Comparison of ontology alignment systems across single matching task via
  the McNemar's test
  Ontology alignment is widely-used to find the correspondences between
different ontologies in diverse fields.After discovering the alignments,several
performance scores are available to evaluate them.The scores typically require
the identified alignment and a reference containing the underlying actual
correspondences of the given ontologies.The current trend in the alignment
evaluation is to put forward a new score(e.g., precision, weighted precision,
etc.)and to compare various alignments by juxtaposing the obtained scores.
However,it is substantially provocative to select one measure among others for
comparison.On top of that, claiming if one system has a better performance than
one another cannot be substantiated solely by comparing two scalars.In this
paper,we propose the statistical procedures which enable us to theoretically
favor one system over one another.The McNemar's test is the statistical means
by which the comparison of two ontology alignment systems over one matching
task is drawn.The test applies to a 2x2 contingency table which can be
constructed in two different ways based on the alignments,each of which has
their own merits/pitfalls.The ways of the contingency table construction and
various apposite statistics from the McNemar's test are elaborated in minute
detail.In the case of having more than two alignment systems for comparison,
the family-wise error rate is expected to happen. Thus, the ways of preventing
such an error are also discussed.A directed graph visualizes the outcome of the
McNemar's test in the presence of multiple alignment systems.From this graph,
it is readily understood if one system is better than one another or if their
differences are imperceptible.The proposed statistical methodologies are
applied to the systems participated in the OAEI 2016 anatomy track, and also
compares several well-known similarity metrics for the same matching problem.
