Onetoone (invertible) transformations
Onetoone transformations do not change the
information content of the data but they are important for
feature conditioning prior to PDF estimation.
For 1:1 transformations,
the Jfunction (2.3) reduces to the absolute value
of the determinant of the Jacobian matrix (2.24),
The PDF projection theorem (2.2) may be thought of as a generalization of
the wellknown change of variables theorem from basic probability.
Let
, where
is an invertible and differentiable
multidimensional transformation. Then,

(2.24) 
where
is the
determinant of the Jacobian matrix of the transformation
Baggenstoss
20170519