// 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 rank_features() function
from the dlib C++ Library.
This example creates a simple set of data and then shows
you how to use the rank_features() function to find a good
set of features (where "good" means the feature set will probably
work well with a classification algorithm).
The data used in this example will be 4 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. Note that this data is conceptually 2 dimensional but we
will add two extra features for the purpose of showing what
the rank_features() function does.
*/
#include <iostream>
#include <dlib/svm.h>
#include <dlib/rand.h>
#include <vector>
using namespace std;
using namespace dlib;
int main()
{
// This first typedef declares a matrix with 4 rows and 1 column. It will be the
// object that contains each of our 4 dimensional samples.
typedef matrix<double, 4, 1> sample_type;
// Now let's make some vector objects that can hold our samples
std::vector<sample_type> samples;
std::vector<double> labels;
dlib::rand rnd;
for (int x = -30; x <= 30; ++x)
{
for (int y = -30; y <= 30; ++y)
{
sample_type samp;
// the first two features are just the (x,y) position of our points and so
// we expect them to be good features since our two classes here are points
// close to the origin and points far away from the origin.
samp(0) = x;
samp(1) = y;
// This is a worthless feature since it is just random noise. It should
// be indicated as worthless by the rank_features() function below.
samp(2) = rnd.get_random_double();
// This is a version of the y feature that is corrupted by random noise. It
// should be ranked as less useful than features 0, and 1, but more useful
// than the above feature.
samp(3) = y*0.2 + (rnd.get_random_double()-0.5)*10;
// add this sample into our vector of samples.
samples.push_back(samp);
// if this point is less than 15 from the origin then label it as a +1 class point.
// otherwise it is a -1 class point
if (sqrt((double)x*x + y*y) <= 15)
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.
const sample_type m(mean(mat(samples))); // compute a mean vector
const sample_type sd(reciprocal(stddev(mat(samples)))); // compute a standard deviation vector
// now normalize each sample
for (unsigned long i = 0; i < samples.size(); ++i)
samples[i] = pointwise_multiply(samples[i] - m, sd);
// This is another thing that is often good to do from a numerical stability point of view.
// However, in our case it doesn't really matter. It's just here to show you how to do it.
randomize_samples(samples,labels);
// 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
// 4D sample_type objects. In general, I would suggest using the same kernel for
// classification and feature ranking.
typedef radial_basis_kernel<sample_type> kernel_type;
// The radial_basis_kernel has a parameter called gamma that we need to set. Generally,
// you should try the same gamma that you are using for training. But if you don't
// have a particular gamma in mind then you can use the following function to
// find a reasonable default gamma for your data. Another reasonable way to pick a gamma
// is often to use 1.0/compute_mean_squared_distance(randomly_subsample(samples, 2000)).
// It computes the mean squared distance between 2000 randomly selected samples and often
// works quite well.
const double gamma = verbose_find_gamma_with_big_centroid_gap(samples, labels);
// Next we declare an instance of the kcentroid object. It is used by rank_features()
// two represent the centroids of the two classes. The kcentroid has 3 parameters
// you need to set. The first argument to the constructor is the kernel we wish to
// use. The second is a parameter that determines the numerical accuracy with which
// the object will perform part of the ranking algorithm. Generally, smaller values
// give better results but cause the algorithm to attempt to use more dictionary vectors
// (and thus run slower and use more memory). The third argument, however, is the
// maximum number of dictionary vectors a kcentroid is allowed to use. So you can use
// it to put an upper limit on the runtime complexity.
kcentroid<kernel_type> kc(kernel_type(gamma), 0.001, 25);
// And finally we get to the feature ranking. Here we call rank_features() with the kcentroid we just made,
// the samples and labels we made above, and the number of features we want it to rank.
cout << rank_features(kc, samples, labels) << endl;
// The output is:
/*
0 0.749265
1 1
3 0.933378
2 0.825179
*/
// The first column is a list of the features in order of decreasing goodness. So the rank_features() function
// is telling us that the samples[i](0) and samples[i](1) (i.e. the x and y) features are the best two. Then
// after that the next best feature is the samples[i](3) (i.e. the y corrupted by noise) and finally the worst
// feature is the one that is just random noise. So in this case rank_features did exactly what we would
// intuitively expect.
// The second column of the matrix is a number that indicates how much the features up to that point
// contribute to the separation of the two classes. So bigger numbers are better since they
// indicate a larger separation. The max value is always 1. In the case below we see that the bad
// features actually make the class separation go down.
// So to break it down a little more.
// 0 0.749265 <-- class separation of feature 0 all by itself
// 1 1 <-- class separation of feature 0 and 1
// 3 0.933378 <-- class separation of feature 0, 1, and 3
// 2 0.825179 <-- class separation of feature 0, 1, 3, and 2
}