Related papers: Distributed Estimation for Principal Component Ana…

Recently, distributed algorithms for power system state estimation have attracted significant attention. Along with such advantages as decomposition, parallelization of the original problem and absence of a central computation unit,…

The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…

As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine…

We present a novel view on principal component analysis (PCA) as a competitive game in which each approximate eigenvector is controlled by a player whose goal is to maximize their own utility function. We analyze the properties of this PCA…

We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables…

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…

This paper proposes an innovative extension of Principal Component Analysis (PCA) that transcends the traditional assumption of data lying in Euclidean space, enabling its application to data on Riemannian manifolds. The primary challenge…

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…

We study distributed estimation and learning problems in a networked environment where agents exchange information to estimate unknown statistical properties of random variables from their privately observed samples. The agents can…

Nowadays, more and more datasets are stored in a distributed way for the sake of memory storage or data privacy. The generalized eigenvalue problem (GEP) plays a vital role in a large family of high-dimensional statistical models. However,…

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,…

This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and…

Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by…

We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors…

In recent work, we proposed a distributed Banach-Picard iteration (DBPI) that allows a set of agents, linked by a communication network, to find a fixed point of a locally contractive (LC) map that is the average of individual maps held by…

Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…

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…

Massive data analysis calls for distributed algorithms and theories. We design a multi-round distributed algorithm for canonical correlation analysis. We construct principal directions through the convex formulation of canonical correlation…

This article studies the robustness of the eigenvalue ordering, an important issue when estimating the leading eigen-subspace by principal component analysis (PCA). In Yata and Aoshima (2010), cross-data-matrix PCA (CDM-PCA) was proposed…

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…