Abstract
We develop a method for tracing out the shape of a cloud of sample observations, in arbitrary dimensions, called the data cloud wrapper (DCW). The DCW have strong theoretical properties, have algorithmic scalability and parallel computational features. We further use the DCW to develop a new fast, robust and accurate classification method in high dimensions, called the geometric learning algorithm (GLA). Two of the main features of the proposed algorithm are that there are no assumptions made about the geometric properties of the underlying data generating distribution, and that there are no parametric or other restrictive assumptions made either for the data or the algorithm. The proposed methods are typically faster and more robust than established classification techniques, while being comparably accurate in most cases.
Keywords
- Feature Selection
- Random Forest
- Supervise Learning
- Data Cloud
- Quadratic Discriminant Analysis
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Alon, A., et al.: Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc. Natl. Acad. Sci. USA 96, 6745–6750 (1999)
Bache, K., Lichman, M.: UCI machine learning repository (2013)
Chaudhuri, P.: On a geometric notion of quantiles for multivariate data. J. Am. Stat. Assoc. 91, 862–872 (1996)
Ferguson, T.S.: Mathematical Statistics. A Decision Theoretic Approach. Academic Press, New York (1967)
Guyon, I., et al.: Feature selection with the CLOP package. Technical report (2006)
Guyon, I., et al.: Competitive baseline methods set new standards for the NIPS 2003 feature selection benchmark. Pattern Recogn. Lett. 28, 1438–1444 (2007)
Haldane, J.B.S.: Note on the median of a multivariate distribution. Biometrika 35, 414–415 (1948)
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, New York (2009)
Mukhopadhyay, N., Chatterjee, S.B.: High dimensional data analysis using multivariate generalized spatial quantiles. J. Mult. Anal. 102–4, 768–780 (2011)
Acknowledgements
This research is partially supported by NSF grant # IIS-1029711, NASA grant #-1502546) the Institute on the Environment (IonE), and College of Liberal Arts (CLA) at the University of Minnesota.
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Mukherjee, U.K., Majumdar, S., Chatterjee, S. (2015). Fast and Robust Supervised Learning in High Dimensions Using the Geometry of the Data. In: Perner, P. (eds) Advances in Data Mining: Applications and Theoretical Aspects. ICDM 2015. Lecture Notes in Computer Science(), vol 9165. Springer, Cham. https://doi.org/10.1007/978-3-319-20910-4_9
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DOI: https://doi.org/10.1007/978-3-319-20910-4_9
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