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+// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
+/*
+ This is an example illustrating the use of the kernel ridge 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 kernel ridge 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 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 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 krr_trainer object. This is the
+ // object that we will later use to do the training.
+ krr_trainer<kernel_type> trainer;
+
+ // Here we set the kernel we want to use for training. The radial_basis_kernel
+ // has a parameter called gamma that we need to determine. As a rule of thumb, a good
+ // gamma to try is 1.0/(mean squared distance between your sample points). So
+ // below we are using a similar value computed from at most 2000 randomly selected
+ // samples.
+ const double gamma = 3.0/compute_mean_squared_distance(randomly_subsample(samples, 2000));
+ cout << "using gamma of " << gamma << endl;
+ trainer.set_kernel(kernel_type(gamma));
+
+ // 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:
+ //using gamma of 0.075
+ // 0.239389 0.239389
+ // 0.998334 0.998362
+ // -0.189201 -0.189254
+ // -0.191785 -0.186618
+
+ // The first column is the true value of the sinc function and the second
+ // column is the output from the krr estimate.
+
+
+ // Note that the krr_trainer has the ability to tell us the leave-one-out predictions
+ // for each sample.
+ std::vector<double> loo_values;
+ trainer.train(samples, labels, loo_values);
+ cout << "mean squared LOO error: " << mean_squared_error(labels,loo_values) << endl;
+ cout << "R^2 LOO value: " << r_squared(labels,loo_values) << endl;
+ // Which outputs the following:
+ // mean squared LOO error: 8.29575e-07
+ // R^2 LOO value: 0.999995
+
+
+
+
+
+ // Another thing that is worth knowing is that just about everything in dlib is serializable.
+ // So for example, you can save the test object to disk and recall it later like so:
+ serialize("saved_function.dat") << test;
+
+ // Now let's open that file back up and load the function object it contains.
+ deserialize("saved_function.dat") >> test;
+
+}
+
+