Function test_manifold_regularization

examples/linear_manifold_regularizer_ex.cpp:150–257

// ----------------------------------------------------------------------------------------

void test_manifold_regularization (
    const double intrinsic_regularization_strength
)
{
    cout << "Testing manifold regularization with an intrinsic_regularization_strength of " 
         << intrinsic_regularization_strength << ".\n";

    std::vector<sample_type> samples;

    // Declare an instance of the kernel we will be using.  
    const kernel_type kern(0.1);

    const unsigned long num_points = 100000;

    // create a large dataset with two concentric circles.  There will be 100000 points on each circle
    // for a total of 200000 samples.
    generate_circle(samples, 2, num_points);  // circle of radius 2
    generate_circle(samples, 4, num_points);  // circle of radius 4

    // Create a set of sample_pairs that tells us which samples are "close" and should thus 
    // be classified similarly.  These edges will be used to define the manifold regularizer.
    // To find these edges we use a simple function that samples point pairs randomly and 
    // returns the top 5% with the shortest edges.
    std::vector<sample_pair> edges;
    find_percent_shortest_edges_randomly(samples, squared_euclidean_distance(), 0.05, 1000000, time(0), edges);

    cout << "number of edges generated: " << edges.size() << endl;

    empirical_kernel_map<kernel_type> ekm;

    // Since the circles are not linearly separable we will use an empirical kernel map to 
    // map them into a space where they are separable.  We create an empirical_kernel_map 
    // using a random subset of our data samples as basis samples.  Note, however, that even
    // though the circles are linearly separable in this new space given by the empirical_kernel_map
    // we still won't be able to correctly classify all the points given just the 2 labeled examples.
    // We will need to make use of the nearest neighbor information stored in edges.  To do that
    // we will use the linear_manifold_regularizer.
    ekm.load(kern, randomly_subsample(samples, 50));

    // Project all the samples into the span of our 50 basis samples
    for (unsigned long i = 0; i < samples.size(); ++i)
        samples[i] = ekm.project(samples[i]);


    // Now create the manifold regularizer.  The result is a transformation matrix that
    // embodies the manifold assumption discussed above.  
    linear_manifold_regularizer<sample_type> lmr;
    // use_gaussian_weights is a function object that tells lmr how to weight each edge.  In this
    // case we let the weight decay as edges get longer.  So shorter edges are more important than
    // longer edges.
    lmr.build(samples, edges, use_gaussian_weights(0.1));
    const matrix<double> T = lmr.get_transformation_matrix(intrinsic_regularization_strength);

    // Apply the transformation generated by the linear_manifold_regularizer to 
    // all our samples.
    for (unsigned long i = 0; i < samples.size(); ++i)
        samples[i] = T*samples[i];