  This work briefly explores the possibility of approximating spatial distance
(alternatively, similarity) between data points using the Isolation Forest
method envisioned for outlier detection. The logic is similar to that of
isolation: the more similar or closer two points are, the more random splits it
will take to separate them. The separation depth between two points can be
standardized in the same way as the isolation depth, transforming it into a
distance metric that is limited in range, centered, and in compliance with the
axioms of distance. This metric presents some desirable properties such as
being invariant to the scales of variables or being able to account for
non-linear relationships between variables, which other metrics such as
Euclidean or Mahalanobis distance do not. Extensions to the Isolation Forest
method are also proposed for handling categorical variables and missing values,
resulting in a more generalizable and robust metric.
