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-// 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 kcentroid object
- from the dlib C++ Library.
-
- The kcentroid object is an implementation of an algorithm that recursively
- computes the centroid (i.e. average) of a set of points. The interesting
- thing about dlib::kcentroid is that it does so in a kernel induced feature
- space. This means that you can use it as a non-linear one-class classifier.
- So you might use it to perform online novelty detection (although, it has
- other uses, see the svm_pegasos or kkmeans examples for example).
-
- This example will train an instance of it on points from the sinc function.
-
-*/
-
-#include <iostream>
-#include <vector>
-
-#include <dlib/svm.h>
-#include <dlib/statistics.h>
-
-using namespace std;
-using namespace dlib;
-
-// Here is the sinc function we will be trying to learn with the kcentroid
-// object.
-double sinc(double x)
-{
- if (x == 0)
- return 1;
- return sin(x)/x;
-}
-
-int main()
-{
- // Here we declare that our samples will be 2 dimensional column vectors.
- // (Note that if you don't know the dimensionality of your vectors at compile time
- // you can change the 2 to a 0 and then set the size at runtime)
- typedef matrix<double,2,1> sample_type;
-
- // 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 kcentroid object. 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 the centroid estimation. 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 control the runtime complexity.
- kcentroid<kernel_type> test(kernel_type(0.1),0.01, 15);
-
-
- // now we train our object on a few samples of the sinc function.
- sample_type m;
- for (double x = -15; x <= 8; x += 1)
- {
- m(0) = x;
- m(1) = sinc(x);
- test.train(m);
- }
-
- running_stats<double> rs;
-
- // Now let's output the distance from the centroid to some points that are from the sinc function.
- // These numbers should all be similar. We will also calculate the statistics of these numbers
- // by accumulating them into the running_stats object called rs. This will let us easily
- // find the mean and standard deviation of the distances for use below.
- cout << "Points that are on the sinc function:\n";
- m(0) = -1.5; m(1) = sinc(m(0)); cout << " " << test(m) << endl; rs.add(test(m));
- m(0) = -1.5; m(1) = sinc(m(0)); cout << " " << test(m) << endl; rs.add(test(m));
- m(0) = -0; m(1) = sinc(m(0)); cout << " " << test(m) << endl; rs.add(test(m));
- m(0) = -0.5; m(1) = sinc(m(0)); cout << " " << test(m) << endl; rs.add(test(m));
- m(0) = -4.1; m(1) = sinc(m(0)); cout << " " << test(m) << endl; rs.add(test(m));
- m(0) = -1.5; m(1) = sinc(m(0)); cout << " " << test(m) << endl; rs.add(test(m));
- m(0) = -0.5; m(1) = sinc(m(0)); cout << " " << test(m) << endl; rs.add(test(m));
-
- cout << endl;
- // Let's output the distance from the centroid to some points that are NOT from the sinc function.
- // These numbers should all be significantly bigger than previous set of numbers. We will also
- // use the rs.scale() function to find out how many standard deviations they are away from the
- // mean of the test points from the sinc function. So in this case our criterion for "significantly bigger"
- // is > 3 or 4 standard deviations away from the above points that actually are on the sinc function.
- cout << "Points that are NOT on the sinc function:\n";
- m(0) = -1.5; m(1) = sinc(m(0))+4; cout << " " << test(m) << " is " << rs.scale(test(m)) << " standard deviations from sinc." << endl;
- m(0) = -1.5; m(1) = sinc(m(0))+3; cout << " " << test(m) << " is " << rs.scale(test(m)) << " standard deviations from sinc." << endl;
- m(0) = -0; m(1) = -sinc(m(0)); cout << " " << test(m) << " is " << rs.scale(test(m)) << " standard deviations from sinc." << endl;
- m(0) = -0.5; m(1) = -sinc(m(0)); cout << " " << test(m) << " is " << rs.scale(test(m)) << " standard deviations from sinc." << endl;
- m(0) = -4.1; m(1) = sinc(m(0))+2; cout << " " << test(m) << " is " << rs.scale(test(m)) << " standard deviations from sinc." << endl;
- m(0) = -1.5; m(1) = sinc(m(0))+0.9; cout << " " << test(m) << " is " << rs.scale(test(m)) << " standard deviations from sinc." << endl;
- m(0) = -0.5; m(1) = sinc(m(0))+1; cout << " " << test(m) << " is " << rs.scale(test(m)) << " standard deviations from sinc." << endl;
-
- // And finally print out the mean and standard deviation of points that are actually from sinc().
- cout << "\nmean: " << rs.mean() << endl;
- cout << "standard deviation: " << rs.stddev() << endl;
-
- // The output is as follows:
- /*
- Points that are on the sinc function:
- 0.869913
- 0.869913
- 0.873408
- 0.872807
- 0.870432
- 0.869913
- 0.872807
-
- Points that are NOT on the sinc function:
- 1.06366 is 119.65 standard deviations from sinc.
- 1.02212 is 93.8106 standard deviations from sinc.
- 0.921382 is 31.1458 standard deviations from sinc.
- 0.918439 is 29.3147 standard deviations from sinc.
- 0.931428 is 37.3949 standard deviations from sinc.
- 0.898018 is 16.6121 standard deviations from sinc.
- 0.914425 is 26.8183 standard deviations from sinc.
-
- mean: 0.871313
- standard deviation: 0.00160756
- */
-
- // So we can see that in this example the kcentroid object correctly indicates that
- // the non-sinc points are definitely not points from the sinc function.
-}
-
-