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TheAlgorithms-C/machine_learning/kohonen_som_topology.c

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/**
* \file
* \brief [Kohonen self organizing
* map](https://en.wikipedia.org/wiki/Self-organizing_map) (topological map)
*
* This example implements a powerful unsupervised learning algorithm called as
* a self organizing map. The algorithm creates a connected network of weights
* that closely follows the given data points. This thus creates a topological
* map of the given data i.e., it maintains the relationship between various
* data points in a much higher dimensional space by creating an equivalent in a
* 2-dimensional space.
* <img alt="Trained topological maps for the test cases in the program"
* src="https://raw.githubusercontent.com/TheAlgorithms/C/docs/images/machine_learning/kohonen/2D_Kohonen_SOM.svg"
* />
* \author [Krishna Vedala](https://github.com/kvedala)
* \warning MSVC 2019 compiler generates code that does not execute as expected.
* However, MinGW, Clang for GCC and Clang for MSVC compilers on windows perform
* as expected. Any insights and suggestions should be directed to the author.
* \see kohonen_som_trace.c
*/
#define _USE_MATH_DEFINES /**< required for MS Visual C */
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#ifdef _OPENMP // check if OpenMP based parallellization is available
#include <omp.h>
#endif
/**
* @addtogroup machine_learning Machine learning algorithms
* @{
* @addtogroup kohonen_2d Kohonen SOM topology algorithm
* @{
*/
#ifndef max
/** shorthand for maximum value */
#define max(a, b) (((a) > (b)) ? (a) : (b))
#endif
#ifndef min
/** shorthand for minimum value */
#define min(a, b) (((a) < (b)) ? (a) : (b))
#endif
/** to store info regarding 3D arrays */
struct kohonen_array_3d
{
int dim1; /**< lengths of first dimension */
int dim2; /**< lengths of second dimension */
int dim3; /**< lengths of thirddimension */
double *data; /**< pointer to data */
};
/** Function that returns the pointer to (x, y, z) ^th location in the
* linear 3D array given by:
* \f[
* X_{i,j,k} = i\times M\times N + j\times N + k
* \f]
* where \f$L\f$, \f$M\f$ and \f$N\f$ are the 3D matrix dimensions.
* \param[in] arr pointer to ::kohonen_array_3d structure
* \param[in] x first index
* \param[in] y second index
* \param[in] z third index
* \returns pointer to (x,y,z)^th location of data
*/
double *kohonen_data_3d(const struct kohonen_array_3d *arr, int x, int y, int z)
{
int offset = (x * arr->dim2 * arr->dim3) + (y * arr->dim3) + z;
return arr->data + offset;
}
/**
* Helper function to generate a random number in a given interval.
* \n Steps:
* 1. `r1 = rand() % 100` gets a random number between 0 and 99
* 2. `r2 = r1 / 100` converts random number to be between 0 and 0.99
* 3. scale and offset the random number to given range of \f$[a,b)\f$
* \f[
* y = (b - a) \times \frac{\text{(random number between 0 and RAND_MAX)} \;
* \text{mod}\; 100}{100} + a \f]
*
* \param[in] a lower limit
* \param[in] b upper limit
* \returns random number in the range \f$[a,b)\f$
*/
double _random(double a, double b)
{
return ((b - a) * (rand() % 100) / 100.f) + a;
}
/**
* Save a given n-dimensional data martix to file.
*
* \param[in] fname filename to save in (gets overwritten without confirmation)
* \param[in] X matrix to save
* \param[in] num_points rows in the matrix = number of points
* \param[in] num_features columns in the matrix = dimensions of points
* \returns 0 if all ok
* \returns -1 if file creation failed
*/
int save_2d_data(const char *fname, double **X, int num_points,
int num_features)
{
FILE *fp = fopen(fname, "wt");
if (!fp) // error with fopen
{
char msg[120];
sprintf(msg, "File error (%s): ", fname);
perror(msg);
return -1;
}
for (int i = 0; i < num_points; i++) // for each point in the array
{
for (int j = 0; j < num_features; j++) // for each feature in the array
{
fprintf(fp, "%.4g", X[i][j]); // print the feature value
if (j < num_features - 1) // if not the last feature
fputc(',', fp); // suffix comma
}
if (i < num_points - 1) // if not the last row
fputc('\n', fp); // start a new line
}
fclose(fp);
return 0;
}
/**
* Create the distance matrix or
* [U-matrix](https://en.wikipedia.org/wiki/U-matrix) from the trained weights
* and save to disk.
