Added an RVM example

--HG--
extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%402511

examples/CMakeLists.txt

@@ -47,6 +47,7 @@ add_example(multithreaded_object_ex)
 add_example(pipe_ex)
 add_example(queue_ex)
 add_example(rank_features_ex)
+add_example(rvm_ex)
 add_example(server_http_ex)
 add_example(sockets_ex)
 add_example(sockets_ex_2)

examples/rvm_ex.cpp

+/*
+
+    This is an example illustrating the use of the relevance vector machine
+    utilities from the dlib C++ Library.  
+
+    This example creates a simple set of data to train on and then shows
+    you how to use the cross validation and rvm training functions
+    to find a good decision function that can classify examples in our
+    data set.
+
+
+    The data used in this example will be 2 dimensional data and will
+    come from a distribution where points with a distance less than 10
+    from the origin are labeled +1 and all other points are labeled
+    as -1.
+        
+*/
+
+
+#include <iostream>
+#include "dlib/svm.h"
+
+using namespace std;
+using namespace dlib;
+
+
+int main()
+{
+    // The rvm functions use column vectors to contain a lot of the data on which they they 
+    // operate. So the first thing we do here is declare a convenient typedef.  
+
+    // This typedef declares a matrix with 2 rows and 1 column.  It will be the
+    // object that contains each of our 2 dimensional samples.   (Note that if you wanted 
+    // more than 2 features in this vector you can simply change the 2 to something else.
+    // Or if you don't know how many features you want until runtime then you can put a 0
+    // here and use the matrix.set_size() member function)
+    typedef matrix<double, 2, 1> sample_type;
+
+    // This is a typedef for the type of kernel we are going to use in this example.
+    // In this case I have selected the radial basis kernel that can operate on our
+    // 2D sample_type objects
+    typedef radial_basis_kernel<sample_type> kernel_type;
+
+
+    // Now we make objects to contain our samples and their respective labels.
+    std::vector<sample_type> samples;
+    std::vector<double> labels;
+
+    // Now lets put some data into our samples and labels objects.  We do this
+    // by looping over a bunch of points and labeling them according to their
+    // distance from the origin.
+    for (int r = -20; r <= 20; ++r)
+    {
+        for (int c = -20; c <= 20; ++c)
+        {
+            sample_type samp;
+            samp(0) = r;
+            samp(1) = c;
+            samples.push_back(samp);
+
+            // if this point is less than 10 from the origin
+            if (sqrt((double)r*r + c*c) <= 10)
+                labels.push_back(+1);
+            else
+                labels.push_back(-1);
+
+        }
+    }
+
+
+    // Here we normalize all the samples by subtracting their mean and dividing by their standard deviation.
+    // This is generally a good idea since it often heads off numerical stability problems and also 
+    // prevents one large feature from smothering others.  Doing this doesn't matter much in this example
+    // so I'm just doing this here so you can see an easy way to accomplish this with 
+    // the library.  
+    const sample_type m(mean(vector_to_matrix(samples)));  // compute a mean vector
+    const sample_type sd(reciprocal(sqrt(variance(vector_to_matrix(samples))))); // compute a standard deviation vector
+    // now normalize each sample
+    for (unsigned long i = 0; i < samples.size(); ++i)
+        samples[i] = pointwise_multiply(samples[i] - m, sd); 
+
+
+
+    // Now that we have some data we want to train on it.  However, there is a parameter to the 
+    // training.  This is the gamma parameter of the RBF kernel.  Our choice for this parameter will 
+    // influence how good the resulting decision function is.  To test how good a particular choice of
+    // kernel parameters are we can use the cross_validate_trainer() function to perform n-fold cross
+    // validation on our training data.  However, there is a problem with the way we have sampled 
+    // our distribution.  The problem is that there is a definite ordering to the samples.  
+    // That is, the first half of the samples look like they are from a different distribution 
+    // than the second half do.  This would screw up the cross validation process but we can 
+    // fix it by randomizing the order of the samples with the following function call.
+    randomize_samples(samples, labels);
+
+
+    // here we make an instance of the rvm_trainer object that uses our kernel type.
+    rvm_trainer<kernel_type> trainer;
+
+    // Now we loop over some different gamma values to see how good they are.  Note
