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 large por...
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| Published in: | PloS one Vol. 16; no. 3; p. e0248896 |
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| Format: | Journal Article |
| Language: | English |
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30.03.2021
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| ISSN: | 1932-6203, 1932-6203 |
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| Abstract | “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. |
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| AbstractList | "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. "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."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. Streaming data is possibly subject to noise, drift or other influences, so that the optimal dimensionality has to be adjusted continuously in order to maintain the desired amount of variance in PCA. [...]for an online method to be effective, it is necessary to continuously add or remove dimensions with each data point when appropriate [6]. [...]training many unnecessary components increases the computational effort. [...]the efficient adjustment of dimensionality by an arbitrary number after the presentation of each data point is necessary. Objectives and structure The contribution of this work is the continuous dimensionality adjustment in neural network-based PCA by arbitrary steps, without the constraint to learn all principal components at every timestep. [...]stopping rules previously not directly applicable to neural network-based PCA are extended for online learning. On the downside, it is costly to update non-linear methods continuously and they have many hyperparameters to tune. [...]linear techniques are preferable for many applications, and the focus of this work lies on further improving linear methods, in particular in a streaming setting in which the subspace is updated without knowledge of the data history [23]. Streaming data is possibly subject to noise, drift or other influences, so that the optimal dimensionality has to be adjusted continuously in order to maintain the desired amount of variance in PCA. [...]for an online method to be effective, it is necessary to continuously add or remove dimensions with each data point when appropriate [6]. [...]training many unnecessary components increases the computational effort. [...]the efficient adjustment of dimensionality by an arbitrary number after the presentation of each data point is necessary. Objectives and structure The contribution of this work is the continuous dimensionality adjustment in neural network-based PCA by arbitrary steps, without the constraint to learn all principal components at every timestep. [...]stopping rules previously not directly applicable to neural network-based PCA are extended for online learning. On the downside, it is costly to update non-linear methods continuously and they have many hyperparameters to tune. [...]linear techniques are preferable for many applications, and the focus of this work lies on further improving linear methods, in particular in a streaming setting in which the subspace is updated without knowledge of the data history [23]. |
| Audience | Academic |
| Author | Schenck, Wolfram Migenda, Nico Möller, Ralf |
| AuthorAffiliation | 2 Computer Engineering Group, Faculty of Technology, Bielefeld University, Bielefeld, Germany Fuzhou University, CHINA 1 Center for Applied Data Science Gütersloh, Faculty of Engineering and Mathematics, Bielefeld University of Applied Sciences, Bielefeld, Germany |
| AuthorAffiliation_xml | – name: Fuzhou University, CHINA – name: 1 Center for Applied Data Science Gütersloh, Faculty of Engineering and Mathematics, Bielefeld University of Applied Sciences, Bielefeld, Germany – name: 2 Computer Engineering Group, Faculty of Technology, Bielefeld University, Bielefeld, Germany |
| Author_xml | – sequence: 1 givenname: Nico orcidid: 0000-0002-7223-1735 surname: Migenda fullname: Migenda, Nico – sequence: 2 givenname: Ralf surname: Möller fullname: Möller, Ralf – sequence: 3 givenname: Wolfram orcidid: 0000-0003-3300-2048 surname: Schenck fullname: Schenck, Wolfram |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/33784333$$D View this record in MEDLINE/PubMed |
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| Title | Adaptive dimensionality reduction for neural network-based online principal component analysis |
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