Related papers: Few-Round Distributed Principal Component Analysis…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA…
We study a distributed Principal Component Analysis (PCA) framework where each worker targets a distinct eigenvector and refines its solution by updating from intermediate solutions provided by peers deemed as "superior". Drawing intuition…
Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…
Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…
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…
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…
In light of the rapidly growing large-scale data in federated ecosystems, the traditional principal component analysis (PCA) is often not applicable due to privacy protection considerations and large computational burden. Algorithms were…
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…
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 components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Principal component analysis (PCA) is an essential algorithm for dimensionality reduction in many data science domains. We address the problem of performing a federated PCA on private data distributed among multiple data providers while…
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
When the dimension of data is comparable to or larger than the number of data samples, Principal Components Analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an Empirical Bayes PCA method that reduces…
Principal Component Analysis (PCA) is a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs to the original data. We consider an extension of PCA which…
In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a…
Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report,…
Accurate predictions of pollutant concentrations at new locations are often of interest in air pollution studies on fine particulate matters (PM$_{2.5}$), in which data is usually not measured at all study locations. PM$_{2.5}$ is also a…
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) 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…