Cumulative Distribution Transform (CDT) has special properties with regards to classification. CDT can be useful in 'parsing out' variations (confounds) that are Lagrangian.
Discriminating data classes emanating from sensors is an important problem
with many applications in science and technology. We describe a new transform
for pattern identification that interprets patterns as probability density
functions, and has special properties with regards to classification. The
transform, which we denote as the Cumulative Distribution Transform (CDT) is
invertible, with well defined forward and inverse operations. We show that it
can be useful in `parsing out' variations (confounds) that are `Lagrangian'
(displacement and intensity variations) by converting these to `Eulerian'
(intensity variations) in transform space. This conversion is the basis for our
main result that describes when the CDT can allow for linear classification to
be possible in transform space. We also describe several properties of the
transform and show, with computational experiments that used both real and
simulated data, that the CDT can help render a variety of real world problems
simpler to solve.