// 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 support vector machine
utilities from the dlib C++ Library. In particular, we show how to use the
C parametrization of the SVM in this example.
This example creates a simple set of data to train on and then shows
you how to use the cross validation and svm 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 svm functions use column vectors to contain a lot of the data on
// which 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. You can use your own custom
// kernels with these tools as well, see custom_trainer_ex.cpp for an
// example.
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 (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 it.
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]);
// Now that we have some data we want to train on it. However, there are
// two parameters to the training. These are the C and gamma parameters.
// Our choice for these parameters will influence how good the resulting
// decision function is. To test how good a particular choice of these
// 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 above. 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. 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 svm_c_trainer object that uses our kernel
// type.
svm_c_trainer<kernel_type> trainer;
// Now we loop over some different C and gamma values to see how good they
// are. Note that this is a very simple way to try out a few possible
// parameter choices. You should look at the model_selection_ex.cpp program
// for examples of more sophisticated strategies for determining good
// parameter choices.
cout << "doing cross validation" << endl;
for (double gamma = 0.00001; gamma <= 1; gamma *= 5)
{
for (double C = 1; C < 100000; C *= 5)
{
// tell the trainer the parameters we want to use
trainer.set_kernel(kernel_type(gamma));
trainer.set_c(C);
cout << "gamma: " << gamma << " C: " << C;
// Print out the cross validation accuracy for 3-fold cross validation using
// the current gamma and C. 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 good
// values for C and gamma for this problem are 5 and 0.15625 respectively.
// So that is what we will use.
// Now we train on the full set of data and obtain the resulting decision
// function. 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(0.15625));
trainer.set_c(5);
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 SVM training and save the results
// print out the number of support vectors in the resulting decision function
cout << "\nnumber of support 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.
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;
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 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_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;
// Note that there is also an example program that comes with dlib called
// the file_to_code_ex.cpp example. It is a simple program that takes a
// file and outputs a piece of C++ code that is able to fully reproduce the
// file's contents in the form of a std::string object. So you can use that
// along with the std::istringstream to save learned decision functions
// inside your actual C++ code files if you want.
// Lastly, note that the decision functions we trained above involved well
// over 200 basis vectors. Support vector machines in general tend to find
// decision functions that involve a lot of basis vectors. This is
// significant because the more basis vectors in a decision function, the
// longer it takes to classify new examples. So dlib provides the ability
// to find an approximation to the normal output of a trainer using fewer
// basis vectors.
// Here we determine the cross validation accuracy when we approximate the
// output using only 10 basis vectors. To do this we use the reduced2()
// function. It takes a trainer object and the number of basis vectors to
// use and returns a new trainer object that applies the necessary post
// processing during the creation of decision function objects.
cout << "\ncross validation accuracy with only 10 support vectors: "
<< cross_validate_trainer(reduced2(trainer,10), samples, labels, 3);
// Let's print out the original cross validation score too for comparison.
cout << "cross validation accuracy with all the original support vectors: "
<< cross_validate_trainer(trainer, samples, labels, 3);
// When you run this program you should see that, for this problem, you can
// reduce the number of basis vectors down to 10 without hurting the cross
// validation accuracy.
// To get the reduced decision function out we would just do this:
learned_function.function = reduced2(trainer,10).train(samples, labels);
// And similarly for the probabilistic_decision_function:
learned_pfunct.function = train_probabilistic_decision_function(reduced2(trainer,10), samples, labels, 3);
}