The Canonical Distortion Measure in Feature Space and 1-NN Classification

Part of Advances in Neural Information Processing Systems 10 (NIPS 1997)

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Jonathan Baxter, Peter Bartlett


We prove that the Canonical Distortion Measure (CDM) [2, 3] is the optimal distance measure to use for I nearest-neighbour (l-NN) classifi(cid:173) cation, and show that it reduces to squared Euclidean distance in feature space for function classes that can be expressed as linear combinations of a fixed set of features. PAC-like bounds are given on the sample(cid:173) complexity required to learn the CDM. An experiment is presented in which a neural network CDM was learnt for a Japanese OCR environ(cid:173) ment and then used to do I-NN classification.