ArticleProceedings of the IEEE. Institute of Electrical and Electronics Engineers2018
PCA in High Dimensions: An orientation.
Article in Proceedings of the IEEE. Institute of Electrical and Electronics Engineers, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 21 papers.
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Who cites it
21 citing papers in PubMed.
- Localized Sparse Principal Component Analysis of Multivariate Time Series in the Frequency Domain.Journal of the American Statistical Association · 2026Article
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- Multivariate classification of livestock production systems in Mexico.Tropical animal health and production · 2025Article
- Improved liver fat andMagnetic resonance in medicine · 2025Article
- The Dyson equalizer: adaptive noise stabilization for low-rank signal detection and recovery.Information and inference : a journal of the IMA · 2025Article
- Semisynthetic simulation for microbiome data analysis.Briefings in bioinformatics · 2024Review
- JASPER: Fast, powerful, multitrait association testing in structured samples gives insight on pleiotropy in gene expression.American journal of human genetics · 2024Article
- Explaining deep learning-based representations of resting state functional connectivity data: focusing on interpreting nonlinear patterns in autism spectrum disorder.Frontiers in psychiatry · 2024Article
- Structural Analysis and Classification of Low-Molecular-Weight Hyaluronic Acid by Near-Infrared Spectroscopy: A Comparison between Traditional Machine Learning and Deep Learning.Molecules (Basel, Switzerland) · 2023Article
- James-Stein for the leading eigenvector.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Optimally Weighted PCA for High-Dimensional Heteroscedastic Data.SIAM journal on mathematics of data science · 2023Article
- Denoise Functional Magnetic Resonance Imaging With Random Matrix Theory Based Principal Component Analysis.IEEE transactions on bio-medical engineering · 2022Article
- Biwhitening Reveals the Rank of a Count Matrix.SIAM journal on mathematics of data science · 2022Article
- How to reduce dimension with PCA and random projections?IEEE transactions on information theory · 2021Article
- SNR-enhanced diffusion MRI with structure-preserving low-rank denoising in reproducing kernel Hilbert spaces.Magnetic resonance in medicine · 2021Article
- A spectral theory for Wright's inbreeding coefficients and related quantities.PLoS genetics · 2021Article
- Principal component analysis is limited to low-resolution analysis in cryoEM.Acta crystallographica. Section D, Structural biology · 2021Article
- Article
- Continuous flexibility analysis of SARS-CoV-2 Spike prefusion structures.bioRxiv : the preprint server for biology · 2020Article
- Steerable ePCA: Rotationally Invariant Exponential Family PCA.IEEE transactions on image processing : a publication of the IEEE Signal Processing Society · 2020Article
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2 authors.
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Abstract
When the data are high dimensional, widely used multivariate statistical methods such as principal component analysis can behave in unexpected ways. In settings where the dimension of the observations is comparable to the sample size, upward bias in sample eigenvalues and inconsistency of sample eigenvectors are among the most notable phenomena that appear. These phenomena, and the limiting behavior of the rescaled extreme sample eigenvalues, have recently been investigated in detail under the spiked covariance model. The behavior of the bulk of the sample eigenvalues under weak distributional assumptions on the observations has been described. These results have been exploited to develop new estimation and hypothesis testing methods for the population covariance matrix. Furthermore, partly in response to these phenomena, alternative classes of estimation procedures have been developed by exploiting sparsity of the eigenvectors or the covariance matrix. This paper gives an orientation to these areas.
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