Adaptive dimensionality reduction for neural network-based online principal component analysis.
"Principal Component Analysis" (PCA) is an established linear technique for dimensionality reduction. It performs an orthonormal transformation to replace possibly correlated variables with a smaller set of linearly independent variables, the so-called principal components, which capture a...
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Public Library of Science (PLoS)
2021-01-01
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| Series: | PLoS ONE |
| Online Access: | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0248896&type=printable |
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| author | Nico Migenda Ralf Möller Wolfram Schenck |
| author_facet | Nico Migenda Ralf Möller Wolfram Schenck |
| author_sort | Nico Migenda |
| collection | DOAJ |
| description | "Principal Component Analysis" (PCA) is an established linear technique for dimensionality reduction. It performs an orthonormal transformation to replace possibly correlated variables with a smaller set of linearly independent variables, the so-called principal components, which capture a large portion of the data variance. The problem of finding the optimal number of principal components has been widely studied for offline PCA. However, when working with streaming data, the optimal number changes continuously. This requires to update both the principal components and the dimensionality in every timestep. While the continuous update of the principal components is widely studied, the available algorithms for dimensionality adjustment are limited to an increment of one in neural network-based and incremental PCA. Therefore, existing approaches cannot account for abrupt changes in the presented data. The contribution of this work is to enable in neural network-based PCA the continuous dimensionality adjustment by an arbitrary number without the necessity to learn all principal components. A novel algorithm is presented that utilizes several PCA characteristics to adaptivly update the optimal number of principal components for neural network-based PCA. A precise estimation of the required dimensionality reduces the computational effort while ensuring that the desired amount of variance is kept. The computational complexity of the proposed algorithm is investigated and it is benchmarked in an experimental study against other neural network-based and incremental PCA approaches where it produces highly competitive results. |
| format | Article |
| id | doaj-art-95e4150aae6943e6ab483738bcbfc3c9 |
| institution | OA Journals |
| issn | 1932-6203 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj-art-95e4150aae6943e6ab483738bcbfc3c92025-08-20T02:17:49ZengPublic Library of Science (PLoS)PLoS ONE1932-62032021-01-01163e024889610.1371/journal.pone.0248896Adaptive dimensionality reduction for neural network-based online principal component analysis.Nico MigendaRalf MöllerWolfram Schenck"Principal Component Analysis" (PCA) is an established linear technique for dimensionality reduction. It performs an orthonormal transformation to replace possibly correlated variables with a smaller set of linearly independent variables, the so-called principal components, which capture a large portion of the data variance. The problem of finding the optimal number of principal components has been widely studied for offline PCA. However, when working with streaming data, the optimal number changes continuously. This requires to update both the principal components and the dimensionality in every timestep. While the continuous update of the principal components is widely studied, the available algorithms for dimensionality adjustment are limited to an increment of one in neural network-based and incremental PCA. Therefore, existing approaches cannot account for abrupt changes in the presented data. The contribution of this work is to enable in neural network-based PCA the continuous dimensionality adjustment by an arbitrary number without the necessity to learn all principal components. A novel algorithm is presented that utilizes several PCA characteristics to adaptivly update the optimal number of principal components for neural network-based PCA. A precise estimation of the required dimensionality reduces the computational effort while ensuring that the desired amount of variance is kept. The computational complexity of the proposed algorithm is investigated and it is benchmarked in an experimental study against other neural network-based and incremental PCA approaches where it produces highly competitive results.https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0248896&type=printable |
| spellingShingle | Nico Migenda Ralf Möller Wolfram Schenck Adaptive dimensionality reduction for neural network-based online principal component analysis. PLoS ONE |
| title | Adaptive dimensionality reduction for neural network-based online principal component analysis. |
| title_full | Adaptive dimensionality reduction for neural network-based online principal component analysis. |
| title_fullStr | Adaptive dimensionality reduction for neural network-based online principal component analysis. |
| title_full_unstemmed | Adaptive dimensionality reduction for neural network-based online principal component analysis. |
| title_short | Adaptive dimensionality reduction for neural network-based online principal component analysis. |
| title_sort | adaptive dimensionality reduction for neural network based online principal component analysis |
| url | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0248896&type=printable |
| work_keys_str_mv | AT nicomigenda adaptivedimensionalityreductionforneuralnetworkbasedonlineprincipalcomponentanalysis AT ralfmoller adaptivedimensionalityreductionforneuralnetworkbasedonlineprincipalcomponentanalysis AT wolframschenck adaptivedimensionalityreductionforneuralnetworkbasedonlineprincipalcomponentanalysis |