*
* \param [in] fname filename to save in (gets overwriten without confirmation)
* \param [in] W model matrix to save
* \returns 0 if all ok
* \returns -1 if file creation failed
*/
int save_u_matrix(const char *fname, struct kohonen_array_3d *W)
{
FILE *fp = fopen(fname, "wt");
if (!fp) // error with fopen
{
char msg[120];
sprintf(msg, "File error (%s): ", fname);
perror(msg);
return -1;
}
int R = max(W->dim1 >> 3, 2); /* neighborhood range */
for (int i = 0; i < W->dim1; i++) // for each x
{
for (int j = 0; j < W->dim2; j++) // for each y
{
double distance = 0.f;
int k;
int from_x = max(0, i - R);
int to_x = min(W->dim1, i + R + 1);
int from_y = max(0, j - R);
int to_y = min(W->dim2, j + R + 1);
int l;
#ifdef _OPENMP
#pragma omp parallel for reduction(+ : distance)
#endif
for (l = from_x; l < to_x; l++) // scan neighborhoor in x
{
for (int m = from_y; m < to_y; m++) // scan neighborhood in y
{
double d = 0.f;
for (k = 0; k < W->dim3; k++) // for each feature
{
double *w1 = kohonen_data_3d(W, i, j, k);
double *w2 = kohonen_data_3d(W, l, m, k);
d += (w1[0] - w2[0]) * (w1[0] - w2[0]);
// distance += w1[0] * w1[0];
}
distance += sqrt(d);
// distance += d;
}
}
distance /= R * R; // mean distance from neighbors
fprintf(fp, "%.4g", distance); // print the mean separation
if (j < W->dim2 - 1) // if not the last column
fputc(',', fp); // suffix comma
}
if (i < W->dim1 - 1) // if not the last row
fputc('\n', fp); // start a new line
}
fclose(fp);
return 0;
}
/**
* Get minimum value and index of the value in a matrix
* \param[in] X matrix to search
* \param[in] N number of points in the vector
* \param[out] val minimum value found
* \param[out] x_idx x-index where minimum value was found
* \param[out] y_idx y-index where minimum value was found
*/
void get_min_2d(double **X, int N, double *val, int *x_idx, int *y_idx)
{
val[0] = INFINITY; // initial min value
for (int i = 0; i < N; i++) // traverse each x-index
{
for (int j = 0; j < N; j++) // traverse each y-index
{
if (X[i][j] < val[0]) // if a lower value is found
{ // save the value and its index
x_idx[0] = i;
y_idx[0] = j;
val[0] = X[i][j];
}
}
}
}
/**
* Update weights of the SOM using Kohonen algorithm
*
* \param[in] X data point
* \param[in,out] W weights matrix
* \param[in,out] D temporary vector to store distances
* \param[in] num_out number of output points
* \param[in] num_features number of features per input sample
* \param[in] alpha learning rate \f$0<\alpha\le1\f$
* \param[in] R neighborhood range
* \returns minimum distance of sample and trained weights
*/
double kohonen_update_weights(const double *X, struct kohonen_array_3d *W,
double **D, int num_out, int num_features,
double alpha, int R)
{
int x, y, k;
double d_min = 0.f;
#ifdef _OPENMP
#pragma omp for
#endif
// step 1: for each 2D output point
for (x = 0; x < num_out; x++)
{
for (y = 0; y < num_out; y++)
{
D[x][y] = 0.f;
// compute Euclidian distance of each output
// point from the current sample
for (k = 0; k < num_features; k++)
{
double *w = kohonen_data_3d(W, x, y, k);
D[x][y] += (w[0] - X[k]) * (w[0] - X[k]);
}
D[x][y] = sqrt(D[x][y]);
}
}
// step 2: get closest node i.e., node with smallest Euclidian distance to
// the current pattern
int d_min_x, d_min_y;
get_min_2d(D, num_out, &d_min, &d_min_x, &d_min_y);
// step 3a: get the neighborhood range
int from_x = max(0, d_min_x - R);
int to_x = min(num_out, d_min_x + R + 1);
int from_y = max(0, d_min_y - R);
int to_y = min(num_out, d_min_y + R + 1);
// step 3b: update the weights of nodes in the
// neighborhood
#ifdef _OPENMP
#pragma omp for
#endif
for (x = from_x; x < to_x; x++)
{
for (y = from_y; y < to_y; y++)
{
/* you can enable the following normalization if needed.
personally, I found it detrimental to convergence */
// const double s2pi = sqrt(2.f * M_PI);
// double normalize = 1.f / (alpha * s2pi);
/* apply scaling inversely proportional to distance from the
current node */
double d2 =
(d_min_x - x) * (d_min_x - x) + (d_min_y - y) * (d_min_y - y);
double scale_factor = exp(-d2 / (2.f * alpha * alpha));
for (k = 0; k < num_features; k++)
{
double *w = kohonen_data_3d(W, x, y, k);
// update weights of nodes in the neighborhood
w[0] += alpha * scale_factor * (X[k] - w[0]);
}
}
}
return d_min;
}
/**
* Apply incremental algorithm with updating neighborhood and learning rates
* on all samples in the given datset.
