Related papers: Single-Pass PCA of Large High-Dimensional Data

Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and…

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…

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…

The literature provides strong evidence that stock prices can be predicted from past price data. Principal component analysis (PCA) is a widely used mathematical technique for dimensionality reduction and analysis of data by identifying a…

Cryo-electron microscopy nowadays often requires the analysis of hundreds of thousands of 2D images as large as a few hundred pixels in each direction. Here we introduce an algorithm that efficiently and accurately performs principal…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most…

Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…

In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is…

Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

Principal Component Analysis (PCA) is a dimensionality reduction technique widely used to reduce the computational cost associated with numerical simulations of combustion phenomena. However, PCA, which transforms the thermo-chemical state…

Principal component analysis (PCA) is routinely used in population genetics to assess genetic structure. With chromosomal reference genomes and population-scale whole genome-sequencing becoming increasingly accessible, contemporary studies…

Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…

Discovering dominant patterns and exploring dynamic behaviors especially critical state transitions and tipping points in high-dimensional time-series data are challenging tasks in study of real-world complex systems, which demand…

In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…

Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…

Principal Components Analysis (PCA) is a common way to study the sources of variation in a high-dimensional data set. Typically, the leading principal components are used to understand the variation in the data or to reduce the dimension of…

Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data…

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…