mirror of
https://github.com/TheAlgorithms/C
synced 2024-11-29 00:33:14 +03:00
690 lines
22 KiB
C
690 lines
22 KiB
C
/**
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* \file
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* \author [Krishna Vedala](https://github.com/kvedala)
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* \brief [Kohonen self organizing
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* map](https://en.wikipedia.org/wiki/Self-organizing_map) (topological map)
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*
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* This example implements a powerful unsupervised learning algorithm called as
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* a self organizing map. The algorithm creates a connected network of weights
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* that closely follows the given data points. This thus creates a topological
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* map of the given data i.e., it maintains the relationship between varipus
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* data points in a much higher dimesional space by creating an equivalent in a
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* 2-dimensional space.
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* <img alt="Trained topological maps for the test cases in the program"
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* src="https://raw.githubusercontent.com/kvedala/C/docs/images/machine_learning/kohonen/2D_Kohonen_SOM.svg"
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* />
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* \warning MSVC 2019 compiler generates code that does not execute as expected.
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* However, MinGW, Clang for GCC and Clang for MSVC compilers on windows perform
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* as expected. Any insights and suggestions should be directed to the author.
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* \see kohonen_som_trace.c
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*/
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#define _USE_MATH_DEFINES /**< required for MS Visual C */
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <time.h>
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#ifdef _OPENMP // check if OpenMP based parallellization is available
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#include <omp.h>
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#endif
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#ifndef max
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#define max(a, b) \
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(((a) > (b)) ? (a) : (b)) /**< shorthand for maximum value \
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*/
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#endif
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#ifndef min
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#define min(a, b) \
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(((a) < (b)) ? (a) : (b)) /**< shorthand for minimum value \
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*/
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#endif
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/** to store info regarding 3D arrays */
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struct array_3d
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{
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int dim1; /**< lengths of first dimension */
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int dim2; /**< lengths of second dimension */
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int dim3; /**< lengths of thirddimension */
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double *data; /**< pointer to data */
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};
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/** Function that returns the pointer to (x, y, z) ^th location in the
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* linear 3D array given by:
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* \f[
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* X_{i,j,k} = i\times M\times N + j\times N + k
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* \f]
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* where \f$L\f$, \f$M\f$ and \f$N\f$ are the 3D matrix dimensions.
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* \param[in] arr pointer to ::array_3d structure
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* \param[in] x first index
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* \param[in] y second index
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* \param[in] z third index
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* \returns pointer to (x,y,z)^th location of data
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*/
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double *data_3d(const struct array_3d *arr, int x, int y, int z)
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{
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int offset = (x * arr->dim2 * arr->dim3) + (y * arr->dim3) + z;
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return arr->data + offset;
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}
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/**
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* Helper function to generate a random number in a given interval.
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* \n Steps:
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* 1. `r1 = rand() % 100` gets a random number between 0 and 99
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* 2. `r2 = r1 / 100` converts random number to be between 0 and 0.99
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* 3. scale and offset the random number to given range of \f$[a,b)\f$
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* \f[
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* y = (b - a) \times \frac{\text{(random number between 0 and RAND_MAX)} \;
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* \text{mod}\; 100}{100} + a \f]
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*
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* \param[in] a lower limit
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* \param[in] b upper limit
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* \returns random number in the range \f$[a,b)\f$
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*/
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double _random(double a, double b)
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{
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return ((b - a) * (rand() % 100) / 100.f) + a;
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}
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/**
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* Save a given n-dimensional data martix to file.
