The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization
Abstract
Principal component analysis (PCA) minimizes the sum of squared errors (L2-norm) and is sensitive to the presence of outliers. We propose a rotational invariant L1-norm PCA (R1-PCA). R1-PCA is similar to PCA in that (1) it has a unique global solution, (2) the solution are principal eigenvectors of a robust covariance matrix (re-weighted to soften the effects of outliers), (3) the solution is rotational invariant. These properties are not shared by the L1-norm PCA. A new subspace iteration algorithm is given to compute R1-PCA efficiently. Experiments on several real-life datasets show R1-PCA can effectively handle outliers. We extend R1-norm to K-means clustering and show that L1-norm K-means leads to poor results while R1-K-means outperforms standard K-means.
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Cites
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Sparse Principal Component Analysis
Zou, H., Hastie, T., & Tibshirani, R. (2006) · Journal of Computational and Graphical Statistics · doi:10.1198/106186006x113430 · Cited by 3,152
Feature selection, L 1 vs. L 2 regularization, and rotational invariance
Ng, A. Y. (2004) · Twenty-first international conference on Machine learning - ICML '04 · doi:10.1145/1015330.1015435 · Cited by 1,572
Cited by
Feature Selection: A Data Perspective
Li, J., Cheng, K., Wang, S., Morstatter, F., Trevino, R. P., Tang, J., & Liu, H. (2018) · ACM Computing Surveys · doi:10.1145/3136625 · Cited by 2,442
Face2Face: Real-Time Face Capture and Reenactment of RGB Videos
Thies, J., Zollhofer, M., Stamminger, M., Theobalt, C., & Niessner, M. (2016) · 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2016.262 · Cited by 1,747
Hyperspectral anomaly detection with robust graph autoencoders
Fan, G., Ma, Y., Mei, X., Fan, F., Huang, J., & Ma, J. (2022) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2021.3097097 · Cited by 212
Blind Hyperspectral Unmixing Using Autoencoders: A Critical Comparison
Palsson, B., Sveinsson, J. R., & Ulfarsson, M. O. (2022) · IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing · doi:10.1109/jstars.2021.3140154 · Cited by 107
Loss Functions, Axioms, and Peer Review
Noothigattu, R., Shah, N., & Procaccia, A. (2021) · Journal of Artificial Intelligence Research · doi:10.1613/jair.1.12554 · Cited by 28
Metadata
- Authors
- Ding, C., Zhou, D., He, X., & Zha, H.
- Venue
- Proceedings of the 23rd international conference on Machine learning - ICML '06
- Publisher
- ACM Press
- Published
- 2006
- Pages
- 281-288
- OpenAlex
- W2053090063
- Cited by
- 633
- References
- 3
- FWCI
- 6.41
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Ding, C., Zhou, D., He, X., & Zha, H. (2006). R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization. Proceedings of the 23rd international conference on Machine learning - ICML '06. https://doi.org/10.1145/1143844.1143880
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