层次聚类算法之single-linkage和complete-linkage（C语言实现）

2023-10-11 04:48
文章标签 算法 语言 实现 层次 聚类 single complete linkage

本文主要是介绍层次聚类算法之single-linkage和complete-linkage（C语言实现），希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

层次聚类试图在不同层次上对数据集合进行划分， 从而形成树形的聚类结构。数据集的划分可采用“自底向上”的聚合策略，也可以采用“自顶向下”的分拆策略。

AGNES是一种采用自底向上的聚合策略的层次聚合算法，它先将数据集中的每个样本看作是一个初始的聚类簇，然后在算法进行的每一步中找出距离最近的两个聚类来进行合并，该过程不断的重复，直到到达预设的聚类簇的个数。

改算法的关键是如何计算聚类之间的距离， 实际上，每一个聚类是一个样本的集合，因此，只需要采用关于集合的某种距离即可。

最近距离由两个簇的最近的样本来决定， 最大距离由两个簇的最远的样本来决定，由此分别产生的AGNES算法又分别称为single-linkage和complete-linkage算法。


single-linkage算法

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#include<io.h>int sample_size;
int sample_dimension;
char filename[200];double** data;
double** distance;
int cluster_count;void initialization();
void readDataFromFile();
double calculateDistance_BetweenTwoObject(int, int);
void initializationDistanceMatrix();
void AGNES();
void findMinDistance_BetweenClsuter_MIN(int*, int*);
void combineCluster(int, int);
void writeToFile(int);int main(int argc, char* argv[])
{if( argc != 4 ){printf("This algorithm requires 4 user-specified parameter""\n\t\tthe number of sample""\n\t\tthe dimension of sample""\n\t\tthe filename contain the sample""\n\n");exit(0);}sample_size = atoi(argv[1]);sample_dimension = atoi(argv[2]);strcat(filename, argv[3]);initialization();readDataFromFile();initializationDistanceMatrix();AGNES();return 0;
}/** initialize the dynamic array for storing sample* */
void initialization()
{//initializaion the sample dataint i, j;data = (double**)malloc(sizeof(double*) * (sample_size + 1));if( !data ){printf("data malloc error: 0");exit(0);}for( i = 1; i <= sample_size; i++ ){data[i] = (double*)malloc(sizeof(double) * (sample_dimension + 1));if( !data[i] ){printf("data malloc error: %d", i);exit(0);}}//initialiation the distance datadistance = (double**)malloc(sizeof(double*) * (sample_size + 1));if( !distance ){printf("distance malloc error: 0");exit(0);}for( i = 1; i <= sample_size; i++ ){distance[i] = (double*)malloc(sizeof(double) * (sample_size + 1));if( !distance[i] ){printf("distance malloc error: %d", i);exit(0);}}//the 0th element of all row indicate the clauterID of the objectfor( i = 1; i <= sample_size; i++ ){distance[i][0] = i;}
}/** read the sample data from file* */
void readDataFromFile()
{FILE* fread;int i;int j;if( NULL == (fread = fopen(filename, "r"))){printf("open file(%s) error: ", filename);exit(0);}for( i = 1; i <= sample_size; i++ ){for( j = 1; j <= sample_dimension; j++ ){if( 1 != fscanf(fread, "%lf ", &data[i][j])){printf("fscanf error: (%d, %d)", i, j);exit(0);}}}//testprintf("print the origin data:\n");for( i = 1; i <= sample_size; i++ ){for( j = 1; j <= sample_dimension; j++ ){printf("%f\t", data[i][j]);}printf("\n");}//test END
}/** calculate distance between two objects* */
double calculateDistance_BetweenTwoObject(int firstID, int secondID)
{double distance = 0.0;int i;for( i = 1; i <= sample_dimension; i++ ){distance = distance + pow(data[firstID][i] - data[secondID][i], 2);}return sqrt(distance);
}/** calculate initialization distance matrix* */
void initializationDistanceMatrix()
{int i, j;for( i = 1; i <= sample_size; i++ ){for( j = i; j <= sample_size; j++ ){distance[i][j] = calculateDistance_BetweenTwoObject(i, j);distance[j][i] = distance[i][j];}}//testprintf("print the origin distance matrix\n");for( i = 1; i <= sample_size; i++ ){for( j = 0; j <= sample_size; j++ ){printf("%f ", distance[i][j]);}printf("\n");}//test END
