kohonen_som_trace.cpp File Reference

Kohonen self organizing map (data tracing) More...

#include <algorithm>
#include <array>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <fstream>
#include <iostream>
#include <valarray>
#include <vector>

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Namespaces
namespace	machine_learning
	A* search algorithm

Functions
double	_random (double a, double b)
int	save_nd_data (const char *fname, const std::vector< std::valarray< double > > &X)
void	machine_learning::update_weights (const std::valarray< double > &x, std::vector< std::valarray< double > > *W, std::valarray< double > *D, double alpha, int R)
void	machine_learning::kohonen_som_tracer (const std::vector< std::valarray< double > > &X, std::vector< std::valarray< double > > *W, double alpha_min)
void	test_circle (std::vector< std::valarray< double > > *data)
void	test1 ()
void	test_lamniscate (std::vector< std::valarray< double > > *data)
void	test2 ()
void	test_3d_classes (std::vector< std::valarray< double > > *data)
void	test3 ()
double	get_clock_diff (clock_t start_t, clock_t end_t)
int	main (int argc, char **argv)

Detailed Description

Kohonen self organizing map (data tracing)

This example implements a powerful self organizing map algorithm. The algorithm creates a connected network of weights that closely follows the given data points. This this creates a chain of nodes that resembles the given input shape.

Author

Krishna Vedala

Note

This C++ version of the program is considerable slower than its C counterpart

The compiled code is much slower when compiled with MS Visual C++ 2019 than with GCC on windows

See also

kohonen_som_topology.cpp

Function Documentation

get_clock_diff()

double get_clock_diff	(	clock_t	start_t,
		clock_t	end_t )

Convert clock cycle difference to time in seconds

Parameters

[in]	start_t	start clock
[in]	end_t	end clock

Returns

time difference in seconds

                                                      {
    return static_cast<double>(end_t - start_t) / CLOCKS_PER_SEC;
}

main()

int main	(	int	argc,
		char **	argv )

Main function

                                {
#ifdef _OPENMP
    std::cout << "Using OpenMP based parallelization\n";
#else
    std::cout << "NOT using OpenMP based parallelization\n";
#endif
 
    std::srand(std::time(nullptr));
 
    std::clock_t start_clk = std::clock();
    test1();
    auto end_clk = std::clock();
    std::cout << "Test 1 completed in " << get_clock_diff(start_clk, end_clk)
              << " sec\n";
 
    start_clk = std::clock();
    test2();
    end_clk = std::clock();
    std::cout << "Test 2 completed in " << get_clock_diff(start_clk, end_clk)
              << " sec\n";
 
    start_clk = std::clock();
    test3();
    end_clk = std::clock();
    std::cout << "Test 3 completed in " << get_clock_diff(start_clk, end_clk)
              << " sec\n";
 
    std::cout
        << "(Note: Calculated times include: creating test sets, training "
           "model and writing files to disk.)\n\n";
    return 0;
}

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test1()

void test1

(

)

Test that creates a random set of points distributed near the circumference of a circle and trains an SOM that finds that circular pattern. The following CSV files are created to validate the execution:

• test1.csv: random test samples points with a circular pattern
• w11.csv: initial random map
• w12.csv: trained SOM map

The outputs can be readily plotted in gnuplot using the following snippet

set datafile separator ','
plot "test1.csv" title "original", \
     "w11.csv" title "w1", \
     "w12.csv" title "w2"

             {
    int j = 0, N = 500;
    int features = 2;
    int num_out = 50;
    std::vector<std::valarray<double>> X(N);
    std::vector<std::valarray<double>> W(num_out);
    for (int i = 0; i < std::max(num_out, N); i++) {
        // loop till max(N, num_out)
        if (i < N) {  // only add new arrays if i < N
            X[i] = std::valarray<double>(features);
        }
        if (i < num_out) {  // only add new arrays if i < num_out
            W[i] = std::valarray<double>(features);
 
