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256 lines
12 KiB
256 lines
12 KiB
// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
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/*
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This is an example illustrating the use of the support vector machine
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utilities from the dlib C++ Library.
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This example creates a simple set of data to train on and then shows
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you how to use the cross validation and svm training functions
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to find a good decision function that can classify examples in our
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data set.
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The data used in this example will be 2 dimensional data and will
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come from a distribution where points with a distance less than 10
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from the origin are labeled +1 and all other points are labeled
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as -1.
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*/
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#include <iostream>
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#include <dlib/svm.h>
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using namespace std;
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using namespace dlib;
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int main()
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{
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// The svm functions use column vectors to contain a lot of the data on which they
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// operate. So the first thing we do here is declare a convenient typedef.
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// This typedef declares a matrix with 2 rows and 1 column. It will be the object that
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// contains each of our 2 dimensional samples. (Note that if you wanted more than 2
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// features in this vector you can simply change the 2 to something else. Or if you
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// don't know how many features you want until runtime then you can put a 0 here and
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// use the matrix.set_size() member function)
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typedef matrix<double, 2, 1> sample_type;
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// This is a typedef for the type of kernel we are going to use in this example. In
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// this case I have selected the radial basis kernel that can operate on our 2D
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// sample_type objects
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typedef radial_basis_kernel<sample_type> kernel_type;
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// Now we make objects to contain our samples and their respective labels.
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std::vector<sample_type> samples;
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std::vector<double> labels;
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// Now let's put some data into our samples and labels objects. We do this by looping
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// over a bunch of points and labeling them according to their distance from the
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// origin.
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for (int r = -20; r <= 20; ++r)
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{
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for (int c = -20; c <= 20; ++c)
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{
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sample_type samp;
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samp(0) = r;
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samp(1) = c;
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samples.push_back(samp);
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// if this point is less than 10 from the origin
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if (sqrt((double)r*r + c*c) <= 10)
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labels.push_back(+1);
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else
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labels.push_back(-1);
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}
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}
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// Here we normalize all the samples by subtracting their mean and dividing by their
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// standard deviation. This is generally a good idea since it often heads off
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// numerical stability problems and also prevents one large feature from smothering
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// others. Doing this doesn't matter much in this example so I'm just doing this here
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// so you can see an easy way to accomplish this with the library.
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vector_normalizer<sample_type> normalizer;
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// let the normalizer learn the mean and standard deviation of the samples
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normalizer.train(samples);
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// now normalize each sample
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for (unsigned long i = 0; i < samples.size(); ++i)
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samples[i] = normalizer(samples[i]);
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// Now that we have some data we want to train on it. However, there are two
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// parameters to the training. These are the nu and gamma parameters. Our choice for
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// these parameters will influence how good the resulting decision function is. To
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// test how good a particular choice of these parameters is we can use the
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// cross_validate_trainer() function to perform n-fold cross validation on our training
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// data. However, there is a problem with the way we have sampled our distribution
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// above. The problem is that there is a definite ordering to the samples. That is,
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// the first half of the samples look like they are from a different distribution than
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// the second half. This would screw up the cross validation process but we can fix it
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// by randomizing the order of the samples with the following function call.
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randomize_samples(samples, labels);
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// The nu parameter has a maximum value that is dependent on the ratio of the +1 to -1
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// labels in the training data. This function finds that value.
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const double max_nu = maximum_nu(labels);
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// here we make an instance of the svm_nu_trainer object that uses our kernel type.
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svm_nu_trainer<kernel_type> trainer;
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// Now we loop over some different nu and gamma values to see how good they are. Note
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// that this is a very simple way to try out a few possible parameter choices. You
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// should look at the model_selection_ex.cpp program for examples of more sophisticated
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// strategies for determining good parameter choices.
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cout << "doing cross validation" << endl;
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for (double gamma = 0.00001; gamma <= 1; gamma *= 5)
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{
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for (double nu = 0.00001; nu < max_nu; nu *= 5)
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{
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// tell the trainer the parameters we want to use
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trainer.set_kernel(kernel_type(gamma));
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trainer.set_nu(nu);
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cout << "gamma: " << gamma << " nu: " << nu;
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// Print out the cross validation accuracy for 3-fold cross validation using
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// the current gamma and nu. cross_validate_trainer() returns a row vector.
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// The first element of the vector is the fraction of +1 training examples
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// correctly classified and the second number is the fraction of -1 training
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// examples correctly classified.
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cout << " cross validation accuracy: " << cross_validate_trainer(trainer, samples, labels, 3);
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}
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}
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// From looking at the output of the above loop it turns out that a good value for nu
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// and gamma for this problem is 0.15625 for both. So that is what we will use.
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// Now we train on the full set of data and obtain the resulting decision function. We
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// use the value of 0.15625 for nu and gamma. The decision function will return values
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// >= 0 for samples it predicts are in the +1 class and numbers < 0 for samples it
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// predicts to be in the -1 class.