}/****************************************************************************************************************						AGNES***************************************************************************************************************/
void AGNES()
{cluster_count = sample_size;int cluster_1, cluster_2;int count = 1;while( cluster_count > 3 ){printf("-------------------%d--------------------\n", count);findMinDistance_BetweenClsuter_MIN(&cluster_1, &cluster_2);combineCluster(cluster_1, cluster_2);				cluster_count--;writeToFile(count++);}
}/** find two clusters the distance between them is minimun, and store the clusterID in @cluster_1 and @cluster_2, respectively.* */
void findMinDistance_BetweenClsuter_MIN(int* cluster_1, int* cluster_2)
{int i, j;double min_distance;int flag = 1;for( i = 1; i <= sample_size; i++ ){for( j = i + 1; j <= sample_size; j++ ){if( distance[i][0] == distance[j][0] ){printf("same cluster!!!! %d and %d\n\n", i , j);continue;}else if( flag == 1 ){min_distance = distance[i][j];*cluster_1 = i;*cluster_2 = j;flag = 0;printf("----get the initial minimum distance is %f(%d, %d)\n", min_distance, i, j);continue;}if( distance[i][j] < min_distance ){min_distance = distance[i][j];*cluster_1 = i;*cluster_2 = j;}}}printf("the minimum is %f :(%d, %d)\n", min_distance, *cluster_1, *cluster_2);
}/** combine the two clusters to one* */
void combineCluster(int cluster_1, int cluster_2)
{int i;int buffer;buffer = distance[cluster_2][0];for( i = 1; i <= sample_size; i++ ){if( distance[i][0] == buffer ){distance[i][0] = distance[cluster_1][0];}}//testprintf(" the minimum distance is %f, and the object is %d and %d\n", distance[cluster_1][cluster_2], cluster_1, cluster_2);int j;for( i = 1; i <= sample_size; i++ ){for( j = 0; j <= sample_size; j++ ){printf("%f ", distance[i][j]);}printf("\n");}
}/** write the result of clustering information to file* */
void writeToFile(int round)
{int i;int j;int* auxiliary = (int*)malloc(sizeof(int) * (sample_size + 1));if( !auxiliary ){printf("auxiliary malloc error");exit(0);}for( i = 1; i <= sample_size; i++ )auxiliary[i] = 0;for( i = 1; i <= sample_size; i++ ){auxiliary[(int)distance[i][0]]++;}int *clusterID = (int*)malloc(sizeof(int) * (sample_size - round + 1));if( !clusterID ){printf("clusterID malloc error");exit(0);}int counter = 1;for( i = 1; i <= sample_size; i++ ){if( auxiliary[i] != 0 )clusterID[counter++] = i;}//testprintf("cluster ID:");for( i = 1; i <= sample_size - round; i++ ){printf("%d ", clusterID[i]);}printf("\n");//test ENDprintf("writeToFile -----------round: %d\n", round);FILE** fwrite;fwrite = (FILE**)malloc(sizeof(FILE*) * (sample_size + 1));if( !fwrite ){printf("fwrite malloc error\n");exit(0);}char filename[200] = "";char instruction[200] = "";sprintf(instruction, "md  Round_%d", round);system(instruction);for( i = 1; i <= sample_size - round; i++ ){sprintf(filename, ".//Round_%d//cluster_%d.data", round, clusterID[i]);if( NULL == (fwrite[clusterID[i]] = fopen(filename, "w"))){printf("open file(%s) error\n", filename);exit(0);}}for( i = 1; i <= sample_size; i++ ){printf("%d ", (int)distance[i][0]);for( j = 1; j <= sample_dimension; j++ ){fprintf(fwrite[(int)distance[i][0]], "%f\t", data[i][j]);printf("%f ", data[i][j]);}fprintf(fwrite[(int)distance[i][0]], "\n");printf("\n");}for( i = 1; i <= sample_size - round; i++ ){fclose(fwrite[clusterID[i]]);}
}

