Why do we need the auxiliary vector representation for the metric pattern recognition problem?

Description

"Direct" pattern recognition algorithms in metric spaces, i.e., those that do not use auxiliary vector space, are inferior to the pattern recognition algorithms that rely on the vector approximation of the original, metric, recognition problem. The critical issues associated with the role of the auxiliary vector space representation for the metric pattern recognition problem are considered. Keywords: Pattern recognition in Metric Spaces, Efficiency, Auxiliary Vector Representation.