Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Practical applications of metric space magnitude and weighting vectors   Metric space magnitude, an active subject of research in algebraic topology,
originally arose in the context of biology, where it was used to represent the
effective number of distinct species in an environment. In a more general
setting, the magnitude of a metric space is a real number that aims to quantify
the effective number of distinct points in the space. The contribution of each
point to a metric space's global magnitude, which is encoded by the {\em
weighting vector}, captures much of the underlying geometry of the original
metric space.
  Surprisingly, when the metric space is Euclidean, the weighting vector also
serves as an effective tool for boundary detection. This allows the weighting
vector to serve as the foundation of novel algorithms for classic machine
learning tasks such as classification, outlier detection and active learning.
We demonstrate, using experiments and comparisons on classic benchmark
datasets, the promise of the proposed magnitude and weighting vector-based
approaches.

5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn