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Added some examples for kernel ridge regression.

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Davis King 2010-07-24 00:38:22 +00:00
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2
examples/CMakeLists.txt
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@ -43,6 +43,8 @@ add_example(kcentroid_ex)
add_example(kkmeans_ex)
add_example(krls_ex)
add_example(krls_filter_ex)
add_example(krr_classification_ex)
add_example(krr_regression_ex)
add_example(linear_manifold_regularizer_ex)
add_example(logger_ex)
add_example(logger_ex_2)

195
examples/krr_classification_ex.cpp Normal file
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@ -0,0 +1,195 @@
// 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 lets 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(vector_to_matrix(labels) > 0) << endl;
cout << " number of -1 samples: " << sum(vector_to_matrix(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.
// 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. Which is what we want to do since we are performing classification.
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));
double loo_error;
trainer.train(samples, labels, loo_error);
// Print gamma and the fraction of samples misclassified during LOO cross-validation.
cout << "gamma: " << gamma << " LOO error: " << loo_error << endl;
}
// From looking at the output of the above loop it turns out that a good value for
// gamma for this problem is 0.015. So that is what we will use.
trainer.set_kernel(kernel_type(0.015));
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 lets 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 sample should be >= 0 and it is classified as a " << learned_function(sample) << endl;
sample(0) = 3.123;
sample(1) = 9.3545;
cout << "This sample should be >= 0 and it is classified as a " << learned_function(sample) << endl;
sample(0) = 13.123;
sample(1) = 9.3545;
cout << "This sample should be < 0 and it is classified as a " << learned_function(sample) << endl;
sample(0) = 13.123;
sample(1) = 0;
cout << "This sample should be < 0 and it is classified as a " << 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 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 example should have high probability. Its probability is: " << learned_pfunct(sample) << endl;
sample(0) = 3.123;
sample(1) = 9.3545;
cout << "This +1 example should have high probability. Its probability is: " << learned_pfunct(sample) << endl;
sample(0) = 13.123;
sample(1) = 9.3545;
cout << "This -1 example should have low probability. Its probability is: " << learned_pfunct(sample) << endl;
sample(0) = 13.123;
sample(1) = 0;
cout << "This -1 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:
ofstream fout("saved_function.dat",ios::binary);
serialize(learned_pfunct,fout);
fout.close();
// now lets open that file back up and load the function object it contains
ifstream fin("saved_function.dat",ios::binary);
deserialize(learned_pfunct, fin);
}

105
examples/krr_regression_ex.cpp Normal file
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@ -0,0 +1,105 @@
// 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 will train on data from the sinc function.
*/
#include <iostream>
#include <vector>
#include "dlib/svm.h"
using namespace std;
using namespace dlib;
// Here is the sinc function we will be trying to learn with kernel ridge regression
double sinc(double x)
{
if (x == 0)
return 1;
return sin(x)/x;
}
int main()
{
// Here we declare that our samples will be 1 dimensional column vectors.
typedef matrix<double,1,1> sample_type;
// Now sample some points from the sinc() function
sample_type m;
std::vector<sample_type> samples;
std::vector<double> labels;
for (double x = -10; x <= 4; x += 1)
{
m(0) = x;
samples.push_back(m);
labels.push_back(sinc(x));
}
// Now we are making a typedef for the kind of kernel we want to use. I picked the
// radial basis kernel because it only has one parameter and generally gives good
// results without much fiddling.
typedef radial_basis_kernel<sample_type> kernel_type;
// Here we declare an instance of the krr_trainer object. This is the
// object that we will later use to do the training.
krr_trainer<kernel_type> trainer;
// Here we set the kernel we want to use for training. The radial_basis_kernel
// has a parameter called gamma that we need to determine. As a rule of thumb, a good
// gamma to try is 1.0/(mean squared distance between your sample points). So
// below we are using a similar value.
const double gamma = 3.0/compute_mean_squared_distance(samples);
cout << "using gamma of " << gamma << endl;
trainer.set_kernel(kernel_type(gamma));
// now train a function based on our sample points
decision_function<kernel_type> test = trainer.train(samples, labels);
// now we output the value of the sinc function for a few test points as well as the
// value predicted by our regression.
m(0) = 2.5; cout << sinc(m(0)) << " " << test(m) << endl;
m(0) = 0.1; cout << sinc(m(0)) << " " << test(m) << endl;
m(0) = -4; cout << sinc(m(0)) << " " << test(m) << endl;
m(0) = 5.0; cout << sinc(m(0)) << " " << test(m) << endl;
// The output is as follows:
//using gamma of 0.075
// 0.239389 0.239388
// 0.998334 0.998363
// -0.189201 -0.189254
// -0.191785 -0.186669
// The first column is the true value of the sinc function and the second
// column is the output from the krr estimate.
// Note that the krr_trainer has the ability to tell us the leave-one-out cross-validation
// accuracy. The train() function has an optional 3rd argument and if we give it a double
// it will give us back the LOO error.
double loo_error;
trainer.train(samples, labels, loo_error);
cout << "mean squared LOO error: " << loo_error << endl;
// Which outputs the following:
// mean squared LOO error: 8.29813e-07
// Another thing that is worth knowing is that just about everything in dlib is serializable.
// So for example, you can save the test object to disk and recall it later like so:
ofstream fout("saved_function.dat",ios::binary);
serialize(test,fout);
fout.close();
// now lets open that file back up and load the function object it contains
ifstream fin("saved_function.dat",ios::binary);
deserialize(test, fin);
}