svMathematica: A Machine Learning Mathematica package

svMathematica is a Wolfram Mathematica package implementing support vector-based learning algorithms.

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Install instructions

1. Download and uncompress the package in a directory contained in Mathematica's $Path variable. Suggested choices for a user-based installation are as in the following table:

   OS	Directory
   Mac OS X	~/Library/Mathematica/Applications
   Linux	~/.Mathematica/Applications

   where ~ denotes the user's home directory in Mac OS X and Linux.

   Analogously, suggested choices for a system-wide installation are as follows:

   OS	Directory
   Mac OS X	/Library/Mathematica/Applications
   Linux	~/AddOns/Applications

   where ~ denotes the Mathematica root directory.

2. The algorithms implemented in svMathemtica are based on external solvers that must be previouvsly installed in the correct location. In brackets there are my default locations.

   • Ampl and Snopt - (/usr/local/bin)
   • SvmLight - (/usr/local/bin)
   • Python - Default installation path (on my machine):/opt/local/bin
   Anyway if you have installed these programs in any other location, please modify the corrispondent simlink you will find into the package directory.
   
   If you want to use the python based implementation you must also install two additional packages:
   • CvxOpt
   • NumPy

Using the package

The package is loaded as follows

<<svMathematica`

The graphics routines to plot samples are: svmClassificationSamplePlot and svmRegressionSamplePlot. The first one plots classification samples and the second one is for regression samples.

grClassPoints = svmClassificationSamplePlot[pattern, label,Frame -> True]

grRegrPoints = svmRegressionSamplePlot[pattern, label, Frame ->True]

There are also routines to plot the classifier function or the regression function, respectively (The first argument in both routines will be explained after this example):

grClassifier = svmDecisionFunctionPlot[classifier, {x, 0, 1}, {y, 0, 1}, margin -> False];
Show[grClassPoints,grClassifier]

grRegressor = Plot[regressor, {x, 0, 1}, PlotRange -> All, AspectRatio -> 1/GoldenRatio, Frame -> True];
Show[grRegrPoints,grRegressor]

To get the classification function the routine is:

classifier = svmClassification[pattern, label, implementation -> svmClassificationPython, kernel -> "linear"]

Function[{svMathematica`Private`q$}, -1.09075 - 39.8389 {0.12426, 0.0648096}.svMathematica`Private`q$ + 50.1273 {0.222514, 0.326598}.svMathematica`Private`q$ - 10.2883 {0.996295, 0.450105}.svMathematica`Private`q$]

To get the regression function the routine is (kernel options is set for using a Gaussian kernel of parameter 0.4):

regressor = svmRegression[pattern, label, kernel -> {"Gaussian",0.4}];

>> Output suppressed here because it's too long <<

To know what options are provided by routines use Options:

Options[svmClassification]

{c -> \[Infinity], kernel -> "linear", bVarThreshold -> 0.0001,
implementation -> svmClassificationPython, verbose -> False,
classifierOutput -> "real", classifierInput -> "pattern"}

Send comments to malchiodi[at]dsi[dot]unimi[dot]it.