Optimal Mean Robust Principal Component Analysis

Feiping Nie, Jianjun Yuan, Heng Huang
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):1062-1070, 2014.

Abstract

Dimensionality reduction techniques extract low-dimensional structure from high-dimensional data and are widespread in machine learning research. In practice, due to lacking labeled data, the unsupervised dimensionality reduction algorithms are more desired. Among them, Principal Component Analysis (PCA) is the most widely used approach. In recent research, several robust PCA algorithms were presented to enhance the robustness of PCA model. However, all existing robust PCA methods incorrectly center the data using the L2-norm distance to calculate the mean, which actually is not the optimal mean due to the L1-norm used in the objective functions. It is non-trivial to remove the optimal mean in the robust PCA, because of the sparsity-inducing norms used in the robust formulations. In this paper, we propose novel robust PCA objective functions with removing optimal mean automatically. We naturally integrate the mean calculation into the dimensionality reduction optimization, such that the optimal mean can be obtained to enhance the dimensionality reduction. Both theoretical analysis and empirical studies demonstrate our new methods can more effectively reduce data dimensionality than previous robust PCA methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-nieb14, title = {Optimal Mean Robust Principal Component Analysis}, author = {Nie, Feiping and Yuan, Jianjun and Huang, Heng}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {1062--1070}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/nieb14.pdf}, url = {https://proceedings.mlr.press/v32/nieb14.html}, abstract = {Dimensionality reduction techniques extract low-dimensional structure from high-dimensional data and are widespread in machine learning research. In practice, due to lacking labeled data, the unsupervised dimensionality reduction algorithms are more desired. Among them, Principal Component Analysis (PCA) is the most widely used approach. In recent research, several robust PCA algorithms were presented to enhance the robustness of PCA model. However, all existing robust PCA methods incorrectly center the data using the L2-norm distance to calculate the mean, which actually is not the optimal mean due to the L1-norm used in the objective functions. It is non-trivial to remove the optimal mean in the robust PCA, because of the sparsity-inducing norms used in the robust formulations. In this paper, we propose novel robust PCA objective functions with removing optimal mean automatically. We naturally integrate the mean calculation into the dimensionality reduction optimization, such that the optimal mean can be obtained to enhance the dimensionality reduction. Both theoretical analysis and empirical studies demonstrate our new methods can more effectively reduce data dimensionality than previous robust PCA methods.} }
Endnote
%0 Conference Paper %T Optimal Mean Robust Principal Component Analysis %A Feiping Nie %A Jianjun Yuan %A Heng Huang %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-nieb14 %I PMLR %P 1062--1070 %U https://proceedings.mlr.press/v32/nieb14.html %V 32 %N 2 %X Dimensionality reduction techniques extract low-dimensional structure from high-dimensional data and are widespread in machine learning research. In practice, due to lacking labeled data, the unsupervised dimensionality reduction algorithms are more desired. Among them, Principal Component Analysis (PCA) is the most widely used approach. In recent research, several robust PCA algorithms were presented to enhance the robustness of PCA model. However, all existing robust PCA methods incorrectly center the data using the L2-norm distance to calculate the mean, which actually is not the optimal mean due to the L1-norm used in the objective functions. It is non-trivial to remove the optimal mean in the robust PCA, because of the sparsity-inducing norms used in the robust formulations. In this paper, we propose novel robust PCA objective functions with removing optimal mean automatically. We naturally integrate the mean calculation into the dimensionality reduction optimization, such that the optimal mean can be obtained to enhance the dimensionality reduction. Both theoretical analysis and empirical studies demonstrate our new methods can more effectively reduce data dimensionality than previous robust PCA methods.
RIS
TY - CPAPER TI - Optimal Mean Robust Principal Component Analysis AU - Feiping Nie AU - Jianjun Yuan AU - Heng Huang BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-nieb14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 1062 EP - 1070 L1 - http://proceedings.mlr.press/v32/nieb14.pdf UR - https://proceedings.mlr.press/v32/nieb14.html AB - Dimensionality reduction techniques extract low-dimensional structure from high-dimensional data and are widespread in machine learning research. In practice, due to lacking labeled data, the unsupervised dimensionality reduction algorithms are more desired. Among them, Principal Component Analysis (PCA) is the most widely used approach. In recent research, several robust PCA algorithms were presented to enhance the robustness of PCA model. However, all existing robust PCA methods incorrectly center the data using the L2-norm distance to calculate the mean, which actually is not the optimal mean due to the L1-norm used in the objective functions. It is non-trivial to remove the optimal mean in the robust PCA, because of the sparsity-inducing norms used in the robust formulations. In this paper, we propose novel robust PCA objective functions with removing optimal mean automatically. We naturally integrate the mean calculation into the dimensionality reduction optimization, such that the optimal mean can be obtained to enhance the dimensionality reduction. Both theoretical analysis and empirical studies demonstrate our new methods can more effectively reduce data dimensionality than previous robust PCA methods. ER -
APA
Nie, F., Yuan, J. & Huang, H.. (2014). Optimal Mean Robust Principal Component Analysis. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):1062-1070 Available from https://proceedings.mlr.press/v32/nieb14.html.

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