Abstract
Principal Component Analysis (PCA) is a popular method for linear dimensionality reduction. It is often used to discover hidden correlations or to facilitate the interpretation and visualization of data. However, it is liable to suffer from outliers. Strong outliers can skew the principal components and as a consequence lead to a higher reconstruction loss. While there exist several sophisticated approaches to make the PCA more robust, we present an approach which is intriguingly simple: we replace the covariance matrix by a so-called coMAD matrix. The first experiments show that PCA based on the coMAD matrix is more robust towards outliers.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We used python with several libraries. The code can be found at: https://github.com/huenemoerder/MAD-PCA.
- 2.
References
Aggarwal, C.C., Yu, P.S.: Finding generalized projected clusters in high dimensional spaces, vol. 29. ACM (2000)
Böhm, C., Kailing, K., Kröger, P., Zimek, A.: Computing clusters of correlation connected objects. In: Proceedings of the 2004 ACM SIGMOD International Conference on Management of Data, pp. 455–466. ACM (2004)
Falk, M.: On mad and comedians. Ann. Inst. Stat. Math. 49(4), 615–644 (1997)
Hubert, M., Rousseeuw, P.J., Vanden Branden, K.: Robpca: a new approach to robust principal component analysis. Technometrics 47(1), 64–79 (2005)
Pearson, K.: Liii. On lines and planes of closest fit to systems of points in space. London, Edinburgh, Dublin Philos. Mag. J. Sci 2(11), 559–572 (1901)
De la Torre, F., Black, M.J.: Robust principal component analysis for computer vision. In: Proceedings Eighth IEEE International Conference on Computer Vision, ICCV 2001, vol. 1, pp. 362–369. IEEE (2001)
Zhao, Q., Meng, D., Xu, Z., Zuo, W., Zhang, L.: Robust principal component analysis with complex noise. In: International Conference on Machine Learning, pp. 55–63 (2014)
Acknowledgement
This work has been funded by the German Federal Ministry of Education and Research (BMBF) under Grant No. 01IS18036A. The authors of this work take full responsibilities for its content.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Kazempour, D., Hünemörder, M.A.X., Seidl, T. (2019). On coMADs and Principal Component Analysis. In: Amato, G., Gennaro, C., Oria, V., Radovanović , M. (eds) Similarity Search and Applications. SISAP 2019. Lecture Notes in Computer Science(), vol 11807. Springer, Cham. https://doi.org/10.1007/978-3-030-32047-8_24
Download citation
DOI: https://doi.org/10.1007/978-3-030-32047-8_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32046-1
Online ISBN: 978-3-030-32047-8
eBook Packages: Computer ScienceComputer Science (R0)