Abstract
Principal Components Analysis is a widely used technique for dimension reduction and characterization of variability in multivariate populations. Our interest lies in studying when and why the rotation to principal components can be used effectively within a response-predictor set relationship in the context of mode hunting. Specifically focusing on the Patient Rule Induction Method (PRIM), we first develop a fast version of this algorithm (fastPRIM) under normality which facilitates the theoretical studies to follow. Using basic geometrical arguments, we then demonstrate how the Principal Components rotation of the predictor space alone can in fact generate improved mode estimators. Simulation results are used to illustrate our findings.
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Acknowledgements
All authors supported in part by NIH grant NCI R01-CA160593A1. We would like to thank Rob Tibshirani, Steve Marron, and Hemant Ishwaran for helpful discussions of the work. This work made use of the High Performance Computing Resource in the Core Facility for Advanced Research Computing at Case Western Reserve University.
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Díaz-Pachón, D.A., Dazard, JE., Rao, J.S. (2017). Unsupervised Bump Hunting Using Principal Components. In: Ahmed, S. (eds) Big and Complex Data Analysis. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-41573-4_16
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DOI: https://doi.org/10.1007/978-3-319-41573-4_16
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