complete-linkage算法 

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#include<io.h>int sample_size;
int sample_dimension;
char filename[200];double** data;
double** distance;
int cluster_count;void initialization();
void readDataFromFile();
double calculateDistance_BetweenTwoObject(int, int);
void initializationDistanceMatrix();
void findMinDistance_BetweenClsuter_MAX(int*, int*);
void AGNES();
void combineCluster(int, int);
void updateDistance(int);
void writeToFile(int);int main(int argc, char* argv[])
{if( argc != 4 ){printf("This algorithm requires 4 user-specified parameter""\n\t\tthe number of sample""\n\t\tthe dimension of sample""\n\t\tthe filename contain the sample""\n\n");exit(0);}sample_size = atoi(argv[1]);sample_dimension = atoi(argv[2]);strcat(filename, argv[3]);initialization();readDataFromFile();initializationDistanceMatrix();AGNES();return 0;
}/** initialize the dynamic array for storing sample* */
void initialization()
{//initializaion the sample dataint i, j;data = (double**)malloc(sizeof(double*) * (sample_size + 1));if( !data ){printf("data malloc error: 0");exit(0);}for( i = 1; i <= sample_size; i++ ){data[i] = (double*)malloc(sizeof(double) * (sample_dimension + 1));if( !data[i] ){printf("data malloc error: %d", i);exit(0);}}//initialiation the distance datadistance = (double**)malloc(sizeof(double*) * (sample_size + 1));if( !distance ){printf("distance malloc error: 0");exit(0);}for( i = 0; i <= sample_size; i++ ){distance[i] = (double*)malloc(sizeof(double) * (sample_size + 1));if( !distance[i] ){printf("distance malloc error: %d", i);exit(0);}}//the 0th element of all row indicate the clauterID of the objectfor( i = 1; i <= sample_size; i++ ){distance[i][0] = i;}//where reserved if distance[0][i] = 1, for( i = 1; i <= sample_size; i++ ){distance[0][i] = 1;}
}/** read the sample data from file* */
void readDataFromFile()
{FILE* fread;int i;int j;if( NULL == (fread = fopen(filename, "r"))){printf("open file(%s) error: ", filename);exit(0);}for( i = 1; i <= sample_size; i++ ){for( j = 1; j <= sample_dimension; j++ ){if( 1 != fscanf(fread, "%lf ", &data[i][j])){printf("fscanf error: (%d, %d)", i, j);exit(0);}}}
}/** calculate distance between two objects* */
double calculateDistance_BetweenTwoObject(int firstID, int secondID)
{double distance = 0.0;int i;for( i = 1; i <= sample_dimension; i++ ){distance = distance + pow(data[firstID][i] - data[secondID][i], 2);}return sqrt(distance);
}/** calculate initialization distance matrix* */
void initializationDistanceMatrix()
{int i, j;for( i = 1; i <= sample_size; i++ ){for( j = i; j <= sample_size; j++ ){distance[i][j] = calculateDistance_BetweenTwoObject(i, j);distance[j][i] = distance[i][j];}}
}/****************************************************************************************************************						AGNES***************************************************************************************************************/
void AGNES()
{cluster_count = sample_size;int cluster_1, cluster_2;int count = 1;while( cluster_count > 3 ){printf("-------------------%d--------------------\n", count);findMinDistance_BetweenClsuter_MAX(&cluster_1, &cluster_2);combineCluster(cluster_1, cluster_2);updateDistance(cluster_1);		cluster_count--;writeToFile(count++);}
}/** find two clusters the distance between them is minimun, and store the clusterID in @cluster_1 and @cluster_2, respectively.* */
void findMinDistance_BetweenClsuter_MAX(int* cluster_1, int* cluster_2)
{int i, j;double min_distance;int flag = 1;int object_1;int object_2;for( i = 1; i <= sample_size; i++ ){for( j = i + 1; j <= sample_size; j++ ){if( distance[i][0] == distance[j][0] || ( distance[0][i] == 0 || distance[0][j] == 0 ) ){continue;}else if( flag == 1 ){min_distance = distance[i][j];object_1 = i;object_2 = j;flag = 0;continue;}if( distance[i][j] < min_distance ){min_distance = distance[i][j];object_1 = i;object_2 = j;}}}*cluster_1 = distance[object_1][0];*cluster_2 = distance[object_2][0];
}/** combine the two clusters to one* */
void combineCluster(int cluster_1, int cluster_2)
{int i;for( i = 1; i <= sample_size; i++ ){if( distance[i][0] == cluster_2 ){distance[i][0] = cluster_1;}}
}/** update distance data* */
void updateDistance(int clusterID)
{int i, j;int flag = 1;int save_i;for( i = 1; i <= sample_size; i++ ){if( distance[i][0] == clusterID && flag == 1 ){flag = 0;save_i = i;continue;}else if( distance[i][0] == clusterID && flag == 0 ){distance[0][i] = 0;for( j = 1; j <= sample_size; j++ ){if( distance[i][j] > distance[save_i][j] ){distance[save_i][j] = distance[i][j];}}}}for( i = 1; i <= sample_size; i++ ){distance[i][save_i] = distance[save_i][i];}
}/** write the result of clustering information to file* */
void writeToFile(int round)
{int i;int j;int* auxiliary = (int*)malloc(sizeof(int) * (sample_size + 1));if( !auxiliary ){printf("auxiliary malloc error");exit(0);}for( i = 1; i <= sample_size; i++ )auxiliary[i] = 0;for( i = 1; i <= sample_size; i++ ){auxiliary[(int)distance[i][0]]++;}int *clusterID = (int*)malloc(sizeof(int) * (sample_size - round + 1));if( !clusterID ){printf("clusterID malloc error");exit(0);}int counter = 1;for( i = 1; i <= sample_size; i++ ){if( auxiliary[i] != 0 )clusterID[counter++] = i;}printf("writeToFile -----------round: %d\n", round);FILE** fwrite;fwrite = (FILE**)malloc(sizeof(FILE*) * (sample_size + 1));if( !fwrite ){printf("fwrite malloc error\n");exit(0);}char filename[200] = "";char instruction[200] = "";sprintf(instruction, "md  Round_%d", round);system(instruction);for( i = 1; i <= sample_size - round; i++ ){sprintf(filename, ".//Round_%d//cluster_%d.data", round, clusterID[i]);if( NULL == (fwrite[clusterID[i]] = fopen(filename, "w"))){printf("open file(%s) error\n", filename);exit(0);}}for( i = 1; i <= sample_size; i++ ){printf("%d ", (int)distance[i][0]);for( j = 1; j <= sample_dimension; j++ ){fprintf(fwrite[(int)distance[i][0]], "%f\t", data[i][j]);}fprintf(fwrite[(int)distance[i][0]], "\n");}for( i = 1; i <= sample_size - round; i++ ){fclose(fwrite[clusterID[i]]);}
}


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