Weighting vectors for machine learning: numerical harmonic analysis applied to boundary detection

Understand

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space.

• The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space.
• Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection.
• We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM.