Added the kcentroid example

--HG--
extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%402257

examples/CMakeLists.txt

@@ -33,6 +33,7 @@ add_example(dir_nav_ex)
 add_example(file_to_code_ex)
 add_example(gui_api_ex)
 add_example(image_ex)
+add_example(kcentroid_ex)
 add_example(krls_ex)
 add_example(logger_ex)
 add_example(logger_ex_2)

examples/kcentroid_ex.cpp

+/*
+    This is an example illustrating the use of the kcentroid object 
+    from the dlib C++ Library.
+
+    The kcentroid object is an implementation of an algorithm that recursively
+    computes the centroid (i.e. average) of a set of points.  The interesting
+    thing about dlib::kcentroid is that it does so in a kernel induced feature
+    space.  This means that you can use it as a non-linear one-class classifier.
+    So you might use it to perform online novelty detection.  
+    
+    This example will train an instance of it on points 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 the krls
+// object.
+double sinc(double x)
+{
+    if (x == 0)
+        return 1;
+    return sin(x)/x;
+}
+
+int main()
+{
+    // Here we declare that our samples will be 2 dimensional column vectors.  
+    typedef matrix<double,2,1> 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 kcentroid object.  The first argument to the constructor
+    // is the kernel we wish to use.  The second is a parameter that determines the numerical 
+    // accuracy with which the object will perform part of the learning algorithm.  Generally
+    // smaller values give better results but cause the algorithm to run slower.  You just have
+    // to play with it to decide what balance of speed and accuracy is right for your problem.
+    // Here we have set it to 0.01.
+    kcentroid<kernel_type> test(kernel_type(0.1),0.01);
+
+    // now we train our object on a few samples of the sinc function.
+    sample_type m;
+    for (double x = -15; x <= 8; x += 1)
+    {
+        m(0) = x;
+        m(1) = sinc(x);
+        test.train(m);
+    }
+
+
+    // lets output the distance from the centroid to some points that are from the sinc function.
+    // These numbers should all be similar
+    cout << "Points that are on the sinc function:\n";
+    m(0) = -1.5; m(1) = sinc(m(0)); cout << "   " << test(m) << endl;
+    m(0) = -1.5; m(1) = sinc(m(0)); cout << "   " << test(m) << endl;
+    m(0) = -0;   m(1) = sinc(m(0)); cout << "   " << test(m) << endl;
+    m(0) = -0.5; m(1) = sinc(m(0)); cout << "   " << test(m) << endl;
+    m(0) = -4.1; m(1) = sinc(m(0)); cout << "   " << test(m) << endl;
+    m(0) = -1.5; m(1) = sinc(m(0)); cout << "   " << test(m) << endl;
+    m(0) = -0.5; m(1) = sinc(m(0)); cout << "   " << test(m) << endl;
+
+    // lets output the distance from the centroid to some points that are NOT from the sinc function.
+    // These numbers should all be bigger than previous set of numbers.  In fact, if you computed the
+    // standard deviation of the above set of numbers you would note that these following numbers
+    // are many standard deviations away from them which indicates that they are highly unlike
+    // the set of points from above.
+    cout << "Points that are NOT on the sinc function:\n";
+    m(0) = -1.5; m(1) = sinc(m(0))+4;   cout << "   " << test(m) << endl;
+    m(0) = -1.5; m(1) = sinc(m(0))+3;   cout << "   " << test(m) << endl;
+    m(0) = -0;   m(1) = -sinc(m(0));    cout << "   " << test(m) << endl;
+    m(0) = -0.5; m(1) = -sinc(m(0));    cout << "   " << test(m) << endl;
+    m(0) = -4.1; m(1) = sinc(m(0))+2;   cout << "   " << test(m) << endl;
+    m(0) = -1.5; m(1) = sinc(m(0))+0.9; cout << "   " << test(m) << endl;
+    m(0) = -0.5; m(1) = sinc(m(0))+1;   cout << "   " << test(m) << endl;
+}
+
+