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*
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* \param[in] fname filename to save in (gets overwriten without confirmation)
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* \param[in] X matrix to save
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* \param[in] num_points rows in the matrix = number of points
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* \param[in] num_features columns in the matrix = dimensions of points
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* \returns 0 if all ok
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* \returns -1 if file creation failed
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*/
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int save_2d_data(const char *fname, double **X, int num_points,
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int num_features)
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{
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FILE *fp = fopen(fname, "wt");
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if (!fp) // error with fopen
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{
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char msg[120];
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sprintf(msg, "File error (%s): ", fname);
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perror(msg);
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return -1;
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}
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for (int i = 0; i < num_points; i++) // for each point in the array
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{
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for (int j = 0; j < num_features; j++) // for each feature in the array
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{
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fprintf(fp, "%.4g", X[i][j]); // print the feature value
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if (j < num_features - 1) // if not the last feature
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fputc(',', fp); // suffix comma
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}
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if (i < num_points - 1) // if not the last row
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fputc('\n', fp); // start a new line
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}
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fclose(fp);
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return 0;
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}
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/**
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* Create the distance matrix or
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* [U-matrix](https://en.wikipedia.org/wiki/U-matrix) from the trained weights
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* and save to disk.
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*
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* \param [in] fname filename to save in (gets overwriten without confirmation)
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* \param [in] W model matrix to save
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* \returns 0 if all ok
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* \returns -1 if file creation failed
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*/
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int save_u_matrix(const char *fname, struct array_3d *W)
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{
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FILE *fp = fopen(fname, "wt");
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if (!fp) // error with fopen
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{
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char msg[120];
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sprintf(msg, "File error (%s): ", fname);
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perror(msg);
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return -1;
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}
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int R = max(W->dim1 >> 3, 2); /* neighborhood range */
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for (int i = 0; i < W->dim1; i++) // for each x
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{
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for (int j = 0; j < W->dim2; j++) // for each y
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{
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double distance = 0.f;
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int k;
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int from_x = max(0, i - R);
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int to_x = min(W->dim1, i + R + 1);
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int from_y = max(0, j - R);
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int to_y = min(W->dim2, j + R + 1);
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int l;
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#ifdef _OPENMP
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#pragma omp parallel for reduction(+ : distance)
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#endif
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for (l = from_x; l < to_x; l++) // scan neighborhoor in x
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{
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for (int m = from_y; m < to_y; m++) // scan neighborhood in y
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{
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double d = 0.f;
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for (k = 0; k < W->dim3; k++) // for each feature
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{
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double *w1 = data_3d(W, i, j, k);
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double *w2 = data_3d(W, l, m, k);
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d += (w1[0] - w2[0]) * (w1[0] - w2[0]);
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// distance += w1[0] * w1[0];
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}
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distance += sqrt(d);
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// distance += d;
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}
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}
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distance /= R * R; // mean distance from neighbors
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fprintf(fp, "%.4g", distance); // print the mean separation
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if (j < W->dim2 - 1) // if not the last column
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fputc(',', fp); // suffix comma
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}
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if (i < W->dim1 - 1) // if not the last row
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fputc('\n', fp); // start a new line
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}
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fclose(fp);
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return 0;
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}
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/**
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* Get minimum value and index of the value in a matrix
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* \param[in] X matrix to search
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* \param[in] N number of points in the vector
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* \param[out] val minimum value found
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* \param[out] idx_x x-index where minimum value was found
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* \param[out] idx_y y-index where minimum value was found
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*/
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void get_min_2d(double **X, int N, double *val, int *x_idx, int *y_idx)
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{
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val[0] = INFINITY; // initial min value
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for (int i = 0; i < N; i++) // traverse each x-index
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{
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for (int j = 0; j < N; j++) // traverse each y-index
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{
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if (X[i][j] < val[0]) // if a lower value is found
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{ // save the value and its index
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x_idx[0] = i;
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y_idx[0] = j;
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val[0] = X[i][j];
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}
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}
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}
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}
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/**
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* Update weights of the SOM using Kohonen algorithm
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*
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* \param[in] X data point
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* \param[in,out] W weights matrix
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* \param[in,out] D temporary vector to store distances
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* \param[in] num_out number of output points
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* \param[in] num_features number of features per input sample
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* \param[in] alpha learning rate \f$0<\alpha\le1\f$
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* \param[in] R neighborhood range
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* \returns minimum distance of sample and trained weights
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*/
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double update_weights(const double *X, struct array_3d *W, double **D,
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int num_out, int num_features, double alpha, int R)
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{
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int x, y, k;
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double d_min = 0.f;
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#ifdef _OPENMP
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#pragma omp for
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#endif
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// step 1: for each 2D output point