#ifdef _OPENMP
#pragma omp for
#endif
            for (j = 0; j < features; j++) {
                // preallocate with random initial weights
                W[i][j] = _random(-1, 1);
            }
        }
    }
 
    test_circle(&X);  // create test data around circumference of a circle
    save_nd_data("test1.csv", X);    // save test data points
    save_nd_data("w11.csv", W);      // save initial random weights
    kohonen_som_tracer(X, &W, 0.1);  // train the SOM
    save_nd_data("w12.csv", W);      // save the resultant weights
}

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test2()

void test2

(

)

Test that creates a random set of points distributed near the locus of the Lamniscate of Gerono and trains an SOM that finds that circular pattern. The following CSV files are created to validate the execution:

• test2.csv: random test samples points with a lamniscate pattern
• w21.csv: initial random map
• w22.csv: trained SOM map

The outputs can be readily plotted in gnuplot using the following snippet

set datafile separator ','
plot "test2.csv" title "original", \
     "w21.csv" title "w1", \
     "w22.csv" title "w2"

             {
    int j = 0, N = 500;
    int features = 2;
    int num_out = 20;
    std::vector<std::valarray<double>> X(N);
    std::vector<std::valarray<double>> W(num_out);
    for (int i = 0; i < std::max(num_out, N); i++) {
        // loop till max(N, num_out)
        if (i < N) {  // only add new arrays if i < N
            X[i] = std::valarray<double>(features);
        }
        if (i < num_out) {  // only add new arrays if i < num_out
            W[i] = std::valarray<double>(features);
 
#ifdef _OPENMP
#pragma omp for
#endif
            for (j = 0; j < features; j++) {
                // preallocate with random initial weights
                W[i][j] = _random(-1, 1);
            }
        }
    }
 
    test_lamniscate(&X);              // create test data around the lamniscate
    save_nd_data("test2.csv", X);     // save test data points
    save_nd_data("w21.csv", W);       // save initial random weights
    kohonen_som_tracer(X, &W, 0.01);  // train the SOM
    save_nd_data("w22.csv", W);       // save the resultant weights
}

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test3()

void test3

(

)

Test that creates a random set of points distributed in six clusters in 3D space. The following CSV files are created to validate the execution:

• test3.csv: random test samples points with a circular pattern
• w31.csv: initial random map
• w32.csv: trained SOM map

The outputs can be readily plotted in gnuplot using the following snippet

set datafile separator ','
plot "test3.csv" title "original", \
     "w31.csv" title "w1", \
     "w32.csv" title "w2"

             {
    int j = 0, N = 200;
    int features = 3;
    int num_out = 20;
    std::vector<std::valarray<double>> X(N);
    std::vector<std::valarray<double>> W(num_out);
    for (int i = 0; i < std::max(num_out, N); i++) {
        // loop till max(N, num_out)
        if (i < N) {  // only add new arrays if i < N
            X[i] = std::valarray<double>(features);
        }
        if (i < num_out) {  // only add new arrays if i < num_out
            W[i] = std::valarray<double>(features);
 
#ifdef _OPENMP
#pragma omp for
#endif
            for (j = 0; j < features; j++) {
                // preallocate with random initial weights
                W[i][j] = _random(-1, 1);
            }
        }
    }
 
    test_3d_classes(&X);              // create test data around the lamniscate
    save_nd_data("test3.csv", X);     // save test data points
    save_nd_data("w31.csv", W);       // save initial random weights
    kohonen_som_tracer(X, &W, 0.01);  // train the SOM
    save_nd_data("w32.csv", W);       // save the resultant weights
}

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test_3d_classes()

void test_3d_classes

(

std::vector< std::valarray< double > > *

data

)

Creates a random set of points distributed in six clusters in 3D space with centroids at the points

• \({0.5, 0.5, 0.5}\)
• \({0.5, 0.5, -0.5}\)
• \({0.5, -0.5, 0.5}\)
• \({0.5, -0.5, -0.5}\)
• \({-0.5, 0.5, 0.5}\)
• \({-0.5, 0.5, -0.5}\)
• \({-0.5, -0.5, 0.5}\)
• \({-0.5, -0.5, -0.5}\)

