English
Related papers

Related papers: Streaming PCA for Markovian Data

200 papers

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…

Machine Learning · Statistics 2019-05-20 Davoud Ataee Tarzanagh , Mohamad Kazem Shirani Faradonbeh , George Michailidis

We study principal component analysis (PCA), where given a dataset in $\mathbb{R}^d$ from a distribution, the task is to find a unit vector $v$ that approximately maximizes the variance of the distribution after being projected along $v$.…

Machine Learning · Computer Science 2023-05-05 Ilias Diakonikolas , Daniel M. Kane , Ankit Pensia , Thanasis Pittas

Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…

Computation · Statistics 2018-01-11 Jianqing Fan , Dong Wang , Kaizheng Wang , Ziwei Zhu

In streaming PCA, we see a stream of vectors $x_1, \dotsc, x_n \in \mathbb{R}^d$ and want to estimate the top eigenvector of their covariance matrix. This is easier if the spectral ratio $R = \lambda_1 / \lambda_2$ is large. We ask: how…

Data Structures and Algorithms · Computer Science 2024-08-21 Eric Price , Zhiyang Xun

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…

Machine Learning · Computer Science 2021-11-30 Arpita Gang , Waheed U. Bajwa

Streaming principal component analysis (PCA) is an integral tool in large-scale machine learning for rapidly estimating low-dimensional subspaces from very high-dimensional data arriving at a high rate. However, modern datasets increasingly…

Signal Processing · Electrical Eng. & Systems 2025-04-09 Kyle Gilman , David Hong , Jeffrey A. Fessler , Laura Balzano

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…

Numerical Analysis · Mathematics 2023-01-05 Jian-Guo Liu , Zibu Liu

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…

Optimization and Control · Mathematics 2017-07-11 Christopher De Sa , Bryan He , Ioannis Mitliagkas , Christopher Ré , Peng Xu

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…

Optimization and Control · Mathematics 2024-03-06 Xin Liang , Zhen-Chen Guo , Li Wang , Ren-Cang Li , Wen-Wei Lin

In multivariate time series classification, although current sequence analysis models have excellent classification capabilities, they show significant shortcomings when dealing with long sequence multivariate data, such as prolonged…

Machine Learning · Computer Science 2024-10-29 Enshuo Yan , Huachuan Wang , Weihao Xia

We consider a situation in which we see samples in $\mathbb{R}^d$ drawn i.i.d. from some distribution with mean zero and unknown covariance A. We wish to compute the top eigenvector of A in an incremental fashion - with an algorithm that…

Machine Learning · Computer Science 2015-01-16 Akshay Balsubramani , Sanjoy Dasgupta , Yoav Freund

We study the dynamics of an online algorithm for learning a sparse leading eigenvector from samples generated from a spiked covariance model. This algorithm combines the classical Oja's method for online PCA with an element-wise…

Information Theory · Computer Science 2016-09-09 Chuang Wang , Yue M. Lu

This paper considers the problem of estimating the principal eigenvector of a covariance matrix from independent and identically distributed data samples in streaming settings. The streaming rate of data in many contemporary applications…

Machine Learning · Computer Science 2020-01-07 Haroon Raja , Waheed U. Bajwa

We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i.i.d. data points in $\reals^d$. A simple and…

Machine Learning · Computer Science 2016-01-05 Ohad Shamir

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…

Machine Learning · Computer Science 2018-11-19 Enayat Ullah , Poorya Mianjy , Teodor V. Marinov , Raman Arora

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…

Machine Learning · Computer Science 2021-03-18 Ian Gemp , Brian McWilliams , Claire Vernade , Thore Graepel

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…

Information Theory · Computer Science 2022-04-04 Zezhong Zhang , Guangxu Zhu , Rui Wang , Vincent K. N. Lau , Kaibin Huang

This paper studies the complexity of the stochastic gradient algorithm for PCA when the data are observed in a streaming setting. We also propose an online approach for selecting the learning rate. Simulation experiments confirm the…

Statistics Theory · Mathematics 2018-04-04 Stephane Chretien , Christophe Guyeux , Zhen-Wai Olivier HO

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

Machine Learning · Statistics 2017-05-19 Xianghui Luo , Robert J. Durrant

Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…

Statistics Theory · Mathematics 2009-01-22 Boaz Nadler