In this setting, each pattern, represented as an n-dimensional feature vector, is associated with a discrete pattern class, or state of nature (Duda and Hart, 1973). Using available information, (e.g., a statistically representative set of labeled feature vectors

In this setting, each pattern, represented as an n-dimensional feature vector, is associated with a discrete pattern class, or state of nature (Duda and Hart, 1973). Using available information, (e.g., a statistically representative set of labeled feature vectors

Local algorithms such as K-nearest neighbor (NN) perform well in pattern recognition, even though they often assume the simplest distance on the pattern space. It has recently been shown (Simard et al. 1993) that the performance can be further improved by incorporating invariance to specific transformations in the underlying distance metric - the so called tangent distance. The resulting classifier, however, can be prohibitively slow and memory intensive due to the large amount of prototypes that need to be stored and used in the distance comparisons. In this paper we address this problem for the tangent distance algorithm, by developing rich models for representing large subsets of the prototypes. Our leading example of prototype model is a low-dimensional (12) hyperplane defined by a point and a set of basis or tangent vectors.

Local algorithms such as K-nearest neighbor (NN) perform well in pattern recognition, even though they often assume the simplest distance on the pattern space. It has recently been shown (Simard et al. 1993) that the performance can be further improved by incorporating invariance to specific transformations in the underlying distance metric - the so called tangent distance. The resulting classifier, however, can be prohibitively slow and memory intensive due to the large amount of prototypes that need to be stored and used in the distance comparisons. In this paper we address this problem for the tangent distance algorithm, by developing rich models for representing large subsets of the prototypes. Our leading example of prototype model is a low-dimensional (12) hyperplane defined by a point and a set of basis or tangent vectors.

Local algorithms such as K-nearest neighbor (NN) perform well in pattern recognition, eventhough they often assume the simplest distance on the pattern space. It has recently been shown (Simard et al. 1993) that the performance can be further improved by incorporating invariance to specific transformations in the underlying distance metric - the so called tangent distance. The resulting classifier, however, canbe prohibitively slow and memory intensive due to the large amount of prototypes that need to be stored and used in the distance comparisons. In this paper we address this problem for the tangent distance algorithm, by developing richmodels for representing large subsets of the prototypes. Our leading example of prototype model is a low-dimensional (12) hyperplane defined by a point and a set of basis or tangent vectors.

Four versions of a k-nearest neighbor algorithm with locally adaptive k are introduced and compared to the basic k-nearest neighbor algorithm (kNN). Locally adaptive kNN algorithms choose the value of k that should be used to classify a query by consulting the results of cross-validation computations in the local neighborhood of the query. Local kNN methods are shown to perform similar to kNN in experiments with twelve commonly used data sets. Encouraging results in three constructed tasks show that local methods can significantly outperform kNN in specific applications. Local methods can be recommended for online learning and for applications where different regions of the input space are covered by patterns solving different sub-tasks.

Four versions of a k-nearest neighbor algorithm with locally adaptive k are introduced and compared to the basic k-nearest neighbor algorithm (kNN). Locally adaptive kNN algorithms choose the value of k that should be used to classify a query by consulting the results of cross-validation computations in the local neighborhood of the query. Local kNN methods are shown to perform similar to kNN in experiments with twelve commonly used data sets. Encouraging results in three constructed tasks show that local methods can significantly outperform kNN in specific applications. Local methods can be recommended for online learning and for applications where different regions of the input space are covered by patterns solving different sub-tasks.

Four versions of a k-nearest neighbor algorithm with locally adaptive kare introduced and compared to the basic k-nearest neighbor algorithm (kNN). Locally adaptive kNN algorithms choose the value of k that should be used to classify a query by consulting the results of cross-validation computations in the local neighborhood of the query. Local kNN methods are shown to perform similar to kNN in experiments with twelve commonly used data sets. Encouraging resultsin three constructed tasks show that local methods can significantly outperform kNN in specific applications. Local methods can be recommended for online learning and for applications wheredifferent regions of the input space are covered by patterns solving different sub-tasks.

Memory-based classification algorithms such as radial basis functions or K-nearest neighbors typically rely on simple distances (Euclidean, dot product...), which are not particularly meaningful on pattern vectors. More complex, better suited distance measures are often expensive and rather ad-hoc (elastic matching, deformable templates). We propose a new distance measure which (a) can be made locally invariant to any set of transformations of the input and (b) can be computed efficiently. We tested the method on large handwritten character databases provided by the Post Office and the NIST. Using invariances with respect to translation, rotation, scaling, shearing and line thickness, the method consistently outperformed all other systems tested on the same databases.

Memory-based classification algorithms such as radial basis functions or K-nearest neighbors typically rely on simple distances (Euclidean, dot product...), which are not particularly meaningful on pattern vectors. More complex, better suited distance measures are often expensive and rather ad-hoc (elastic matching, deformable templates). We propose a new distance measure which (a) can be made locally invariant to any set of transformations of the input and (b) can be computed efficiently. We tested the method on large handwritten character databases provided by the Post Office and the NIST. Using invariances with respect to translation, rotation, scaling, shearing and line thickness, the method consistently outperformed all other systems tested on the same databases.