CORE Metadata, citation and similar papers at core.ac.uk Provided by VCU Scholars Compass Virginia Commonwealth University VCU Scholars Compass Statistical Sciences and Operations Research Dept. of Statistical Sciences and Operations Publications Research 2015 Principal Component Analysis and Optimization: A Tutorial Robert Reris Virginia Commonwealth University,
[email protected] J. Paul Brooks Virginia Commonwealth University,
[email protected] Follow this and additional works at: http://scholarscompass.vcu.edu/ssor_pubs Part of the Statistics and Probability Commons Creative Commons Attribution 3.0 Unported (CC BY 3.0) Recommended Citation Principal component analysis (PCA) is one of the most widely used multivariate techniques in statistics. It is commonly used to reduce the dimensionality of data in order to examine its underlying structure and the covariance/correlation structure of a set of variables. While singular value decomposition provides a simple means for identification of the principal components (PCs) for classical PCA, solutions achieved in this manner may not possess certain desirable properties including robustness, smoothness, and sparsity. In this paper, we present several optimization problems related to PCA by considering various geometric perspectives. New techniques for PCA can be developed by altering the optimization problems to which principal component loadings are the optimal solutions. This Conference Proceeding is brought to you for free and open access by the Dept. of Statistical Sciences and Operations Research at VCU Scholars Compass. It has been accepted for inclusion in Statistical Sciences and Operations Research Publications by an authorized administrator of VCU Scholars Compass. For more information, please contact
[email protected]. http://dx.doi.org/10.1287/ics.2015.0016 Creative Commons License Computing Society 14th INFORMS Computing Society Conference This work is licensed under a Richmond, Virginia, January 11{13, 2015 Creative Commons Attribution 3.0 License pp.