysis. For large data sets the common approach to PCA computation is based on the standard NIPALS-PCA algorithm, which unfortunately suffers from…

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…

System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…

Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…

Adaptive model predictive control (MPC) robustly ensures safety while reducing uncertainty during operation. In this paper, a distributed version is proposed to deal with network systems featuring multiple agents and limited communication.…

Of particular interest is to discover useful representations solely from observations in an unsupervised generative manner. However, the question of whether existing normalizing flows provide effective representations for downstream tasks…

We investigate convergence properties of a proposed distributed model predictive control (DMPC) scheme, where agents negotiate to compute an optimal consensus point using an incremental subgradient method based on primal decomposition as…

In this paper we propose a novel optimization framework to systematically solve robust PCA problem with rigorous theoretical guarantee, based on which we investigate very computationally economic updating algorithms.