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https://github.com/craigacp/mitoolbox

Mutual Information functions for C and MATLAB
https://github.com/craigacp/mitoolbox

c entropy matlab mutual-information

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Mutual Information functions for C and MATLAB

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README 

        
MIToolbox

=========

v3.0.1 for C/C++ and MATLAB/Octave



MIToolbox contains a set of functions to calculate information theoretic

quantities from data, such as the entropy and mutual information.  The toolbox

contains implementations of the most popular Shannon entropies, and also the

lesser known Renyi entropy. The toolbox also provides implementations of 

the weighted entropy and weighted mutual information from "Information Theory

with Application", S. Guiasu (1977). The toolbox only supports discrete distributions,

as opposed to continuous. All real-valued numbers will be processed by x = floor(x).



These functions are targeted for use with feature selection algorithms rather 

than communication channels and so expect all the data to be available before 

execution and sample their own probability distributions from the data.



All functions expect the inputs to be vectors or matrices of doubles.



Functions contained:

 - Entropy

 - Conditional Entropy

 - Mutual Information

 - Conditional Mutual Information

 - generating a joint variable

 - generating a probability distribution from a discrete random variable

 - Renyi's Entropy

 - Renyi's Mutual Information

 - Weighted Entropy

 - Weighted Mutual Information

 - Weighted Conditional Mutual Information



Note: all functions are calculated in log base 2, so return units of "bits".



MIToolbox works on discrete inputs, and all continuous values **must** be

discretised before use with MIToolbox. Real-valued inputs will be discretised

with x = floor(x) to ensure compatibility. MIToolbox produces unreliable

results when used with continuous inputs, runs slowly and uses much more memory

than usual. The discrete inputs should have small cardinality, MIToolbox will

treat values {1,10,100} the same way it treats {1,2,3} and the latter will be

both faster and use less memory. This limitation is due to the difficulties in

estimating information theoretic functions of continuous variables.



======



Examples:



```

>> y = [1 1 1 0 0]';

>> x = [1 0 1 1 0]';

```

```

>> mi(x,y)       %% mutual information I(X;Y)

ans =

    0.0200

```

```

>> h(x)          %% entropy H(X)

ans =

    0.9710

```

```

>> condh(x,y)    %% conditional entropy H(X|Y)

ans =

    0.9510

```

```

>> h( [x,y] )    %% joint entropy H(X,Y)

ans =

    1.9219

```

```

>> joint([x,y])  %% joint random variable XY

ans =

     1

     2

     1

     3

     4

```

======



All code is licensed under the 3-clause BSD license.



Compilation instructions:

 - MATLAB/OCTAVE 

    - run `CompileMIToolbox.m` from the `matlab` directory.

 - Linux C shared library 

    - run `make x86` or `make x64` for 32-bit or 64-bit versions respectively.

    - run `sudo make install` to install MIToolbox into `/usr/local/lib` and `/usr/local/include`

 - Windows C dll

	- install MinGW from https://sourceforge.net/projects/mingw-w64/

	- add MinGW binaries folders to PATH, e.g. `mingw/bin`, `mingw/msys/bin`

	- run `make x64_win` to compile a 64-bit Windows dll.



Update History

 - 08/02/2017 - v3.0.1 - Bug fix to ensure ANSI C compatibility.

 - 07/01/2017 - v3.0.0 - Refactored internals to expose integer information theoretic calculations.

 - 10/01/2016 - v2.1.2 - Relicense from LGPL to BSD. Added checks to ensure input MATLAB types are doubles.

 - 02/02/2015 - v2.1.1 - Fixed up the Makefile so it installs the headers too.

 - 22/02/2014 - v2.1  - Fixed a couple of bugs related to memory handling.

                     Added a make install for compatibility with PyFeast.

 - 30/07/2011 - v2.00 - Added implementations of the weighted entropy and weighted

                     mutual information. More cleanup of Mex entry point

                     to further check the inputs.

 - 08/11/2011 - v1.03 - Minor documentation changes to accompany the JMLR publication.

 - 15/10/2010 - v1.02 - Fixed bug where MIToolbox would cause a segmentation fault

                     if a x by 0 empty matrix was passed in. Now prints an 

                     error message and returns gracefully.

 - 02/09/2010 - v1.01 - Fixed a bug in CMIM.m where the last feature would not be 

                     selected first if it had the highest MI.

 - 07/07/2010 - v1.00 - Initial Release.