SVMGrad

SVMGrad is a compact library used to evaluate the decision function of a Gaussian RBF Kernel Support Vector Machine, as well as the its first Derivative (Gradient).

y = sign(Gamma(x))
Gamma   = \sum_{i=1}^{N_sv}\alpha_iy_ik(x,x_i) + b 
DGamma  = \sum_{i=1}^{N_sv}-1/2\sigma^2\alpha_iy_ik(x,x_i)(x-x_i)
DDGamma = ...

The evaluated SVM model can be learned with any toolbox: libSVM, SMVlight, EnsembleSVM, etc.. as long as the user creates a simplified struct model. In MATLAB one should create the following struct instance:

model.nClass: # of Classes (2 for binary)
model.nSV   : Total # of Support Vectors
model.b     : Offset for classification function
model.sigma : Gaussian RBF kernel Width
model.alphas: Values for the Lagrangian multipliers per SVs  [nSV]
model.y     : Labels corresponding to SVs                    [nSV]
model.SVs   : Set of Support Vectors                         [DxnSV]

Matlab Usage

In the ./matlab/ folder you can find an example script together with sample 2d datasets and learnt models (through libSVM). Make sure to add all subfolders to your current directory and run the following script:

2d_svmgrad_example.m

This should generate the following plot, which shows the svm Gamma being evaluated on a mesh of points as well as its gradient DGamma:

C++ Installation (Catkin package)

These instrutions are assuming you have a ROS environment and use catkin workspace to compile code. Clone this respository in your ./src folder and make sure that you have the armadillo library, you can install this by

sudo apt-get install libarmadillo-dev

Then, compile the package

$ cd ~/catkin_ws/
$ catkin_make

C++ Usage

First one must have an svm model in the format requested by svm_grad class, this can be generated with the writeSVMGradModel.m function in the matlab folder, then:

SVMGrad svm_(modelFilename);
x = load vector...              // Could Eigen::VectorXd or arma::vec<double> format
svm_.preComputeKernel(true);    // For fast derivative computation
gamma       = svm_.calculateGamma(x);
gamma_grad  = svm_.calculateGammaDerivative(x);

You can try the testing script as well, this was generated by compiling the library, type the following:

rosrun svm_grad test_svmgrad

This test will load a stored svm-model (the one generating the figure above) and a testing dataset. It will check for numerical errors and output average function computation time for Armadillo inputs as well as Eigen inputs:

SVM Model: /home/nbfigueroa/dev/catkin_ws/src/SVMGrad/matlab/models/2d-example2-svm.txt
model.D: 2
model.nSV: 40
model.b: -0.962694
model.sigma: 0.1

SVM Testing File: /home/nbfigueroa/dev/catkin_ws/src/SVMGrad/matlab/models/2d-example2-data.txt
data.D: 2
data.M: 500

---Testing Gamma and DGamma function with Armadillo Inputs---
Average Gamma Numerical Error: 4.8965e-09
Average Norm DGamma Numerical Error: 3.59996e-08
Average Time -Gamma+DGamma Calculation-: 6.944e-06

---Testing Gamma and DGamma function with Eigen Inputs---
Average Gamma Numerical Error: 4.8965e-09
Average Norm DGamma Numerical Error: 3.59996e-08
Average Time -Gamma+DGamma Calculation-: 7.248e-06

Note: Part of this code was derived from the ASVM library implemented by Dr. Ashwini Shukla.