added an rvm regression example

--HG--
rename : examples/krls_ex.cpp => examples/rvm_regression_ex.cpp
extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%402513

examples/CMakeLists.txt

@@ -48,6 +48,7 @@ add_example(pipe_ex)
 add_example(queue_ex)
 add_example(rank_features_ex)
 add_example(rvm_ex)
+add_example(rvm_regression_ex)
 add_example(server_http_ex)
 add_example(sockets_ex)
 add_example(sockets_ex_2)

examples/rvm_regression_ex.cpp

+/*
+    This is an example illustrating the use of the RVM regression object 
+    from the dlib C++ Library.
+
+    This example will train on data from the sinc function.
+
+*/
+
+#include <iostream>
+#include <vector>
+
+#include "dlib/svm.h"
+
+using namespace std;
+using namespace dlib;
+
+// Here is the sinc function we will be trying to learn with rvm regression 
+double sinc(double x)
+{
+    if (x == 0)
+        return 1;
+    return sin(x)/x;
+}
+
+int main()
+{
+    // Here we declare that our samples will be 1 dimensional column vectors.  
+    typedef matrix<double,1,1> sample_type;
+
+    // Now we are making a typedef for the kind of kernel we want to use.  I picked the
+    // radial basis kernel because it only has one parameter and generally gives good
+    // results without much fiddling.
+    typedef radial_basis_kernel<sample_type> kernel_type;
+
+    // Here we declare an instance of the rvm_regression_trainer object.  This is the
+    // object that we will later use to do the training.
+    rvm_regression_trainer<kernel_type> trainer;
+    // Here we set the kernel we want to use for training.  The 0.05 is the gamma 
+    // parameter to the radial_basis_kernel.
+    trainer.set_kernel(kernel_type(0.05));
+
+    // Now sample some points from the sinc() function
+    sample_type m;
+    std::vector<sample_type> samples;
+    std::vector<double> labels;
+    for (double x = -10; x <= 4; x += 1)
+    {
+        m(0) = x;
+        samples.push_back(m);
+        labels.push_back(sinc(x));
+    }
+
+    // now train a function based on our sample points
+    decision_function<kernel_type> test = trainer.train(samples, labels);
+
+    // now we output the value of the sinc function for a few test points as well as the 
+    // value predicted by our regression.
+    m(0) = 2.5; cout << sinc(m(0)) << "   " << test(m) << endl;
+    m(0) = 0.1; cout << sinc(m(0)) << "   " << test(m) << endl;
+    m(0) = -4;  cout << sinc(m(0)) << "   " << test(m) << endl;
+    m(0) = 5.0; cout << sinc(m(0)) << "   " << test(m) << endl;
+
+    // The output is as follows:
+    //0.239389   0.240989
+    //0.998334   0.999538
+    //-0.189201   -0.188453
+    //-0.191785   -0.226516
+
+
+    // The first column is the true value of the sinc function and the second
+    // column is the output from the rvm estimate.  
+
+}
+
+