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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 creates a simple set of data to train on and then shows
-    you how to use the kernel ridge regression tool 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 13
-    from the origin are labeled +1 and all other points are labeled
-    as -1.  All together, the dataset will contain 10201 sample points.
-        
-*/
-
-
-#include <iostream>
-#include <dlib/svm.h>
-
-using namespace std;
-using namespace dlib;
-
-
-int main()
-{
-    // 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 let's 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 (double r = -20; r <= 20; r += 0.4)
-    {
-        for (double c = -20; c <= 20; c += 0.4)
-        {
-            sample_type samp;
-            samp(0) = r;
-            samp(1) = c;
-            samples.push_back(samp);
-
-            // if this point is less than 13 from the origin
-            if (sqrt((double)r*r + c*c) <= 13)
-                labels.push_back(+1);
-            else
-                labels.push_back(-1);
-
-        }
-    }
-
-    cout << "samples generated: " << samples.size() << endl;
-    cout << "  number of +1 samples: " << sum(mat(labels) > 0) << endl;
-    cout << "  number of -1 samples: " << sum(mat(labels) < 0) << endl;
-
-    // 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.  
-    vector_normalizer<sample_type> normalizer;
-    // let the normalizer learn the mean and standard deviation of the samples
-    normalizer.train(samples);
-    // now normalize each sample
-    for (unsigned long i = 0; i < samples.size(); ++i)
-        samples[i] = normalizer(samples[i]); 
-
-
-    // here we make an instance of the krr_trainer object that uses our kernel type.
-    krr_trainer<kernel_type> trainer;
-
-    // The krr_trainer has the ability to perform leave-one-out cross-validation.
-    // It does this to automatically determine the regularization parameter.  Since
-    // we are performing classification instead of regression we should be sure to
-    // call use_classification_loss_for_loo_cv().  This function tells it to measure 
-    // errors in terms of the number of classification mistakes instead of mean squared 
-    // error between decision function output values and labels.  
-    trainer.use_classification_loss_for_loo_cv();
-
-
-    // Now we loop over some different gamma values to see how good they are.  
-    cout << "\ndoing leave-one-out cross-validation" << endl;
-    for (double gamma = 0.000001; gamma <= 1; gamma *= 5)
-    {
-        // tell the trainer the parameters we want to use
-        trainer.set_kernel(kernel_type(gamma));
-
-        // loo_values will contain the LOO predictions for each sample.  In the case
-        // of perfect prediction it will end up being a copy of labels.
-        std::vector<double> loo_values; 
-        trainer.train(samples, labels, loo_values);
-
-        // Print gamma and the fraction of samples correctly classified during LOO cross-validation.
-        const double classification_accuracy = mean_sign_agreement(labels, loo_values);
-        cout << "gamma: " << gamma << "     LOO accuracy: " << classification_accuracy << endl;
-    }
-
-
-    // From looking at the output of the above loop it turns out that a good value for 
-    // gamma for this problem is 0.000625.  So that is what we will use.
-    trainer.set_kernel(kernel_type(0.000625));
-    typedef decision_function<kernel_type> dec_funct_type;
-    typedef normalized_function<dec_funct_type> funct_type;
-
-
-    // Here we are making an instance of the normalized_function object.  This object provides a convenient 
-    // way to store the vector normalization information along with the decision function we are
-    // going to learn.  
-    funct_type learned_function;
-    learned_function.normalizer = normalizer;  // save normalization information
-    learned_function.function = trainer.train(samples, labels); // perform the actual training and save the results
-
-    // print out the number of basis vectors in the resulting decision function
-    cout << "\nnumber of basis vectors in our learned_function is " 
-         << learned_function.function.basis_vectors.size() << endl;
-
-    // Now let's try this decision_function on some samples we haven't seen before.
-    // 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.
-    sample_type sample;
-
-    sample(0) = 3.123;
-    sample(1) = 2;
-    cout << "This is a +1 class example, the classifier output is " << learned_function(sample) << endl;
-
-    sample(0) = 3.123;
-    sample(1) = 9.3545;
-    cout << "This is a +1 class example, the classifier output is " << learned_function(sample) << endl;
-
-    sample(0) = 13.123;
-    sample(1) = 9.3545;
-    cout << "This is a -1 class example, the classifier output is " << learned_function(sample) << endl;
-
-    sample(0) = 13.123;
-    sample(1) = 0;
-    cout << "This is a -1 class example, the classifier output is " << learned_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:
-    typedef probabilistic_decision_function<kernel_type> probabilistic_funct_type;  
-    typedef normalized_function<probabilistic_funct_type> pfunct_type;
-
-    // The train_probabilistic_decision_function() is going to perform 3-fold cross-validation.
-    // So it is important that the +1 and -1 samples be distributed uniformly across all the folds.
-    // calling randomize_samples() will make sure that is the case.   
-    randomize_samples(samples, labels);
-
-    pfunct_type learned_pfunct; 
-    learned_pfunct.normalizer = normalizer;
-    learned_pfunct.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 basis vectors in the resulting decision function.  
-    // (it should be the same as in the one above)
-    cout << "\nnumber of basis vectors in our learned_pfunct is " 
-         << learned_pfunct.function.decision_funct.basis_vectors.size() << endl;
-
-    sample(0) = 3.123;
-    sample(1) = 2;
-    cout << "This +1 class example should have high probability.  Its probability is: " 
-         << learned_pfunct(sample) << endl;
-
-    sample(0) = 3.123;
-    sample(1) = 9.3545;
-    cout << "This +1 class example should have high probability.  Its probability is: " 
-         << learned_pfunct(sample) << endl;
-
-    sample(0) = 13.123;
-    sample(1) = 9.3545;
-    cout << "This -1 class example should have low probability.  Its probability is: " 
-         << learned_pfunct(sample) << endl;
-
-    sample(0) = 13.123;
-    sample(1) = 0;
-    cout << "This -1 class example should have low probability.  Its probability is: " 
-         << learned_pfunct(sample) << endl;
-
-
-
-    // Another thing that is worth knowing is that just about everything in dlib is serializable.
-    // So for example, you can save the learned_pfunct object to disk and recall it later like so:
-    serialize("saved_function.dat") << learned_pfunct;
-
-    // Now let's open that file back up and load the function object it contains.
-    deserialize("saved_function.dat") >> learned_pfunct;
-
-}
-