+    // that this is just a simple brute force way to try out a few possible parameter 
+    // choices.  You may want to investigate more sophisticated strategies for determining 
+    // good parameter choices.
+    cout << "doing cross validation" << endl;
+    for (double gamma = 0.00001; gamma <= 1; gamma += 0.1)
+    {
+        // tell the trainer the parameters we want to use
+        trainer.set_kernel(kernel_type(gamma));
+
+        cout << "gamma: " << gamma;
+        // Print out the cross validation accuracy for 3-fold cross validation using the current gamma.  
+        // cross_validate_trainer() returns a row vector.  The first element of the vector is the fraction
+        // of +1 training examples correctly classified and the second number is the fraction of -1 training 
+        // examples correctly classified.
+        cout << "     cross validation accuracy: " << cross_validate_trainer(trainer, samples, labels, 3);
+    }
+
+
+    // From looking at the output of the above loop it turns out that a good value for 
+    // gamma for this problem is 0.1.  So that is what we will use.
+
+    // Now we train on the full set of data and obtain the resulting decision function.  We use the
+    // value of 0.1 for gamma.  The decision function will return values >= 0 for samples it predicts
+    // are in the +1 class and numbers < 0 for samples it predicts to be in the -1 class.
+    trainer.set_kernel(kernel_type(0.1));
+    decision_function<kernel_type> learned_decision_function = trainer.train(samples, labels);
+
+    // print out the number of support vectors in the resulting decision function
+    cout << "\nnumber of support vectors in our learned_decision_function is " 
+         << learned_decision_function.support_vectors.nr() << endl;
+
+    // now lets try this decision_function on some samples we haven't seen before 
+    sample_type sample;
+
+    sample(0) = 3.123;
+    sample(1) = 2;
+    // don't forget that we have to normalize each new sample the same way we did for the training samples.
+    sample = pointwise_multiply(sample-m, sd);
+
+    cout << "This sample should be >= 0 and it is classified as a " << learned_decision_function(sample) << endl;
+
+    sample(0) = 3.123;
+    sample(1) = 9.3545;
+    sample = pointwise_multiply(sample-m, sd);
+    cout << "This sample should be >= 0 and it is classified as a " << learned_decision_function(sample) << endl;
+
+    sample(0) = 13.123;
+    sample(1) = 9.3545;
+    sample = pointwise_multiply(sample-m, sd);
+    cout << "This sample should be < 0 and it is classified as a " << learned_decision_function(sample) << endl;
+
+    sample(0) = 13.123;
+    sample(1) = 0;
+    sample = pointwise_multiply(sample-m, sd);
+    cout << "This sample should be < 0 and it is classified as a " << learned_decision_function(sample) << endl;
+
+
+    // We can also train a decision function that reports a well conditioned probability 
+    // instead of just a number > 0 for the +1 class and < 0 for the -1 class.  An example 
+    // of doing that follows:
+    probabilistic_decision_function<kernel_type> learned_probabilistic_decision_function;  
+    learned_probabilistic_decision_function = train_probabilistic_decision_function(trainer, samples, labels, 3);
+    // Now we have a function that returns the probability that a given sample is of the +1 class.  
+
+    // print out the number of support vectors in the resulting decision function.  
+    // (it should be the same as in the one above)
+    cout << "\nnumber of support vectors in our learned_probabilistic_decision_function is " 
+         << learned_probabilistic_decision_function.decision_funct.support_vectors.nr() << endl;
+
+    sample(0) = 3.123;
+    sample(1) = 2;
+    sample = pointwise_multiply(sample-m, sd);
+    cout << "This +1 example should have high probability.  It's probability is: " 
+         << learned_probabilistic_decision_function(sample) << endl;
+
+    sample(0) = 3.123;
+    sample(1) = 9.3545;
+    sample = pointwise_multiply(sample-m, sd);
+    cout << "This +1 example should have high probability.  It's probability is: " 
+         << learned_probabilistic_decision_function(sample) << endl;
+
+    sample(0) = 13.123;
+    sample(1) = 9.3545;
+    sample = pointwise_multiply(sample-m, sd);
+    cout << "This -1 example should have low probability.  It's probability is: " 
+         << learned_probabilistic_decision_function(sample) << endl;
+
+    sample(0) = 13.123;
+    sample(1) = 0;
+    sample = pointwise_multiply(sample-m, sd);
+    cout << "This -1 example should have low probability.  It's probability is: " 
+         << learned_probabilistic_decision_function(sample) << endl;
+
+
+}
+