On the estimation of a covariance matrix in designing Parzen classifiers

Pattern Recognition

Volumn 29, Issue 10, 1996, Pages 1751-1759

  Hamamoto, Yoshihiko ^a   Fujimoto, Yasushi ^a   Tomita, Shingo ^a  

^a YAMAGUCHI UNIVERSITY   (Japan)

Author keywords

Error rate; High dimensions; Kernel covariance; Parzen classifier; Small training sample size

Indexed keywords

ERROR ANALYSIS; MATRIX ALGEBRA; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION;

KERNEL COVARIANCE; ORTHOGONAL EXPANSION ESTIMATORS; PARZEN CLASSIFIERS;

PATTERN RECOGNITION;

EID: 0030270491     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/0031-3203(96)00027-1     Document Type: Article

References (11)

1. M. Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Stat. 27, 832-837 (1956).
2. E. Parzen, On the estimation of a probability density function and the mode, Ann. Math. Stat. 33, 1065-1076 (1962).
3. K. Fukunaga, Introduction to Statistical Pattern Recognition, 2nd edn. Academic Press, New York (1990).
4. Y. Hamamoto, S. Uchimura, T. Konaoka and S. Tomita, Comparison of classifiers in small sample size situations, Proc. 8th Scandinavian Conf. Image Anal. I, 11-12, Tromso (1993).
5. J. Van Ness, On the dominance of non-parametric Bayes rule discriminant algorithms in high dimensions, Pattern Recognition 12, pp. 355-368 (1980).
6. A. K. Jain and M. D. Ramaswami, Classifier design with Parzen windows, Pattern Recognition and Artificial Intelligence, E. S. Gelsema and L. N. Kanal (Eds), pp. 211-228. Elsevier, Amsterdam (1988).
7. S. J. Raudys and A. K. Jain, Small sample size effects in statistical pattern recognition: Recommendations for practitioners, IEEE Trans. PAMI-13(3), 252-264 (1991).
8. K. Fukunaga and D. M. Hummels, Bayes error estimation using Parzen and k-NN procedures, IEEE Trans. PAMI-9(5), 634-643 (1987).
9. S. Raudys, On the effectiveness of Parzen window classifier, Informatica. 2(3), 434-454 (1991).
10. F. Kimura, K. Takashima, S. Tsuruoka and Y. Miyake, Modified quadratic discriminant functions and the application to Chinese character recognition, IEEE Trans. PAMI-9(1), 149-153 (1987).
11. A. K. Jain and B. Chandrasekaran, Dimensionality and sample size considerations in pattern recognition practice, Handbook of Statistics, P. R. Krishnaiah and L. N. Kanal (Eds.) Vol. 2, pp. 835-855. North Holland, Amsterdam (1982).