Discarding Variables in a Principal Component Analysis. I: Artificial Data
Abstract
Often, results obtained from the use of principal component analysis are little changed if some of the variables involved are discarded beforehand. This paper examines some of the possible methods for deciding which variables to reject and these rejection methods are tested on artificial data containing variables known to be “redundant”. It is shown that several of the rejection methods, of differing types, each discard precisely those variables known to be redundant, for all but a few sets of data.
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The bounds of Theorem 2 tend to be loose on real-world datasets.
“Such a phenomenon is not a new observation, and much prior work has shown that the bounds tend to be loose on real-world datasets (Broadbent et al., 2010; Paschou et al., 2007; Jolliffe, 1972).”
From Compactor: Calibrated Query-Agnostic KV Cache Compression with Approximate Leverage Scores (2025) · cites this paper as Jolliffe, 1972
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“Then, with probability 1 − δ , we have [5, 30, 21], even deterministically choosing rows corresponding to the top-k leverage scores provides a good spectral sparsification of K .”
- Authors
- Jolliffe, I. T.
- Affiliations
- University of Kent (GB)
- Corresponding author
- Jolliffe, I. T.
- Venue
- Applied Statistics
- Publisher
- JSTOR
- Published
- 1972
- Volume
- 21
- Issue
- 2
- Pages
- 160
- ISSN
- 0035-9254 (ISSN-L)
- OpenAlex
- W2797320655
- Cited by
- 907
- References
- 0
- Citations by year
- 2026: 11 · 2025: 18 · 2024: 36 · 2023: 47 · 2022: 47 · 2021: 33 · 2020: 44 · 2019: 41 · 2018: 38 · 2017: 37 · 2016: 36 · 2015: 34 · 2014: 40 · 2013: 43 · 2012: 43
- FWCI
- 4.15
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the Royal Statistical Society Series C (Applied Statistics) (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Chemistry › Analytical Chemistry › Spectroscopy and Chemometric Analyses
- Keywords
- feature selection, principal component analysis, redundant variables, artificial data, dimensionality reduction
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