Type:	Package
Title:	Clustering with a Novel Non Euclidean Relative Distance
Version:	0.1.0
Author:	Irene Creus Martí [aut, cre]
Maintainer:	Irene Creus Martí <ircrmar@mat.upv.es>
Description:	Using the novel Relative Distance to cluster datasets. Implementation of a clustering approach based on the k-means algorithm that can be used with any distance. In addition, implementation of the Hartigan and Wong method to accommodate alternative distance metrics. Both methods can operate with any distance measure, provided a suitable method is available to compute cluster centers under the chosen metric. Additionally, the k-medoids algorithm is implemented, offering a robust alternative for clustering without the need of computing cluster centers under the chosen metric. All three methods are designed to support Relative distances, Euclidean distances, and any user-defined distance functions. The Hartigan and Wong method is described in Hartigan and Wong (1979) <doi:10.2307/2346830> and an explanation of the k-medoids algorithm can be found in Reynolds et al (2006) <doi:10.1007/s10852-005-9022-1>.
License:	GPL-3
Encoding:	UTF-8
Imports:	compositions, proxy, utils, ggpubr, factoextra, ggplot2
Suggests:	testthat (≥ 3.0.0), clusterSim, fpc, gtools, cluster
Config/testthat/edition:	3
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2025-09-17 13:57:44 UTC; IRENE
Repository:	CRAN
Date/Publication:	2025-09-22 11:50:06 UTC

Aitchison distance

Description

This function calculates the Aitchison distance between two vectors.

Usage

AitchisonDistance(vect1, vect2)

Arguments

Value

A number with the distance between vect1 and vect2.

Examples

  AitchisonDistance(c(1,2,3), c(4,5,6))

Bray-Curtis dissimilarity

Description

This function calculates the Bray-Curtis dissimilarity between two vectors

Usage

BrayCurtisDissimilarity(x, y)

Arguments

Value

A number with the Bray-Curtis dissimilarity between x and y.

Examples

  BrayCurtisDissimilarity(c(1,2,3), c(4,5,6))

Plotting the clustring results

Description

This function performs a PCA to reduce the dataset to two dimensions. Then, it draws the points, marks the center of the groups, the exact groups and the obtained groups.

Usage

ClustPlot(data, grouping, exact_grouping, centers, k)

Arguments

Value

Returns a plot where it is possible to visualize the he points, the center of the groups, the exact groups (represented in the type of point used to represent the data) and the obtained groups (observed in the geometric froms that join the points).

Examples

data=iris[,-5]
exact_grouping=list(which(iris[,5]=="setosa"),
                   which(iris[,5]=="versicolor"),
                   which(iris[,5]=="virginica"))

grouping=list(c(1:40),c(41:90),c(91:150))
k=3
centers=rbind(c(1,2,3,4),c(2,3,4,5),c(4,5,6,7))

ClustPlot(data, grouping, exact_grouping,centers, k)

Davies-Bouldin index

Description

This function calculates the Davies-Bouldin index as is defined by Davies and Bouldin (1979) without imposing that the use of the euclidean distance. This function allows calculating the Davies-Bouldin index using different distances.

Usage

DaviesBouldinIndex(data, FHW_output, distance)

Arguments

Value

Returns a number, the value of the Davies-Bouldin index.

References

Davies, D. L., & Bouldin, D. W. (1979). A cluster separation measure. IEEE transactions on pattern analysis and machine intelligence, (2), 224-227.

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
          matrix(runif(20,20,30), nrow = 2, ncol = 10),
          matrix(runif(20,50,70), nrow = 2, ncol = 10))
k=3
seed=5


FHW_output=Hartigan_and_Wong(data,
                            Euclideandistance,
                            k,
                            centers_function_mean,
                            init_centers_random,
                            seed=seed,
                            10)

DaviesBouldinIndex(data, FHW_output, Euclideandistance)

Finding IC1 and IC2 from a distance matrix

Description

This function finds the IC1 and IC2 from a distance matrix. IC1 and IC2 are the closets and second closest cluster centers.

Usage

Dist_IC1_IC2(Dist_e_cent)

Arguments

Value

Returns a matrix. The first column contain the IC1 and the second column contain the IC2.

Examples

dist=rbind(c(1,2,3),c(6,19,2),c(2,4,1),c(2,3,9))
Dist_IC1_IC2(dist)

Distance between groups

Description

This function calculates the distance between points in two groups. For each point in the first group, it calculates the distance from that point to all points in the second group. Finally, it takes the minimum distance obtained.

Usage

DistanceBetweenGroups(group1, group2, FHW_output, distance, data)

Arguments

Value

Returns a number, the value of the minimum distance between pair of points of the two groups.

