K Means Clustering
A
/**
* @file k_means_clustering.c
* @brief K Means Clustering Algorithm implemented
* @details
* This file has K Means algorithm implemmented
* It prints test output in eps format
*
* Note:
* Though the code for clustering works for all the
* 2D data points and can be extended for any size vector
* by making the required changes, but note that
* the output method i.e. printEPS is only good for
* polar data points i.e. in a circle and both test
* use the same.
* @author [Lakhan Nad](https://github.com/Lakhan-Nad)
*/
#define _USE_MATH_DEFINES /* required for MS Visual C */
#include <float.h> /* DBL_MAX, DBL_MIN */
#include <math.h> /* PI, sin, cos */
#include <stdio.h> /* printf */
#include <stdlib.h> /* rand */
#include <string.h> /* memset */
#include <time.h> /* time */
/*!
* @addtogroup machine_learning Machine Learning Algorithms
* @{
* @addtogroup k_means K-Means Clustering Algorithm
* @{
*/
/*! @struct observation
* a class to store points in 2d plane
* the name observation is used to denote
* a random point in plane
*/
typedef struct observation
{
double x; /**< abscissa of 2D data point */
double y; /**< ordinate of 2D data point */
int group; /**< the group no in which this observation would go */
} observation;
/*! @struct cluster
* this class stores the coordinates
* of centroid of all the points
* in that cluster it also
* stores the count of observations
* belonging to this cluster
*/
typedef struct cluster
{
double x; /**< abscissa centroid of this cluster */
double y; /**< ordinate of centroid of this cluster */
size_t count; /**< count of observations present in this cluster */
} cluster;
/*!
* Returns the index of centroid nearest to
* given observation
*
* @param o observation
* @param clusters array of cluster having centroids coordinates
* @param k size of clusters array
*
* @returns the index of nearest centroid for given observation
*/
int calculateNearst(observation* o, cluster clusters[], int k)
{
double minD = DBL_MAX;
double dist = 0;
int index = -1;
int i = 0;
for (; i < k; i++)
{
/* Calculate Squared Distance*/
dist = (clusters[i].x - o->x) * (clusters[i].x - o->x) +
(clusters[i].y - o->y) * (clusters[i].y - o->y);
if (dist < minD)
{
minD = dist;
index = i;
}
}
return index;
}
/*!
* Calculate centoid and assign it to the cluster variable
*
* @param observations an array of observations whose centroid is calculated
* @param size size of the observations array
* @param centroid a reference to cluster object to store information of
* centroid
*/
void calculateCentroid(observation observations[], size_t size,
cluster* centroid)
{
size_t i = 0;
centroid->x = 0;
centroid->y = 0;
centroid->count = size;
for (; i < size; i++)
{
centroid->x += observations[i].x;
centroid->y += observations[i].y;
observations[i].group = 0;
}
centroid->x /= centroid->count;
centroid->y /= centroid->count;
}
/*!
* --K Means Algorithm--
* 1. Assign each observation to one of k groups
* creating a random initial clustering
* 2. Find the centroid of observations for each
* cluster to form new centroids
* 3. Find the centroid which is nearest for each
* observation among the calculated centroids
* 4. Assign the observation to its nearest centroid
* to create a new clustering.
* 5. Repeat step 2,3,4 until there is no change
* the current clustering and is same as last
* clustering.
*
* @param observations an array of observations to cluster
* @param size size of observations array
* @param k no of clusters to be made
*
* @returns pointer to cluster object
*/
cluster* kMeans(observation observations[], size_t size, int k)
{
cluster* clusters = NULL;
if (k <= 1)
{
/*
If we have to cluster them only in one group
then calculate centroid of observations and
that will be a ingle cluster
*/
clusters = (cluster*)malloc(sizeof(cluster));
memset(clusters, 0, sizeof(cluster));
calculateCentroid(observations, size, clusters);
}
else if (k < size)
{
clusters = malloc(sizeof(cluster) * k);
memset(clusters, 0, k * sizeof(cluster));
/* STEP 1 */
for (size_t j = 0; j < size; j++)
{
observations[j].group = rand() % k;
}
size_t changed = 0;
size_t minAcceptedError =
size /
10000; // Do until 99.99 percent points are in correct cluster
int t = 0;
do
{
/* Initialize clusters */
for (int i = 0; i < k; i++)
{
clusters[i].x = 0;
clusters[i].y = 0;
clusters[i].count = 0;
}
/* STEP 2*/
for (size_t j = 0; j < size; j++)
{
t = observations[j].group;
clusters[t].x += observations[j].x;
clusters[t].y += observations[j].y;
clusters[t].count++;
}
for (int i = 0; i < k; i++)
{
clusters[i].x /= clusters[i].count;
clusters[i].y /= clusters[i].count;
}
/* STEP 3 and 4 */
changed = 0; // this variable stores change in clustering
for (size_t j = 0; j < size; j++)
{
t = calculateNearst(observations + j, clusters, k);
if (t != observations[j].group)
{
changed++;
observations[j].group = t;
}
}
} while (changed > minAcceptedError); // Keep on grouping until we have
// got almost best clustering
}
else
{
/* If no of clusters is more than observations
each observation can be its own cluster
*/
clusters = (cluster*)malloc(sizeof(cluster) * k);
memset(clusters, 0, k * sizeof(cluster));
for (int j = 0; j < size; j++)
{
clusters[j].x = observations[j].x;
clusters[j].y = observations[j].y;
clusters[j].count = 1;
observations[j].group = j;
}
}
return clusters;
}
/**
* @}
* @}
*/
/*!