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for (x = 0; x < num_out; x++)
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{
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for (y = 0; y < num_out; y++)
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{
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D[x][y] = 0.f;
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// compute Euclidian distance of each output
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// point from the current sample
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for (k = 0; k < num_features; k++)
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{
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double *w = data_3d(W, x, y, k);
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D[x][y] += (w[0] - X[k]) * (w[0] - X[k]);
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}
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D[x][y] = sqrt(D[x][y]);
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}
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}
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// step 2: get closest node i.e., node with smallest Euclidian distance to
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// the current pattern
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int d_min_x, d_min_y;
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get_min_2d(D, num_out, &d_min, &d_min_x, &d_min_y);
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// step 3a: get the neighborhood range
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int from_x = max(0, d_min_x - R);
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int to_x = min(num_out, d_min_x + R + 1);
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int from_y = max(0, d_min_y - R);
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int to_y = min(num_out, d_min_y + R + 1);
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// step 3b: update the weights of nodes in the
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// neighborhood
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#ifdef _OPENMP
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#pragma omp for
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#endif
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for (x = from_x; x < to_x; x++)
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{
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for (y = from_y; y < to_y; y++)
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{
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/* you can enable the following normalization if needed.
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personally, I found it detrimental to convergence */
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// const double s2pi = sqrt(2.f * M_PI);
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// double normalize = 1.f / (alpha * s2pi);
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/* apply scaling inversely proportional to distance from the
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current node */
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double d2 =
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(d_min_x - x) * (d_min_x - x) + (d_min_y - y) * (d_min_y - y);
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double scale_factor = exp(-d2 / (2.f * alpha * alpha));
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for (k = 0; k < num_features; k++)
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{
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double *w = data_3d(W, x, y, k);
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// update weights of nodes in the neighborhood
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w[0] += alpha * scale_factor * (X[k] - w[0]);
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}
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}
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}
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return d_min;
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}
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/**
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* Apply incremental algorithm with updating neighborhood and learning rates
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* on all samples in the given datset.
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*
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* \param[in] X data set
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* \param[in,out] W weights matrix
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* \param[in] D temporary vector to store distances
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* \param[in] num_samples number of output points
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* \param[in] num_features number of features per input sample
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* \param[in] num_out number of output points
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* \param[in] alpha_min terminal value of alpha
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*/
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void kohonen_som(double **X, struct array_3d *W, int num_samples,
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int num_features, int num_out, double alpha_min)
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{
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int R = num_out >> 2, iter = 0;
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double **D = (double **)malloc(num_out * sizeof(double *));
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for (int i = 0; i < num_out; i++)
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D[i] = (double *)malloc(num_out * sizeof(double));
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double dmin = 1.f; // average minimum distance of all samples
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// Loop alpha from 1 to slpha_min
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for (double alpha = 1.f; alpha > alpha_min && dmin > 1e-3;
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alpha -= 0.001, iter++)
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{
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dmin = 0.f;
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// Loop for each sample pattern in the data set
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for (int sample = 0; sample < num_samples; sample++)
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{
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// update weights for the current input pattern sample
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dmin += update_weights(X[sample], W, D, num_out, num_features,
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alpha, R);
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}
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// every 20th iteration, reduce the neighborhood range
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if (iter % 100 == 0 && R > 1)
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R--;
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dmin /= num_samples;
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printf("iter: %5d\t alpha: %.4g\t R: %d\td_min: %.4g\r", iter, alpha, R,
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dmin);
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}
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putchar('\n');
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for (int i = 0; i < num_out; i++)
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free(D[i]);
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free(D);
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}
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/** Creates a random set of points distributed in four clusters in
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* 3D space with centroids at the points
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* * \f$(0,5, 0.5, 0.5)\f$
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* * \f$(0,5,-0.5, -0.5)\f$
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* * \f$(-0,5, 0.5, 0.5)\f$
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* * \f$(-0,5,-0.5, -0.5)\f$
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*
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* \param[out] data matrix to store data in
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* \param[in] N number of points required
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*/
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void test_2d_classes(double *const *data, int N)
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{
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const double R = 0.3; // radius of cluster
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int i;
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const int num_classes = 4;
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const double centres[][2] = {
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// centres of each class cluster
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{.5, .5}, // centre of class 1
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{.5, -.5}, // centre of class 2
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{-.5, .5}, // centre of class 3
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{-.5, -.5} // centre of class 4
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};
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#ifdef _OPENMP
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#pragma omp for
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#endif
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for (i = 0; i < N; i++)
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{
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int class = rand() % num_classes; // select a random class for the point
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// create random coordinates (x,y,z) around the centre of the class
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data[i][0] = _random(centres[class][0] - R, centres[class][0] + R);
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data[i][1] = _random(centres[class][1] - R, centres[class][1] + R);
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/* The follosing can also be used
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for (int j = 0; j < 2; j++)
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data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);
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*/
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}
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}
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/** Test that creates a random set of points distributed in four clusters in
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* 2D space and trains an SOM that finds the topological pattern.