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
         matrix(runif(20,20,30), nrow = 2, ncol = 10),
         matrix(runif(20,50,70), nrow = 2, ncol = 10))
k=3
seed=5


FHW_output=Hartigan_and_Wong(data,
                            Euclideandistance,
                            k,
                            centers_function_mean,
                            init_centers_random,
                            seed=seed,
                            10)

DistanceBetweenGroups(1, 2, FHW_output, Euclideandistance, data)

Distance between points in the same group

Description

This function calculates the distance between points in the same group. This function calculates the distance between the pair of points in the group. Then, takes the maximum distance.

Usage

DistanceSameGroup(group1, FHW_output, data, distance)

Arguments

Value

Returns a number, the value of the maximum distance between pair of points of the group.

Examples

set.seed(451)
data=rbind(matrix(runif(30,1,5), nrow = 3, ncol = 10),
          matrix(runif(20,20,30), nrow = 2, ncol = 10),
          matrix(runif(20,50,70), nrow = 2, ncol = 10))
k=3
seed=5


FHW_output=Hartigan_and_Wong(data,
                            Euclideandistance,
                            k,
                            centers_function_mean,
                            init_centers_random,
                            seed=seed,
                            10)

DistanceSameGroup(2,  FHW_output, data, Euclideandistance)

Finding the two smallest values for each row of a matrix

Description

This function finds the two smallest values for each row of a matrix matriz.

Usage

DosMinimos(matriz)

Arguments

Value

Returns a matrix. The row i contains the two minimum values of the row i of the matrix matriz. The first column of the matriz contains the smallest value.

Examples

ma=rbind(c(5,4,3,2,1), c(10,9,8,7,6), c(120,119,103,104,105))
DosMinimos(ma)

Dunn's index

Description

This function calculates the Dunn's index as is defined in Bezdek and Pal (1995) without imposing that the use of the euclidean distance. This function allows calculating the Dunn's index using different distances.

Usage

DunnIndex(data, FHW_output, distance)

Arguments

Value

Returns a number, the value of the Dunn's index.

References

Bezdek, J. C., & Pal, N. R. (1995, November). Cluster validation with generalized Dunn's indices. In Proceedings 1995 second New Zealand international two-stream conference on artificial neural networks and expert systems (pp. 190-193). IEEE.

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
         matrix(runif(20,20,30), nrow = 2, ncol = 10),
         matrix(runif(20,50,70), nrow = 2, ncol = 10))
k=3
seed=5

FHW_output=Hartigan_and_Wong(data,
                            Euclideandistance,
                            k,
                            centers_function_mean,
                            init_centers_random,
                            seed=seed,
                            10)

DunnIndex(data, FHW_output, Euclideandistance)

Sum of squared errors within the cluster

Description

The sum of squared errors within the cluster (also known as inertia) is calculated. We calculate the squared distance between the points that belong to a cluster and the cluster centroid. Then, we sum all the squared distances obtained. In this function the user can choose the distance that want to use to calculate the sum of squared errors within the cluster.

Usage

ECDentroCluster(data, FHW_output, distance)

Arguments

Value

Returns a vector. The component i contains the sum of squared errors value of group i.

Examples

set.seed(231)
data1=gtools::rdirichlet(10,c(1,1,1,4,4))
data=t(data1)
grouping=list(c(1,2,3),c(4,5))
centers=centers_function_mean(data, grouping)
FHW_output=list(centers=centers,   grouping=grouping)
distance=Euclideandistance

ECDentroCluster(data, FHW_output, distance)

Sum of errors within the cluster

Description

We calculate the distance between the points that belong to a cluster and the cluster centroid. Then, we sum all the distances obtained. In this function the user can choose the distance that want to use to calculate the sum of errors within the cluster.

Usage

ECDentroCluster3(data, FHW_output, distance)

Arguments

Value

Returns a vector. The component i contains the sum of squared errors value of group i.

Examples

#'set.seed(231)
data1=gtools::rdirichlet(10,c(1,1,1,4,4))
data=t(data1)
grouping=list(c(1,2,3),c(4,5))
centers=centers_function_mean(data, grouping)
FHW_output=list(centers=centers,   grouping=grouping)
distance=Euclideandistance

ECDentroCluster3(data, FHW_output, distance)

Euclidean distance

Description

This function calculates the euclidean distance between two vectors

Usage

Euclideandistance(vect1, vect2)

Arguments

Value

A number with the distance between vect1 and vect2.

Examples

  Euclideandistance(c(1,2,3), c(4,5,6))

Flexibilization of the Hartigan and Wong algorithm

Description

This function implements the Hartigan and Wong algorithm (Hartigan and Wong, 1979) without imposing the use of the euclidean distance and without imposing that the centers of the groups are calculated by averaging the points. This function allow the use of other distances and different ways to calculate the centers of the groups.