*
* \param[in] X data set
* \param[in,out] W weights matrix
* \param[in] num_samples number of output points
* \param[in] num_features number of features per input sample
* \param[in] num_out number of output points
* \param[in] alpha_min terminal value of alpha
*/
void kohonen_som(double **X, struct kohonen_array_3d *W, int num_samples,
int num_features, int num_out, double alpha_min)
{
int R = num_out >> 2, iter = 0;
double **D = (double **)malloc(num_out * sizeof(double *));
for (int i = 0; i < num_out; i++)
D[i] = (double *)malloc(num_out * sizeof(double));
double dmin = 1.f; // average minimum distance of all samples
// Loop alpha from 1 to slpha_min
for (double alpha = 1.f; alpha > alpha_min && dmin > 1e-3;
alpha -= 0.001, iter++)
{
dmin = 0.f;
// Loop for each sample pattern in the data set
for (int sample = 0; sample < num_samples; sample++)
{
// update weights for the current input pattern sample
dmin += kohonen_update_weights(X[sample], W, D, num_out,
num_features, alpha, R);
}
// every 20th iteration, reduce the neighborhood range
if (iter % 100 == 0 && R > 1)
R--;
dmin /= num_samples;
printf("iter: %5d\t alpha: %.4g\t R: %d\td_min: %.4g\r", iter, alpha, R,
dmin);
}
putchar('\n');
for (int i = 0; i < num_out; i++) free(D[i]);
free(D);
}
/**
* @}
* @}
*/
/** Creates a random set of points distributed in four clusters in
* 3D space with centroids at the points
* * \f$(0,5, 0.5, 0.5)\f$
* * \f$(0,5,-0.5, -0.5)\f$
* * \f$(-0,5, 0.5, 0.5)\f$
* * \f$(-0,5,-0.5, -0.5)\f$
*
* \param[out] data matrix to store data in
* \param[in] N number of points required
*/
void test_2d_classes(double *const *data, int N)
{
const double R = 0.3; // radius of cluster
int i;
const int num_classes = 4;
const double centres[][2] = {
// centres of each class cluster
{.5, .5}, // centre of class 1
{.5, -.5}, // centre of class 2
{-.5, .5}, // centre of class 3
{-.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);
/* The follosing can also be used
for (int j = 0; j < 2; j++)
data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);
*/
}
}
/** Test that creates a random set of points distributed in four clusters in
* 2D space and trains an SOM that finds the topological pattern.
* The following [CSV](https://en.wikipedia.org/wiki/Comma-separated_values)
* files are created to validate the execution:
* * `test1.csv`: random test samples points with a circular pattern
* * `w11.csv`: initial random U-matrix
* * `w12.csv`: trained SOM U-matrix
*/
void test1()
{
int j, N = 300;
int features = 2;
int num_out = 30; // image size - N x N
// 2D space, hence size = number of rows * 2
double **X = (double **)malloc(N * sizeof(double *));
// cluster nodex in 'x' * cluster nodes in 'y' * 2
struct kohonen_array_3d W;
W.dim1 = num_out;
W.dim2 = num_out;
W.dim3 = features;
W.data = (double *)malloc(num_out * num_out * features *
sizeof(double)); // assign rows
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
{
for (int k = 0; k < num_out; k++)
{
#ifdef _OPENMP
#pragma omp for
#endif
// preallocate with random initial weights
for (j = 0; j < features; j++)
{
double *w = kohonen_data_3d(&W, i, k, j);
w[0] = _random(-5, 5);
}
}
}
}
test_2d_classes(X, N); // create test data around circumference of a circle
save_2d_data("test1.csv", X, N, features); // save test data points
save_u_matrix("w11.csv", &W); // save initial random weights
kohonen_som(X, &W, N, features, num_out, 1e-4); // train the SOM
save_u_matrix("w12.csv", &W); // save the resultant weights
for (int i = 0; i < N; i++) free(X[i]);
free(X);
free(W.data);
}
/** Creates a random set of points distributed in four clusters in
* 3D space with centroids at the points
* * \f$(0,5, 0.5, 0.5)\f$
* * \f$(0,5,-0.5, -0.5)\f$
* * \f$(-0,5, 0.5, 0.5)\f$
* * \f$(-0,5,-0.5, -0.5)\f$
*
* \param[out] data matrix to store data in
* \param[in] N number of points required
*/
void test_3d_classes1(double *const *data, int N)
{
const double R = 0.2; // 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);
*/
}
}
/** Test that creates a random set of points distributed in 4 clusters in
* 3D space and trains an SOM that finds the topological pattern. The following
* [CSV](https://en.wikipedia.org/wiki/Comma-separated_values) files are created
* to validate the execution:
