相关论文: Manifold Principle Component Analysis for Large-Di…

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…

I develop a feasible weighted projected principal component (FPPC) analysis for factor models in which observable characteristics partially explain the latent factors. This novel method provides more efficient and accurate estimators than…

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…

Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…

Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank…

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

This paper proposes a probabilistic model of subspaces based on the probabilistic principal component analysis (PCA). Given a sample of vectors in the embedding space -- commonly known as a snapshot matrix -- this method uses quantities…

This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA…

Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets.…

We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of…

Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well in…

The two-dimensional principal component analysis (2DPCA) has become one of the most powerful tools of artificial intelligent algorithms. In this paper, we review 2DPCA and its variations, and propose a general ridge regression model to…

This paper studies the principal components (PC) estimator for high dimensional approximate factor models with weak factors in that the factor loading ($\boldsymbol{\Lambda}^0$) scales sublinearly in the number $N$ of cross-section units,…

Dimensionality reduction methods, such as principal component analysis (PCA) and factor analysis, are central to many problems in data science. There are, however, serious and well-understood challenges to finding robust low dimensional…

This paper proposes a hierarchical approximate-factor approach to analyzing high-dimensional, large-scale heterogeneous time series data using distributed computing. The new method employs a multiple-fold dimension reduction procedure using…

Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…

Multiway data are becoming more and more common. While there are many approaches to extending principal component analysis (PCA) from usual data matrices to multiway arrays, their conceptual differences from the usual PCA, and the…