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Pattern recognition via projection-based kNN rules

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  • Fraiman, Ricardo
  • Justel, Ana
  • Svarc, Marcela

Abstract

A new procedure for pattern recognition is introduced based on the concepts of random projections and nearest neighbors. It can be considered as an improvement of the classical nearest neighbor classification rules. Besides the concept of neighbors, the notion of district, a larger set into which the data will be projected, is introduced. Then a one-dimensional kNN method is applied to the projected data on randomly selected directions. This method, which is more accurate to handle high-dimensional data, has some robustness properties. The procedure is also universally consistent. Moreover, the method is challenged with the Isolet data set where a very high classification score is obtained.

Suggested Citation

  • Fraiman, Ricardo & Justel, Ana & Svarc, Marcela, 2010. "Pattern recognition via projection-based kNN rules," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1390-1403, May.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:5:p:1390-1403
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    References listed on IDEAS

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    1. Croux, Christophe & Joossens, Kristel & Lemmens, Aurelie, 2007. "Trimmed bagging," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 362-368, September.
    2. Chakraborty, Sounak, 2009. "Simultaneous cancer classification and gene selection with Bayesian nearest neighbor method: An integrated approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1462-1474, February.
    3. Wang, Xiaogang & Qiu, Weiliang & Zamar, Ruben H., 2007. "CLUES: A non-parametric clustering method based on local shrinking," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 286-298, September.
    4. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 419-440, December.
    5. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    6. Fraiman, Ricardo & Justel, Ana & Svarc, Marcela, 2008. "Selection of Variables for Cluster Analysis and Classification Rules," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1294-1303.
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