Related papers: Federated Principal Component Analysis
Principal Component Analysis (PCA) aims to find subspaces spanned by the so-called principal components that best represent the variance in the dataset. The deflation method is a popular meta-algorithm that sequentially finds individual…
Federated Learning (FL) is a distributed machine learning framework that inherently allows edge devices to maintain their local training data, thus providing some level of privacy. However, FL's model updates still pose a risk of privacy…
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.…
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…
Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from the data. However, if the process is non-Gaussian, PCA algorithms or their higher order generalisations provide…
This paper proposes a novel sparse principal component analysis algorithm with self-learning ability for successive modes, where synaptic intelligence is employed to measure the importance of variables and a regularization term is added to…
Federated learning has emerged as a powerful framework for analysing distributed data, yet two challenges remain pivotal: heterogeneity across sites and privacy of local data. In this paper, we address both challenges within a federated…
We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
Federated learning (FL), as a type of collaborative machine learning framework, is capable of preserving private data from mobile terminals (MTs) while training the data into useful models. Nevertheless, from a viewpoint of information…
We revisit the task of computing the span of the top $r$ singular vectors $u_1, \ldots, u_r$ of a matrix under differential privacy. We show that a simple and efficient algorithm -- based on singular value decomposition and standard…
Federated Learning (FL) aims to learn a single global model that enables the central server to help the model training in local clients without accessing their local data. The key challenge of FL is the heterogeneity of local data in…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
Machine learning methods allow us to make recommendations to users in applications across fields including entertainment, dating, and commerce, by exploiting similarities in users' interaction patterns. However, in domains that demand…
Fan et al. [$\mathit{Annals}$ $\mathit{of}$ $\mathit{Statistics}$ $\textbf{47}$(6) (2019) 3009-3031] constructed a distributed principal component analysis (PCA) algorithm to reduce the communication cost between multiple servers…
With the growth of machine learning techniques, privacy of data of users has become a major concern. Most of the machine learning algorithms rely heavily on large amount of data which may be collected from various sources. Collecting these…
Federated learning enables collaborative model training across distributed clients while preserving data privacy. However, in practical deployments, device heterogeneity, non-independent, and identically distributed (Non-IID) data often…
Federated learning (FL), as a type of distributed machine learning, is capable of significantly preserving client's private data from being shared among different parties. Nevertheless, private information can still be divulged by analyzing…
Given $n$ i.i.d. random matrices $A_i \in \mathbb{R}^{d \times d}$ that share a common expectation $\Sigma$, the objective of Differentially Private Stochastic PCA is to identify a subspace of dimension $k$ that captures the largest…
We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…