The simple k-nearest neighbor (k-NN) method is often very effective,
especially in classification methods. When the number d of predictors
is large, the nearest neighbors are likely to be quite distant from
the target point. Furthermore they tend to all be on one side of the
target point. Thus, while k-NN sounds like interpolation, it very
often is an extrapolation. Worse still, this extrapolation can easily
be in a direction for which the neighbor set is an unusually poor
experimental design. This work introduces an axial-radial
decomposition of the space around the target point. Prediction at the
target involves interpolation in d-1 (radial) directions and
extrapolation in at most 1 (axial) direction. The interpolation and
extrapolation directions are treated differently when designing a
neighborhood and when selecting a model to fit over the neighborhood.
The neighborhood shapes are chosen from a one parameter family of
ellipsoidal tubes, by cross-validation, along with the neighborhood
size k. The resulting method is competitive on some classification
problems from the U.C. Irvine data repository.
Date: Thurs., April 2; Time: 4:15-5:30PM; Place: Gates 100
Return to seminar schedule.