* * `test2.csv`: random test samples points
* * `w21.csv`: initial random U-matrix
* * `w22.csv`: trained SOM U-matrix
*/
void test2()
{
int j, N = 500;
int features = 3;
int num_out = 30; // image size - N x N
// 3D space, hence size = number of rows * 3
double **X = (double **)malloc(N * sizeof(double *));
// cluster nodex in 'x' * cluster nodes in 'y' * 2
struct kohonen_array_3d W;
W.dim1 = num_out;
W.dim2 = num_out;
W.dim3 = features;
W.data = (double *)malloc(num_out * num_out * features *
sizeof(double)); // assign rows
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
{
for (int k = 0; k < num_out; k++)
{
#ifdef _OPENMP
#pragma omp for
#endif
for (j = 0; j < features; j++)
{ // preallocate with random initial weights
double *w = kohonen_data_3d(&W, i, k, j);
w[0] = _random(-5, 5);
}
}
}
}
test_3d_classes1(X, N); // create test data
save_2d_data("test2.csv", X, N, features); // save test data points
save_u_matrix("w21.csv", &W); // save initial random weights
kohonen_som(X, &W, N, features, num_out, 1e-4); // train the SOM
save_u_matrix("w22.csv", &W); // save the resultant weights
for (int i = 0; i < N; i++) free(X[i]);
free(X);
free(W.data);
}
/** Creates a random set of points distributed in four clusters in
* 3D space with centroids at the points
* * \f$(0,5, 0.5, 0.5)\f$
* * \f$(0,5,-0.5, -0.5)\f$
* * \f$(-0,5, 0.5, 0.5)\f$
* * \f$(-0,5,-0.5, -0.5)\f$
*
* \param[out] data matrix to store data in
* \param[in] N number of points required
*/
void test_3d_classes2(double *const *data, int N)
{
const double R = 0.2; // radius of cluster
int i;
const int num_classes = 8;
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
{-.5, .5, .5}, // centre of class 5
{-.5, .5, -.5}, // centre of class 6
{-.5, -.5, .5}, // centre of class 7
{-.5, -.5, -.5} // centre of class 8
};
#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);
*/
}
}
/** Test that creates a random set of points distributed in eight clusters in
* 3D space and trains an SOM that finds the topological pattern. The following
* [CSV](https://en.wikipedia.org/wiki/Comma-separated_values) files are created
* to validate the execution:
* * `test3.csv`: random test samples points
* * `w31.csv`: initial random U-matrix
* * `w32.csv`: trained SOM U-matrix
*/
void test3()
{
int j, N = 500;
int features = 3;
int num_out = 30;
double **X = (double **)malloc(N * sizeof(double *));
// cluster nodex in 'x' * cluster nodes in 'y' * 2
struct kohonen_array_3d W;
W.dim1 = num_out;
W.dim2 = num_out;
W.dim3 = features;
W.data = (double *)malloc(num_out * num_out * features *
sizeof(double)); // assign rows
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
{
for (int k = 0; k < num_out; k++)
{
#ifdef _OPENMP
#pragma omp for
#endif
// preallocate with random initial weights
for (j = 0; j < features; j++)
{
double *w = kohonen_data_3d(&W, i, k, j);
w[0] = _random(-5, 5);
}
}
}
}
test_3d_classes2(X, N); // create test data around the lamniscate
save_2d_data("test3.csv", X, N, features); // save test data points
save_u_matrix("w31.csv", &W); // save initial random weights
kohonen_som(X, &W, N, features, num_out, 0.01); // train the SOM
save_u_matrix("w32.csv", &W); // save the resultant weights
for (int i = 0; i < N; i++) free(X[i]);
free(X);
free(W.data);
}
/**
* Convert clock cycle difference to time in seconds
*
* \param[in] start_t start clock
* \param[in] end_t end clock
* \returns time difference in seconds
*/
double get_clock_diff(clock_t start_t, clock_t end_t)
{
return (double)(end_t - start_t) / (double)CLOCKS_PER_SEC;
}
/** Main function */
int main(int argc, char **argv)
{
#ifdef _OPENMP
printf("Using OpenMP based parallelization\n");
#else
printf("NOT using OpenMP based parallelization\n");
#endif
clock_t start_clk, end_clk;
start_clk = clock();
test1();
end_clk = clock();
printf("Test 1 completed in %.4g sec\n",
get_clock_diff(start_clk, end_clk));
start_clk = clock();
test2();
end_clk = clock();
printf("Test 2 completed in %.4g sec\n",
get_clock_diff(start_clk, end_clk));
start_clk = clock();
test3();
end_clk = clock();
printf("Test 3 completed in %.4g sec\n",
get_clock_diff(start_clk, end_clk));
printf("(Note: Calculated times include: writing files to disk.)\n\n");
return 0;
}
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