// 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;
}