Related papers: History PCA: A New Algorithm for Streaming PCA

Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests.…

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

We present a federated, asynchronous, and $(\varepsilon, \delta)$-differentially private algorithm for PCA in the memory-limited setting. Our algorithm incrementally computes local model updates using a streaming procedure and adaptively…

We propose a novel statistical inference framework for streaming principal component analysis (PCA) using Oja's algorithm, enabling the construction of confidence intervals for individual entries of the estimated eigenvector. Most existing…

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…

Principal component analysis (PCA) has been widely used in analyzing high-dimensional data. It converts a set of observed data points of possibly correlated variables into a set of linearly uncorrelated variables via an orthogonal…

Oja's algorithm for Streaming Principal Component Analysis (PCA) for $n$ data-points in a $d$ dimensional space achieves the same sin-squared error $O(r_{\mathsf{eff}}/n)$ as the offline algorithm in $O(d)$ space and $O(nd)$ time and a…

We analyze Oja's algorithm for streaming $k$-PCA and prove that it achieves performance nearly matching that of an optimal offline algorithm. Given access to a sequence of i.i.d. $d \times d$ symmetric matrices, we show that Oja's algorithm…

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

Oja's rule [Oja, Journal of mathematical biology 1982] is a well-known biologically-plausible algorithm using a Hebbian-type synaptic update rule to solve streaming principal component analysis (PCA). Computational neuroscientists have…

Low-precision streaming PCA estimates the top principal component in a streaming setting under limited precision. We establish an information-theoretic lower bound on the quantization resolution required to achieve a target accuracy for the…

We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…

In this paper we analyze the behavior of the Oja's algorithm for online/streaming principal component subspace estimation. It is proved that with high probability it performs an efficient, gap-free, global convergence rate to approximate an…

Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…

Big data problems frequently require processing datasets in a streaming fashion, either because all data are available at once but collectively are larger than available memory or because the data intrinsically arrive one data point at a…

We study the statistical and computational aspects of kernel principal component analysis using random Fourier features and show that under mild assumptions, $O(\sqrt{n} \log n)$ features suffices to achieve $O(1/\epsilon^2)$ sample…

We initiate the study of graph algorithms in the streaming setting on massive distributed and parallel systems inspired by practical data processing systems. The objective is to design algorithms that can efficiently process evolving graphs…

Piecewise Linear Approximation (PLA) is a well-established tool to reduce the size of the representation of time series by approximating the series by a sequence of line segments while keeping the error introduced by the approximation…

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…

Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…