Quantifying the estimation error of principal component vectors
Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that approximates a population covariance $\Sigma$, and these eigenvectors...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Oxford University Press
2019
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| _version_ | 1826267014681853952 |
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| author | Hauser, R Lember, J Matzinger, H Kangro, R |
| author_facet | Hauser, R Lember, J Matzinger, H Kangro, R |
| author_sort | Hauser, R |
| collection | OXFORD |
| description | Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that approximates a population covariance $\Sigma$, and these eigenvectors are often used to extract structural information about the variables (or attributes) of the studied population. Since PCA is based on the eigendecomposition of the proxy covariance $\widehat{\Sigma}$ rather than the ground-truth $\Sigma$, it is important to understand the approximation error in each individual eigenvector as a function of the number of available samples. The recent results of Kolchinskii and Lounici yield such bounds. In the present paper we sharpen these bounds and show that eigenvectors can often be reconstructed to a required accuracy from a sample of strictly smaller size order. |
| first_indexed | 2024-03-06T20:47:42Z |
| format | Journal article |
| id | oxford-uuid:3679a50c-07ab-4d5e-ae1e-325e0901a4e9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:47:42Z |
| publishDate | 2019 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:3679a50c-07ab-4d5e-ae1e-325e0901a4e92022-03-26T13:38:15ZQuantifying the estimation error of principal component vectorsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3679a50c-07ab-4d5e-ae1e-325e0901a4e9EnglishSymplectic Elements at OxfordOxford University Press2019Hauser, RLember, JMatzinger, HKangro, RPrincipal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that approximates a population covariance $\Sigma$, and these eigenvectors are often used to extract structural information about the variables (or attributes) of the studied population. Since PCA is based on the eigendecomposition of the proxy covariance $\widehat{\Sigma}$ rather than the ground-truth $\Sigma$, it is important to understand the approximation error in each individual eigenvector as a function of the number of available samples. The recent results of Kolchinskii and Lounici yield such bounds. In the present paper we sharpen these bounds and show that eigenvectors can often be reconstructed to a required accuracy from a sample of strictly smaller size order. |
| spellingShingle | Hauser, R Lember, J Matzinger, H Kangro, R Quantifying the estimation error of principal component vectors |
| title | Quantifying the estimation error of principal component vectors |
| title_full | Quantifying the estimation error of principal component vectors |
| title_fullStr | Quantifying the estimation error of principal component vectors |
| title_full_unstemmed | Quantifying the estimation error of principal component vectors |
| title_short | Quantifying the estimation error of principal component vectors |
| title_sort | quantifying the estimation error of principal component vectors |
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