相关论文: Principal Component Projection Without Principal C…

We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…

Principal component analysis (PCA) is a longstanding and well-studied approach for dimension reduction. It rests upon the assumption that the underlying signal in the data has low rank, and thus can be well-summarized using a small number…

Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…

We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…

Most high-dimensional matrix recovery problems are studied under the assumption that the target matrix has certain intrinsic structures. For image data related matrix recovery problems, approximate low-rankness and smoothness are the two…

For very large datasets, random projections (RP) have become the tool of choice for dimensionality reduction. This is due to the computational complexity of principal component analysis. However, the recent development of randomized…

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 widely used technique in machine learning, data analysis and signal processing. With the increase in the size and complexity of datasets, it has become important to develop low-space usage algorithms…

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…

Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

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…

Tensor Factor Models (TFM) are appealing dimension reduction tools for high-order large-dimensional tensor time series, and have wide applications in economics, finance and medical imaging. In this paper, we propose a projection estimator…

Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components…

Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

In our previous work, a reduced order model (ROM) for a stochastic system was made, where noisy data was projected onto principal component analysis (PCA)-derived basis vectors to obtain an accurate reconstruction of the noise-free data.…

The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes…

Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…