* A function to print observations and clusters
* The code is taken from
* http://rosettacode.org/wiki/K-means%2B%2B_clustering.
* Even the K Means code is also inspired from it
*
* @note To print in a file use pipeline operator
* ```sh
* ./k_means_clustering > image.eps
* ```
*
* @param observations observations array
* @param len size of observation array
* @param cent clusters centroid's array
* @param k size of cent array
*/
void printEPS(observation pts[], size_t len, cluster cent[], int k)
{
int W = 400, H = 400;
double min_x = DBL_MAX, max_x = DBL_MIN, min_y = DBL_MAX, max_y = DBL_MIN;
double scale = 0, cx = 0, cy = 0;
double* colors = (double*)malloc(sizeof(double) * (k * 3));
int i;
size_t j;
double kd = k * 1.0;
for (i = 0; i < k; i++)
{
*(colors + 3 * i) = (3 * (i + 1) % k) / kd;
*(colors + 3 * i + 1) = (7 * i % k) / kd;
*(colors + 3 * i + 2) = (9 * i % k) / kd;
}
for (j = 0; j < len; j++)
{
if (max_x < pts[j].x)
{
max_x = pts[j].x;
}
if (min_x > pts[j].x)
{
min_x = pts[j].x;
}
if (max_y < pts[j].y)
{
max_y = pts[j].y;
}
if (min_y > pts[j].y)
{
min_y = pts[j].y;
}
}
scale = W / (max_x - min_x);
if (scale > (H / (max_y - min_y)))
{
scale = H / (max_y - min_y);
};
cx = (max_x + min_x) / 2;
cy = (max_y + min_y) / 2;
printf("%%!PS-Adobe-3.0 EPSF-3.0\n%%%%BoundingBox: -5 -5 %d %d\n", W + 10,
H + 10);
printf(
"/l {rlineto} def /m {rmoveto} def\n"
"/c { .25 sub exch .25 sub exch .5 0 360 arc fill } def\n"
"/s { moveto -2 0 m 2 2 l 2 -2 l -2 -2 l closepath "
" gsave 1 setgray fill grestore gsave 3 setlinewidth"
" 1 setgray stroke grestore 0 setgray stroke }def\n");
for (int i = 0; i < k; i++)
{
printf("%g %g %g setrgbcolor\n", *(colors + 3 * i),
*(colors + 3 * i + 1), *(colors + 3 * i + 2));
for (j = 0; j < len; j++)
{
if (pts[j].group != i)
{
continue;
}
printf("%.3f %.3f c\n", (pts[j].x - cx) * scale + W / 2,
(pts[j].y - cy) * scale + H / 2);
}
printf("\n0 setgray %g %g s\n", (cent[i].x - cx) * scale + W / 2,
(cent[i].y - cy) * scale + H / 2);
}
printf("\n%%%%EOF");
// free accquired memory
free(colors);
}
/*!
* A function to test the kMeans function
* Generates 100000 points in a circle of
* radius 20.0 with center at (0,0)
* and cluster them into 5 clusters
*
* <img alt="Output for 100000 points divided in 5 clusters" src=
* "https://raw.githubusercontent.com/TheAlgorithms/C/docs/images/machine_learning/k_means_clustering/kMeansTest1.png"
* width="400px" heiggt="400px">
* @returns None
*/
static void test()
{
size_t size = 100000L;
observation* observations =
(observation*)malloc(sizeof(observation) * size);
double maxRadius = 20.00;
double radius = 0;
double ang = 0;
size_t i = 0;
for (; i < size; i++)
{
radius = maxRadius * ((double)rand() / RAND_MAX);
ang = 2 * M_PI * ((double)rand() / RAND_MAX);
observations[i].x = radius * cos(ang);
observations[i].y = radius * sin(ang);
}
int k = 5; // No of clusters
cluster* clusters = kMeans(observations, size, k);
printEPS(observations, size, clusters, k);
// Free the accquired memory
free(observations);
free(clusters);
}
/*!
* A function to test the kMeans function
* Generates 1000000 points in a circle of
* radius 20.0 with center at (0,0)
* and cluster them into 11 clusters
*
* <img alt="Output for 1000000 points divided in 11 clusters" src=
* "https://raw.githubusercontent.com/TheAlgorithms/C/docs/images/machine_learning/k_means_clustering/kMeansTest2.png"
* width="400px" heiggt="400px">
* @returns None
*/
void test2()
{
size_t size = 1000000L;
observation* observations =
(observation*)malloc(sizeof(observation) * size);
double maxRadius = 20.00;
double radius = 0;
double ang = 0;
size_t i = 0;
for (; i < size; i++)
{
radius = maxRadius * ((double)rand() / RAND_MAX);
ang = 2 * M_PI * ((double)rand() / RAND_MAX);
observations[i].x = radius * cos(ang);
observations[i].y = radius * sin(ang);
}
int k = 11; // No of clusters
cluster* clusters = kMeans(observations, size, k);
printEPS(observations, size, clusters, k);
// Free the accquired memory
free(observations);
free(clusters);
}
/*!
* This function calls the test
* function
*/
int main()
{
srand(time(NULL));
test();
/* test2(); */
return 0;
}
