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.

To measure the quality of a set of vector quantization points a means of measuring the distance between a random point and its quantization is required. Common metrics such as the {\em Hamming} and {\em Euclidean} metrics, while mathematically simple, are inappropriate for comparing natural signals such as speech or images. In this paper it is shown how an {\em environment} of functions on an input space $X$ induces a {\em canonical distortion measure} (CDM) on X. The depiction 'canonical" is justified because it is shown that optimizing the reconstruction error of X with respect to the CDM gives rise to optimal piecewise constant approximations of the functions in the environment. The CDM is calculated in closed form for several different function classes. An algorithm for training neural networks to implement the CDM is presented along with some encouraging experimental results.

We prove that the Canonical Distortion Measure (CDM) [2, 3] is the optimal distance measure to use for I nearest-neighbour (l-NN) classification, 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. PAClike bounds are given on the samplecomplexity required to learn the CDM. An experiment is presented in which a neural network CDM was learnt for a Japanese OCR environment and then used to do INN classification.

We prove that the Canonical Distortion Measure (CDM) [2, 3] is the optimal distance measure to use for I nearest-neighbour (l-NN) classification, 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. PAClike bounds are given on the samplecomplexity required to learn the CDM. An experiment is presented in which a neural network CDM was learnt for a Japanese OCR environment and then used to do INN classification.

We prove that the Canonical Distortion Measure (CDM) [2, 3] is the optimal distance measure to use for I nearest-neighbour (l-NN) classification, andshow 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.