kohonen_som_trace.c File Reference

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

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

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Macros
#define	_USE_MATH_DEFINES
	required for MS Visual C
#define	max(a, b)   (((a) > (b)) ? (a) : (b))
	shorthand for maximum value
#define	min(a, b)   (((a) < (b)) ? (a) : (b))
	shorthand for minimum value

Functions
double	_random (double a, double b)
	Helper function to generate a random number in a given interval. More...
int	save_nd_data (const char *fname, double **X, int num_points, int num_features)
	Save a given n-dimensional data martix to file. More...
void	kohonen_get_min_1d (double const *X, int N, double *val, int *idx)
	Get minimum value and index of the value in a vector. More...
void	kohonen_update_weights (double const *x, double *const *W, double *D, int num_out, int num_features, double alpha, int R)
	Update weights of the SOM using Kohonen algorithm. More...
void	kohonen_som_tracer (double **X, double *const *W, int num_samples, int num_features, int num_out, double alpha_min)
	Apply incremental algorithm with updating neighborhood and learning rates on all samples in the given datset. More...
void	test_circle (double *const *data, int N)
	Creates a random set of points distributed near the circumference of a circle and trains an SOM that finds that circular pattern. More...
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. More...
void	test_lamniscate (double *const *data, int N)
	Creates a random set of points distributed near the locus of the Lamniscate of Gerono. More...
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. More...
void	test_3d_classes (double *const *data, int N)
	Creates a random set of points distributed in four clusters in 3D space with centroids at the points. More...
void	test3 ()
	Test that creates a random set of points distributed in six clusters in 3D space. More...
double	get_clock_diff (clock_t start_t, clock_t end_t)
	Convert clock cycle difference to time in seconds. More...
int	main (int argc, char **argv)
	Main function.

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

See also

kohonen_som_topology.c

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 (double)(end_t - start_t) / (double)CLOCKS_PER_SEC;
}

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

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

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

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test_3d_classes()

void test_3d_classes	(	double *const *	data,
		int	N
	)

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

• \((0,5, 0.5, 0.5)\)
• \((0,5,-0.5, -0.5)\)
• \((-0,5, 0.5, 0.5)\)
• \((-0,5,-0.5, -0.5)\)

Parameters

[out]	data	matrix to store data in
[in]	N	number of points required

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

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test_circle()

void test_circle	(	double *const *	data,
		int	N
	)

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
[in]	N	number of points required

{
    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;
 
#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[i][0] = r * cos(theta);       // convert from polar to cartesian
        data[i][1] = r * sin(theta);
    }
}

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test_lamniscate()

void test_lamniscate	(	double *const *	data,
		int	N
	)

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
[in]	N	number of points required

{
    const double dr = 0.2;
    int i;
 
#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[i][0] = dx + cos(theta);     // convert from polar to cartesian
        data[i][1] = dy + sin(2. * theta) / 2.f;
    }
}

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