Usage

Hartigan_and_Wong(
  data,
  distance,
  k,
  centers_function,
  init_centers,
  seed = NULL,
  ITER
)

Arguments

Value

Returns a list with:

• centers: the information of the centers updated. Matrix with dim(centers)[1] centers of dim(centers)[2] dimensions.

• grouping: the information of the groups updated. List. Each component of the list contains a vector with the points that belong to that group. More specifically, the list component i has a vector with the numbers of the row of the matrix data where the points belonging to group i are.

References

Hartigan, J. A., & Wong, M. A. (1979). Algorithm AS 136: A k-means clustering algorithm. Journal of the royal statistical society. series c (applied statistics), 28(1), 100-108.

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
         matrix(runif(20,20,30), nrow = 2, ncol = 10),
         matrix(runif(20,50,70), nrow = 2, ncol = 10))
k=3
seed=5

Hartigan_and_Wong(data,
                 Euclideandistance,
                 k,
                 centers_function_mean,
                 init_centers_random,
                 seed=seed,
                 10)

Hartigan and Wong algorithm

Description

This function apply the Hartigan_and_Wong to different number of groups and calculates quality metrics as Silhouette.

Usage

Hartigan_and_Wong_total(
  data,
  distance,
  centers_function,
  init_centers,
  seed = NULL,
  ITER,
  KK = 10,
  index = "DaviesBouldin",
  k = NULL
)

Arguments

Value

Returns a list with:

• Number_of_groups: Number of groups took into account to cluster.

• Output_of_grouping: list with the centers and the clusters.

• Quality: vector with the Silhouette index, Davies Bouldin Index, the Dunn index, the Within Cluster Sum (WCS) and the time (in seconds) that the function Hartigan_and_Wong needs to be executed. The WCS is equal to the sum of the distance of each point to the center of its group.

References

Hartigan, J. A., & Wong, M. A. (1979). Algorithm AS 136: A k-means clustering algorithm. Journal of the royal statistical society. series c (applied statistics), 28(1), 100-108.

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
          matrix(runif(20,20,30), nrow = 2, ncol = 10),
          matrix(runif(20,50,70), nrow = 2, ncol = 10))



RES=Hartigan_and_Wong_total(data,
                           RelativeDistance,
                           centers_function_RelativeDistance,
                           init_centers_random,
                           seed=10,
                           ITER=10,
                           KK=4,
                           index="DaviesBould",
                           k=NULL)

Manhattan distance

Description

This function calculates the Manhattan distance between two vectors

Usage

ManhattanDistance(x, y)

Arguments

Value

A number with the distance between x and y.

Examples

  ManhattanDistance(c(1,2,3), c(4,5,6))

Non Euclidean Algorithm to Cluster

Description

We give initial centers, calculate the distance between each point and each center and assign each point to the center with minimum distance. Calculate the center of the group and repeat the process. The process is stopped when the distance between a center and the previous one is small than COTA or the maximum number of iterations is reached.

Usage

NEC(data, distance, k, centers_function, init_centers, seed = NULL, ITER, COTA)

Arguments

Value

Returns a list with:

• FHW_output; is a list with

  • centers: the information of the centers updated. Matrix with dim(centers)[1] centers of dim(centers)[2] dimensions.

  • grouping: the information of the groups updated. List. Each component of the list contains a vector with the points that belong to that group. More specifically, the list component i has a vector with the numbers of the row of the matrix data where the points belonging to group i are.

• Stop_Criteria: returns the distance between one center and the previous one for all the iterations

• Chanche_yes_no: matrix, in the position [i,j] returns "yes" if the point i have changed its group in the iteration j and return "no" if the point have not changed.

• all_output: is a list with the information of the center and the groups of each iteration of the process

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
          matrix(runif(20,20,30), nrow = 2, ncol = 10),
          matrix(runif(20,50,70), nrow = 2, ncol = 10))
k=3
seed=5


o2=NEC(data,
      RelativeDistance,
      k,
      centers_function_RelativeDistance,
      init_centers_random,
      seed=seed,
      10,
      0.01)

NEC algorithm

Description

This function apply the NEC to different number of groups and calculates quality metrics as Silhouette.

Usage

NEC_total(
  data,
  distance,
  centers_function,
  init_centers,
  seed = NULL,
  ITER,
  COTA,
  KK = 10,
  index = "DaviesBouldinIndex",
  k = NULL
)

Arguments

Value

Returns a list with:

• Number_of_groups: Number of groups took into account to cluster.

• Output_of_grouping: list with the centers and the clusters.

• Quality: vector with the Silhouette index, Davies Bouldin Index, the Dunn index, the Within Cluster Sum (WCS) and the time (in seconds) that algorithm needs to be executed. The WCS is equal to the sum of the distance of each point to the center of its group.

