The DOI matches its Crossref record; 34 of the 34 references it cites were found in a registry or an index.
On Consistency and Sparsity for Principal Components Analysis in High Dimensions
Open accessAbstract
Principal components analysis (PCA) is a classic method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. Contemporary datasets often have p comparable with or even much larger than n. Our main assertions, in such settings, are (a) that some initial reduction in dimensionality is desirable before applying any PCA-type search for principal modes, and (b) the initial reduction in dimensionality is best achieved by working in a basis in which the signals have a sparse representation. We describe a simple asymptotic model in which the estimate of the leading principal component vector via standard PCA is consistent if and only if p(n)/n→0. We provide a simple algorithm for selecting a subset of coordinates with largest sample variances, and show that if PCA is done on the selected subset, then consistency is recovered, even if p(n) ⪢ n.
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Cited by
Principal component analysis: A review and recent developments
Jolliffe, I. T., & Cadima, J. (2016) · Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rsta.2015.0202 · Cited by 10,117
Comprehensive functional genomic resource and integrative model for the human brain
Wang, D., Liu, S., Warrell, J., Won, H., Shi, X., Navarro, F. C. P., Clarke, D., Gu, M., Emani, P., Yang, Y. T., et al. (2018) · Science · doi:10.1126/science.aat8464 · Cited by 965
Large Covariance Estimation by Thresholding Principal Orthogonal Complements
Fan, J., Liao, Y., & Mincheva, M. (2013) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12016 · Cited by 909
Principal Component Analysis: A Natural Approach to Data Exploration
Gewers, F. L., Ferreira, G. R., Arruda, H. F. D., Silva, F. N., Comin, C. H., Amancio, D. R., & Costa, L. D. F. (2022) · ACM Computing Surveys · doi:10.1145/3447755 · Cited by 508
Morris, J. S. (2015) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-010814-020413 · Cited by 423
Metadata
- Authors
- Johnstone, I. M., & Lu, A. Y.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2009-06
- Volume
- 104
- Issue
- 486
- Pages
- 682-693
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2097714737
- Cited by
- 847
- References
- 34
- FWCI
- 21.86
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
