Various problems in machine learning, databases, and statistics involve pairwise distances among a set of objects. It is often desirable for these distances to satisfy the properties of a metric, especially the triangle inequality. Applications where metric data is useful include clustering, classification, metric-based indexing, and approximation algorithms for various graph problems. This pap...

Many practical applications in machine learning require pairwise distances among a set of objects. It is often desirable that these distance measurements satisfy the properties of a metric, especially the triangle inequality. Applications that could benefit from the metric property include data clustering and metric-based indexing of databases. In this paper, we present the metric nearness prob...

we study algebraic properties of categories of merotopic, nearness, and filter algebras. we show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. the forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...