Refereed full papers (journals, book chapters, international conferences)

1996

@article{HaT1996,
	vgclass =	{refpap},
	author =	{Trevor Hastie and Rolbert Tibshirani},
	title =	{Discriminant Adaptive Nearest Neighbor Classification},
	journal =	{IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume =	{18},
	number =	{6},
	pages =	{607--616},
	month =	{June},
	year =	{1996},
	url =	{http://dx.doi.org/10.1109/34.506411},
	abstract =	{Nearest neighbour classification expects the class
	conditional probabilities to be locally constant, and suffers from bias
	in high dimensions. We propose a locally adaptive form of nearest
	neighbour classification to try to ameliorate this curse of
	dimensionality. We use a local linear discriminant analysis to estimate
	an effective metric for computing neighbourhoods. We determine the
	local decision boundaries from centroid information, and then shrink
	neighbourhoods in directions orthogonal to these local decision
	boundaries, and elongate them parallel to the boundaries. Thereafter,
	any neighbourhood-based classifier can be employed, using the modified
	neighbourhoods. The posterior probabilities tend to be more homogeneous
	in the modified neighbourhoods. We also propose a method for global
	dimension reduction, that combines local dimension information. In a
	number of examples, the methods demonstrate the potential for
	substantial improvements over nearest neighbour classification.},
}