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trainer.set_kernel(kernel_type(0.15625));
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trainer.set_nu(0.15625);
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typedef decision_function<kernel_type> dec_funct_type;
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typedef normalized_function<dec_funct_type> funct_type;
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// Here we are making an instance of the normalized_function object. This object
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// provides a convenient way to store the vector normalization information along with
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// the decision function we are going to learn.
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funct_type learned_function;
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learned_function.normalizer = normalizer; // save normalization information
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learned_function.function = trainer.train(samples, labels); // perform the actual SVM training and save the results
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// print out the number of support vectors in the resulting decision function
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cout << "\nnumber of support vectors in our learned_function is "
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<< learned_function.function.basis_vectors.size() << endl;
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// Now let's try this decision_function on some samples we haven't seen before.
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sample_type sample;
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sample(0) = 3.123;
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sample(1) = 2;
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cout << "This is a +1 class example, the classifier output is " << learned_function(sample) << endl;
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sample(0) = 3.123;
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sample(1) = 9.3545;
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cout << "This is a +1 class example, the classifier output is " << learned_function(sample) << endl;
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sample(0) = 13.123;
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sample(1) = 9.3545;
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cout << "This is a -1 class example, the classifier output is " << learned_function(sample) << endl;
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sample(0) = 13.123;
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sample(1) = 0;
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cout << "This is a -1 class example, the classifier output is " << learned_function(sample) << endl;
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// We can also train a decision function that reports a well conditioned probability
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// instead of just a number > 0 for the +1 class and < 0 for the -1 class. An example
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// of doing that follows:
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typedef probabilistic_decision_function<kernel_type> probabilistic_funct_type;
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typedef normalized_function<probabilistic_funct_type> pfunct_type;
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pfunct_type learned_pfunct;
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learned_pfunct.normalizer = normalizer;
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learned_pfunct.function = train_probabilistic_decision_function(trainer, samples, labels, 3);
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// Now we have a function that returns the probability that a given sample is of the +1 class.
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// print out the number of support vectors in the resulting decision function.
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// (it should be the same as in the one above)
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cout << "\nnumber of support vectors in our learned_pfunct is "
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<< learned_pfunct.function.decision_funct.basis_vectors.size() << endl;
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sample(0) = 3.123;
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sample(1) = 2;
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cout << "This +1 class example should have high probability. Its probability is: "
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<< learned_pfunct(sample) << endl;
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sample(0) = 3.123;
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sample(1) = 9.3545;
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cout << "This +1 class example should have high probability. Its probability is: "
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<< learned_pfunct(sample) << endl;
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sample(0) = 13.123;
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sample(1) = 9.3545;
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cout << "This -1 class example should have low probability. Its probability is: "
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<< learned_pfunct(sample) << endl;
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sample(0) = 13.123;
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sample(1) = 0;
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cout << "This -1 class example should have low probability. Its probability is: "
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<< learned_pfunct(sample) << endl;
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// Another thing that is worth knowing is that just about everything in dlib is
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// serializable. So for example, you can save the learned_pfunct object to disk and
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// recall it later like so:
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serialize("saved_function.dat") << learned_pfunct;
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// Now let's open that file back up and load the function object it contains.
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deserialize("saved_function.dat") >> learned_pfunct;
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// Note that there is also an example program that comes with dlib called the
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// file_to_code_ex.cpp example. It is a simple program that takes a file and outputs a
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// piece of C++ code that is able to fully reproduce the file's contents in the form of
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// a std::string object. So you can use that along with the std::istringstream to save
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// learned decision functions inside your actual C++ code files if you want.
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// Lastly, note that the decision functions we trained above involved well over 200
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// basis vectors. Support vector machines in general tend to find decision functions
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// that involve a lot of basis vectors. This is significant because the more basis
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// vectors in a decision function, the longer it takes to classify new examples. So
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// dlib provides the ability to find an approximation to the normal output of a trainer
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// using fewer basis vectors.
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// Here we determine the cross validation accuracy when we approximate the output using
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// only 10 basis vectors. To do this we use the reduced2() function. It takes a
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// trainer object and the number of basis vectors to use and returns a new trainer
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// object that applies the necessary post processing during the creation of decision
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// function objects.
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cout << "\ncross validation accuracy with only 10 support vectors: "
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<< cross_validate_trainer(reduced2(trainer,10), samples, labels, 3);
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// Let's print out the original cross validation score too for comparison.
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cout << "cross validation accuracy with all the original support vectors: "
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<< cross_validate_trainer(trainer, samples, labels, 3);
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// When you run this program you should see that, for this problem, you can reduce the
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// number of basis vectors down to 10 without hurting the cross validation accuracy.
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// To get the reduced decision function out we would just do this:
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learned_function.function = reduced2(trainer,10).train(samples, labels);
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// And similarly for the probabilistic_decision_function:
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learned_pfunct.function = train_probabilistic_decision_function(reduced2(trainer,10), samples, labels, 3);
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}
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