Digital Signal Processing Reference
In-Depth Information
And for a point
p
on the Poincaré disk, the mapping with a point
k
on the Klein
disk is:
−
√
1
1
−
k
,
k
2
p
=
k
=
p
(16.44)
k
,
k
1
+
p
,
p
16.5 Software Library
16.5.1 Presentation
Several tools are already available to build mixture models, either for mixtures of
Gaussian distributions or for mixtures of other distributions. But these tools are
usually dedicated to a particular family of distributions.
In order to provide a unified and powerful framework for the manipulation of
arbitrary mixture models, we develop
pyMEF
,a
Python
library dedicated to the
mixtures of exponential families.
Given the success of the Gaussian mixture models, there are already numerous
other software available to deal with it:
•
some
R
packages: MCLUST (
http://www.stat.washington.edu/mclust/
) and MIX
(
http://icarus.math.mcmaster.ca/peter/mix/
),
•
MIXMOD
[
3
] which also works on multinomial and provides bindings for
Matlab
and
Scilab
,
•
PyMIX
[
10
], another
Python
library which goes beyond simple mixture with
Context-specific independence mixtures and dependence trees,
•
scikits.learn
,a
Python
module for machine learning (
http://scikit-learn.
sf.net
),
•
jMEF
[
15
,
9
] which is the only other library dealing with mixtures of exponential
families, written in
Java
.
Although exponential families other than normal distributions have been suc-
cessfully used in the literature (see [
11
] as an example for the Beta distribution),
it was made using an implementation specific to the underlying distribution per se.
The improvement of libraries such as
jMEF
and
pyMEF
is to introduce genericity:
changing the exponential family means simply changing a parameter of the Bregman
Soft clustering (equivalent to performing an EM task), and not completely rewriting
the algorithm.
Moreover, the choice of the good distribution is a difficult problem in itself, and
is often inspected experimentally, by looking at the shape of the histogram or by
comparing a performance score (the log-likelihood or any meaningful score in the
considered application) computed with mixtures of various distributions. It is worth
here to use a unified framework instead of using different libraries from various
sources with various interfaces.
The goal of the
pyMEF
library is to provide a consistent framework with various
algorithms to build mixtures (Bregman Soft clustering) and various Information-