Parameters

[out]

data

matrix to store data in

                                                           {
    const int N = data->size();
    const double R = 0.1;  // radius of cluster
    int i = 0;
    const int num_classes = 8;
    const std::array<const std::array<double, 3>, num_classes> centres = {
        // centres of each class cluster
        std::array<double, 3>({.5, .5, .5}),    // centre of class 0
        std::array<double, 3>({.5, .5, -.5}),   // centre of class 1
        std::array<double, 3>({.5, -.5, .5}),   // centre of class 2
        std::array<double, 3>({.5, -.5, -.5}),  // centre of class 3
        std::array<double, 3>({-.5, .5, .5}),   // centre of class 4
        std::array<double, 3>({-.5, .5, -.5}),  // centre of class 5
        std::array<double, 3>({-.5, -.5, .5}),  // centre of class 6
        std::array<double, 3>({-.5, -.5, -.5})  // centre of class 7
    };
 
#ifdef _OPENMP
#pragma omp for
#endif
    for (i = 0; i < N; i++) {
        int cls =
            std::rand() % num_classes;  // select a random class for the point
 
        // create random coordinates (x,y,z) around the centre of the class
        data[0][i][0] = _random(centres[cls][0] - R, centres[cls][0] + R);
        data[0][i][1] = _random(centres[cls][1] - R, centres[cls][1] + R);
        data[0][i][2] = _random(centres[cls][2] - R, centres[cls][2] + R);
 
        /* The follosing can also be used
        for (int j = 0; j < 3; j++)
            data[0][i][j] = _random(centres[cls][j] - R, centres[cls][j] + R);
        */
    }
}

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test_circle()

void test_circle

(

std::vector< std::valarray< double > > *

data

)

Creates a random set of points distributed near the circumference of a circle and trains an SOM that finds that circular pattern. The generating function is

\begin{eqnarray*} r &\in& [1-\delta r, 1+\delta r)\\ \theta &\in& [0, 2\pi)\\ x &=& r\cos\theta\\ y &=& r\sin\theta \end{eqnarray*}

Parameters

[out]

data

matrix to store data in

                                                       {
    const int N = data->size();
    const double R = 0.75, dr = 0.3;
    double a_t = 0., b_t = 2.f * M_PI;  // theta random between 0 and 2*pi
    double a_r = R - dr, b_r = R + dr;  // radius random between R-dr and R+dr
    int i = 0;
 
#ifdef _OPENMP
#pragma omp for
#endif
    for (i = 0; i < N; i++) {
        double r = _random(a_r, b_r);      // random radius
        double theta = _random(a_t, b_t);  // random theta
        data[0][i][0] = r * cos(theta);    // convert from polar to cartesian
        data[0][i][1] = r * sin(theta);
    }
}

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test_lamniscate()

void test_lamniscate

(

std::vector< std::valarray< double > > *

data

)

Creates a random set of points distributed near the locus of the Lamniscate of Gerono.

\begin{eqnarray*} \delta r &=& 0.2\\ \delta x &\in& [-\delta r, \delta r)\\ \delta y &\in& [-\delta r, \delta r)\\ \theta &\in& [0, \pi)\\ x &=& \delta x + \cos\theta\\ y &=& \delta y + \frac{\sin(2\theta)}{2} \end{eqnarray*}

Parameters

[out]

data

matrix to store data in

                                                           {
    const int N = data->size();
    const double dr = 0.2;
    int i = 0;
 
#ifdef _OPENMP
#pragma omp for
#endif
    for (i = 0; i < N; i++) {
        double dx = _random(-dr, dr);     // random change in x
        double dy = _random(-dr, dr);     // random change in y
        double theta = _random(0, M_PI);  // random theta
        data[0][i][0] = dx + cos(theta);  // convert from polar to cartesian
        data[0][i][1] = dy + sin(2. * theta) / 2.f;
    }
}

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