Pattern Recognition:

Local Polynomial Models:

Local Polynomial Models have recently become a very popular method for regression and density estimation in the statistics literature. The following paper discusses how they may be used for pattern classification:

• ``Local polynomial models for classification,'' with Ron Meir, submitted, 1999 [ pdf ] (7 pages).

k-Nearest-Neighbor Algorithm:

Much of my work centers around the k-nearest-neighbor classifier. The fastest implementation of this algorithm that I know of, is described in

• ``The labeled cell classifier: a fast approximation of k nearest neighbors,'' with Alessandro M. Palau, Proceedings of the 14th International Conference on Pattern Recognition, (Brisbane, Australia), vol. 1, IEEE Computer Society Press: Los Alamitos, CA,1998 [ pdf ] (8 pages).

The finite sample risk of the k-nearest-neighbor classifier with different metrics is described in

• ``Asymptotic expansions of the k nearest neighbor risk,'' with Santosh S. Venkatesh, The Annals of Statistics, vol. 26, no. 3, pp. 850-878, 1998.
• ``Asymptotic derivation of the finite-sample risk of the k nearest neighbor classifier,'' with Santosh S. Venkatesh, Technical Report UVM-CS-1998-0101, Department of Computer Science, University of Vermont. [pdf (340kb) | ps.Z (1.8mb)] (40 pages).

Related work is contained in:

• ``The finite-sample risk of the k-nearest-neighbor classifier under the Lp metric,'' with S. S. Venkatesh, Proceedings of the 1994 IEEE-IMS Workshop on Information Theory and Statistics, (Alexandria, VA), IEEE-Service Center, Piscataway, NJ, 1994, p. 98.
• ``Asymptotic Predictions of the finite-sample risk of the k-nearest-neighbor classifier,'' in Proceedings of the 12th International Conference on Pattern Recognition, (Jerusalem, Israel), vol. 2, IEEE Computer Society Press: Los Alamitos, CA, (1994), pp. 1-7.
• ``On the finite-sample performance of the nearest-neighbor classifier,'' with D. Psaltis and S. S. Venkatesh, IEEE Transactions on Information Theory, 40 (1994), pp. 93-102; also presented at the 1993 IEEE International Symposium on Information Theory (San Antonio, TX, 1993).
• ``Bellman Strikes Again: The rate of growth of sample complexity with dimension for the nearest-neighbor classifier,'' with D. Psaltis and S. S. Venkatesh, Proceedings of the Fifth Annual ACM Workshop on Computational Learning Theory (COLT92), pp. 93-102.
• ``Asymptotic slowing down of the nearest-neighbor classifier,'' with D. Psaltis and S. S. Venkatesh, in R. P. Lippmann, J. E. Moody, and D. S. Touretzky, ed., Advances in Neural Information Processing Systems, 3, Morgan Kaufmann, (San Mateo, CA: 1991), pp. 932-938.

Empirical Estimation of the Bayes Risk:

The result of the finite sample analysis can be used to construct a statistical estimator of the Bayes risk. These studies are described in

• ``Estimating the Bayes Risk from Sample Data,'' with T. Xu, in D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo, ed. Advances in Neural Information Systems 8, MIT Press: Cambridge MA, 1996, pp. 232--238.
• ``Predicting the accuracy of Bayes classifiers,'' in K. M. Hanson and R. N. Silver, Maximum Entropy and Bayesian Methods, Kluwer Acadmeic Publishers: Dordrecht, Netherlands, 1996, pp. 295--302.

Neural Networks:

An early study on pruning neural networks to obtain more accurate generalation for approximating continuous functions is described in

• ``Generalizing smoothness constraints from discrete samples,'' with C. Ji and D. Psaltis, Neural Computation 2 (1990), pp. 188-197.

Physics:

• ``Retardation effects on collective excitations in correlated superlattices,'' with Kenneth I. Golden, G. Kalman, and Limin Miao, to appear in Physical Review B, 1998.
• ``Plasmon and shear modes in correlated superlattices,'' with Kenneth I. Golden, G. Kalman, and Limin Miao, Physical Review B 55, 16349, 1997-II.
• ``Singular perturbation analysis of the mean-field limit of semiclassical optics,'' with W. C. Schieve, Physical Review A41 (1990), pp. 421-425.
• ``Fluctuations, instabilities, and chaos in the laser driven nonlinear ring cavity,'' with J. C. Englund and W. C. Schieve, in E. Wolf, ed. Progress in Optics, Vol XXI, North Holland Physics Publishing: Amsterdam (1984), pp. 355-428.
• ``Fluctuations and instabilities in laser-like systems,'' with J. C. Englund, R. F. Gragg, and W. C. Schieve, Peralta Fabi, ed., Proc. 1st Escuela Mexicana de Fisica Estadstica, Soc. Mex. Fisica, 1983.
• ``Oscillatory instabilities leading to `optical turbulence' in a bistable ring cavity,'' with H. J. Carmichael and W. C. Schieve, Physical Review A26 (1982), pp. 3408-3422.
• ``The path to `turbulence': optical bistability and universality in the ring cavity,'' with H. J. Charmichael and W. C. Schieve, Optics Communications40 (1981), pp. 69-72.