  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. As one consequence, we apply this new
insight to the task of outlier detection, and we demonstrate performance that
is competitive or exceeds performance of state-of-the-art techniques on
benchmark data sets. Under mild assumptions, we show the weighting vector,
which has computational cost of matrix inversion, can be efficiently
approximated in linear time. We show how nearest neighbor methods can
approximate solutions to the minimization problems defined by SVMs.
