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267 lines
12 KiB
267 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. In particular, we show how to use the
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C parametrization of the SVM in this example.
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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
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// which they operate. So the first thing we do here is declare a convenient
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// typedef.
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// This typedef declares a matrix with 2 rows and 1 column. It will be the
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// object that contains each of our 2 dimensional samples. (Note that if
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// you wanted more than 2 features in this vector you can simply change the
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// 2 to something else. Or if you don't know how many features you want
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// until runtime then you can put a 0 here and use the matrix.set_size()
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// 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
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// example. In this case I have selected the radial basis kernel that can
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// operate on our 2D sample_type objects. You can use your own custom
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// kernels with these tools as well, see custom_trainer_ex.cpp for an
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// example.
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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
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// by looping over a bunch of points and labeling them according to their
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// distance from the 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
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// by their standard deviation. This is generally a good idea since it
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// often heads off numerical stability problems and also prevents one large
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// feature from smothering others. Doing this doesn't matter much in this
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// example so I'm just doing this here so you can see an easy way to
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// accomplish it.
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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
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// two parameters to the training. These are the C and gamma parameters.
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// Our choice for these parameters will influence how good the resulting
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// decision function is. To test how good a particular choice of these
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// parameters are we can use the cross_validate_trainer() function to perform
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// n-fold cross validation on our training data. However, there is a
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// problem with the way we have sampled our distribution above. The problem
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// is that there is a definite ordering to the samples. That is, the first
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// 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
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// can fix it by randomizing the order of the samples with the following
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// function call.
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randomize_samples(samples, labels);
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// here we make an instance of the svm_c_trainer object that uses our kernel
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// type.
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svm_c_trainer<kernel_type> trainer;
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// Now we loop over some different C and gamma values to see how good they
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// are. Note that this is a very simple way to try out a few possible
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// parameter choices. You should look at the model_selection_ex.cpp program
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// for examples of more sophisticated strategies for determining good
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// 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 C = 1; C < 100000; C *= 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_c(C);
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cout << "gamma: " << gamma << " C: " << C;
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// Print out the cross validation accuracy for 3-fold cross validation using
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// the current gamma and C. 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: "
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<< 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 good
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// values for C and gamma for this problem are 5 and 0.15625 respectively.
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// 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
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// function. The decision function will return values >= 0 for samples it
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// predicts are in the +1 class and numbers < 0 for samples it predicts to
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// be in the -1 class.
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trainer.set_kernel(kernel_type(0.15625));
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trainer.set_c(5);
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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
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// object provides a convenient way to store the vector normalization
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// information along with 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
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// probability instead of just a number > 0 for the +1 class and < 0 for the
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// -1 class. An example 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
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// is serializable. So for example, you can save the learned_pfunct object
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// to disk and 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
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// the file_to_code_ex.cpp example. It is a simple program that takes a
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// file and outputs a piece of C++ code that is able to fully reproduce the
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// file's contents in the form of a std::string object. So you can use that
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// along with the std::istringstream to save learned decision functions
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// inside your actual C++ code files if you want.
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// Lastly, note that the decision functions we trained above involved well
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// over 200 basis vectors. Support vector machines in general tend to find
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// decision functions that involve a lot of basis vectors. This is
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// significant because the more basis vectors in a decision function, the
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// longer it takes to classify new examples. So dlib provides the ability
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// to find an approximation to the normal output of a trainer using fewer
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// basis vectors.
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// Here we determine the cross validation accuracy when we approximate the
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// output using only 10 basis vectors. To do this we use the reduced2()
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// function. It takes a trainer object and the number of basis vectors to
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// use and returns a new trainer object that applies the necessary post
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// processing during the creation of decision 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
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// reduce the number of basis vectors down to 10 without hurting the cross
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// 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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