Related papers: Distributed Learning for Principle Eigenspaces wit…
Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…
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,…
Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…
The problem of Non-Gaussian Component Analysis (NGCA) is about finding a maximal low-dimensional subspace $E$ in $\mathbb{R}^n$ so that data points projected onto $E$ follow a non-gaussian distribution. Although this is an appropriate model…
Methods for analysis of principal components in discrete data have existed for some time under various names such as grade of membership modelling, probabilistic latent semantic analysis, and genotype inference with admixture. In this paper…
Several statistical problems, such as multiple heterogeneous graph analysis, distributed PCA, integrative data analysis, and simultaneous dimension reduction of images, can involve a collection of $m$ matrices whose leading subspaces…
We study efficient distributed algorithms for the fundamental problem of principal component analysis and leading eigenvector computation on the sphere, when the data are randomly distributed among a set of computational nodes. We propose a…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…
We propose a novel Decentralized Differentially Private Power Method (D-DP-PM) for performing Principal Component Analysis (PCA) in networked multi-agent settings. Unlike conventional decentralized PCA approaches where each agent accesses…
Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…
Principal component analysis (PCA) is one of the most fundamental procedures in exploratory data analysis and is the basic step in applications ranging from quantitative finance and bioinformatics to image analysis and neuroscience.…
We study the robust principal component analysis (RPCA) problem in a distributed setting. The goal of RPCA is to find an underlying low-rank estimation for a raw data matrix when the data matrix is subject to the corruption of gross sparse…
In this paper we derive and analyze two algorithms -- referred to as decentralized power method (DPM) and decentralized Lanczos algorithm (DLA) -- for distributed computation of one (the largest) or multiple eigenvalues of a sample…
Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…
Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding.…
Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…
Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…
Estimating statistical models within sensor networks requires distributed algorithms, in which both data and computation are distributed across the nodes of the network. We propose a general approach for distributed learning based on…