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* The following [CSV](https://en.wikipedia.org/wiki/Comma-separated_values)
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* files are created to validate the execution:
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* * `test1.csv`: random test samples points with a circular pattern
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* * `w11.csv`: initial random U-matrix
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* * `w12.csv`: trained SOM U-matrix
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*/
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void test1()
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{
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int j, N = 300;
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int features = 2;
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int num_out = 30; // image size - N x N
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// 2D space, hence size = number of rows * 2
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double **X = (double **)malloc(N * sizeof(double *));
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// cluster nodex in 'x' * cluster nodes in 'y' * 2
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struct array_3d W;
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W.dim1 = num_out;
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W.dim2 = num_out;
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W.dim3 = features;
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W.data = (double *)malloc(num_out * num_out * features *
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sizeof(double)); // assign rows
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for (int i = 0; i < max(num_out, N); i++) // loop till max(N, num_out)
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{
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if (i < N) // only add new arrays if i < N
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X[i] = (double *)malloc(features * sizeof(double));
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if (i < num_out) // only add new arrays if i < num_out
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{
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for (int k = 0; k < num_out; k++)
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{
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#ifdef _OPENMP
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#pragma omp for
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#endif
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// preallocate with random initial weights
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for (j = 0; j < features; j++)
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{
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double *w = data_3d(&W, i, k, j);
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w[0] = _random(-5, 5);
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}
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}
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}
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}
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test_2d_classes(X, N); // create test data around circumference of a circle
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save_2d_data("test1.csv", X, N, features); // save test data points
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save_u_matrix("w11.csv", &W); // save initial random weights
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kohonen_som(X, &W, N, features, num_out, 1e-4); // train the SOM
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save_u_matrix("w12.csv", &W); // save the resultant weights
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for (int i = 0; i < N; i++)
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free(X[i]);
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free(X);
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free(W.data);
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}
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/** Creates a random set of points distributed in four clusters in
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* 3D space with centroids at the points
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* * \f$(0,5, 0.5, 0.5)\f$
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* * \f$(0,5,-0.5, -0.5)\f$
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* * \f$(-0,5, 0.5, 0.5)\f$
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* * \f$(-0,5,-0.5, -0.5)\f$
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*
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* \param[out] data matrix to store data in
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* \param[in] N number of points required
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*/
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void test_3d_classes1(double *const *data, int N)
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{
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const double R = 0.2; // radius of cluster
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int i;
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const int num_classes = 4;
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const double centres[][3] = {
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// centres of each class cluster
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{.5, .5, .5}, // centre of class 1
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{.5, -.5, -.5}, // centre of class 2
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{-.5, .5, .5}, // centre of class 3
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{-.5, -.5 - .5} // centre of class 4
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};
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#ifdef _OPENMP
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#pragma omp for
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#endif
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for (i = 0; i < N; i++)
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{
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int class = rand() % num_classes; // select a random class for the point
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|
|
|
// 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 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 = 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 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 = 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;
|
|
}
|