TY - JOUR

T1 - Classification based on prototypes with spheres of influence

AU - Anthony, Martin

AU - Ratsaby, Joel

N1 - Publisher Copyright:
© 2017 Elsevier Inc.

PY - 2017/10

Y1 - 2017/10

N2 - We present a family of binary classifiers and analyse their performance. Each classifier is determined by a set of ‘prototypes’, with given labels. The classification of a given point is determined through the sign of a discriminant function. For each prototype, its sphere of influence is the largest sphere centred on it that contains no prototypes of opposite label, and, given a point to be classified, there is a contribution to the discriminant function at that point from precisely those prototypes whose spheres of influence contain the point. This contribution is positive from positive prototypes and negative from negative prototypes. These contributions are larger in absolute value the closer the point is (relative to the sphere's radius) to the prototype. We quantify the generalization error of such classifiers in a standard probabilistic learning model which involves the values of the discriminant function on the points of a random training sample.

AB - We present a family of binary classifiers and analyse their performance. Each classifier is determined by a set of ‘prototypes’, with given labels. The classification of a given point is determined through the sign of a discriminant function. For each prototype, its sphere of influence is the largest sphere centred on it that contains no prototypes of opposite label, and, given a point to be classified, there is a contribution to the discriminant function at that point from precisely those prototypes whose spheres of influence contain the point. This contribution is positive from positive prototypes and negative from negative prototypes. These contributions are larger in absolute value the closer the point is (relative to the sphere's radius) to the prototype. We quantify the generalization error of such classifiers in a standard probabilistic learning model which involves the values of the discriminant function on the points of a random training sample.

KW - Classification

KW - Generalisation error

KW - Learning

UR - http://www.scopus.com/inward/record.url?scp=85028592169&partnerID=8YFLogxK

U2 - 10.1016/j.ic.2017.08.004

DO - 10.1016/j.ic.2017.08.004

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AN - SCOPUS:85028592169

SN - 0890-5401

VL - 256

SP - 372

EP - 380

JO - Information and Computation

JF - Information and Computation

ER -