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
         matrix(runif(20,20,30), nrow = 2, ncol = 10),
         matrix(runif(20,50,70), nrow = 2, ncol = 10))

RES=NEC_total(data,
             RelativeDistance,
             centers_function_RelativeDistance,
             init_centers_random,
             seed=10,
             ITER=10,
             0.01,
             KK=4,
             index="DaviesBould",
             k=NULL)

Comparison of groupings

Description

This function compares the real clustering with a clustering obtained with some mathematical method. For each group, this function calculates the number of components that are in the expected grouping that are not in the real grouping. This function adds this value for all groups. It calculates it for all possible combinations of groups and returns the minimum value.

Usage

Number_of_failes(grouping_exact, grouping_obtained)

Arguments

Value

Returns a number with the quantity of points that are misclassified in the grouping_obtained.

Examples

grouping_exact=list(c(1,2,3,4,5),c(6,7),c(8,9))
grouping_obtained=list(c(1,3,7),c(2,4,6),c(8,9,5))

Number_of_failes(grouping_exact, grouping_obtained)

Relative Distance

Description

This function calculates the Relative Distance between two vectors.

Usage

RelativeDistance(vect1, vect2)

Arguments

Value

A number with the distance between vect1 and vect2.

Examples

  RelativeDistance(c(1,2,3), c(4,5,6))

Silhouette

Description

This function calculates the Silhouette as is defined in Rousseeuw (1987) without imposing that the use of the euclidean distance. This allows calculating the Silhouette using different distances. Note that the Silhouette must be calculated using a distance that is a a ratio scale (Rousseeuw, 1987).

Usage

Silhouette(data, FHW_output, distance)

Arguments

Value

Returns a vector. The component i contains the Silhouette value of the point in the row i of the data matrix.

References

Rousseeuw, P.J. (1987) Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math., 20, 53–65.

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
          matrix(runif(20,20,30), nrow = 2, ncol = 10),
          matrix(runif(20,50,70), nrow = 2, ncol = 10))
k=3
seed=5

FHW_output=Hartigan_and_Wong(data,
                            Euclideandistance,
                            k,
                            centers_function_mean,
                            init_centers_random,
                            seed=seed,
                            10)

Silhouette(data, FHW_output, Euclideandistance)

Step 4 of the Hartigan and Wong algorithm

Description

This function implements the Step 4 of the Hartigan and Wong (Hartigan and Wong, 1979) algorithm without imposing that the use of the euclidean distance and without imposing that the centers of the groups are calculated by averaging the points. This function allows other distances to be used and allows the centers of the groups to be calculated in different ways.

Usage

Step4(
  data,
  centers,
  grouping,
  LIVE_SET_original,
  distance,
  centers_function,
  Ic12_change,
  index
)

Arguments

Value

Returns a list with:

• centers: the information of the centers updated. Matrix with dim(centers)[1] centers of dim(centers)[2] dimensions.

• IC1andIC2: the information of the IC1 and IC2 updated. Matrix. The first row contains the IC1 of each point. The second column contains the IC2 of each point. IC1 and IC2 are the closets and second closest cluster centers.

• grouping: the information of the groups updated. List. Each component of the list contains a vector with the points that belong to that group. More specifically, the list component i has a vector with the numbers of the row of the matrix data where the points belonging to group i are.

• Live_set: Vector. Contains the groups that have been modified during the Step 4.

• no_Change: vector with the points that do not change its group. More specifically, contains the row of the matrix data where these points are.

References

Hartigan, J. A., & Wong, M. A. (1979). Algorithm AS 136: A k-means clustering algorithm. Journal of the royal statistical society. series c (applied statistics), 28(1), 100-108.

Examples

set.seed(231)
data1=gtools::rdirichlet(10,c(1,1,4,4,20,20))
data=t(data1)
k=3
seed=5



if(!is.null(seed)){
 set.seed(seed)
}
centers <- data[sample(1:nrow(data), k), ]

#We calculate the distance between each row of the data matrix and the centers
Dist_e_cent=matrix(0,dim(data)[1],dim(centers)[1])
for (i in 1:(dim(data)[1])){
for (j in 1:(dim(centers)[1])){
 Dist_e_cent[i,j]=Euclideandistance(data[i,],centers[j,])
}
}


Ic12=Dist_IC1_IC2(Dist_e_cent)
Ic12_change=Ic12
Group=Ic12[,1]
grouping<-list()
for(i in 1:(max(Group))){
grouping[[i]]=which(Group==i)
}

#Update the clusters centers.
centers=centers_function_mean(data, grouping)

#Live set.
LIVE_SET_original1=c(1:length(grouping))

index=0

P1=Step4(data,
        centers,
        grouping,
        LIVE_SET_original1,
        Euclideandistance,
        centers_function_mean,
        Ic12_change,
        index)

Step 6 of the Hartigan and Wong algorithm

Description

This function implements the Step 6 of the Hartigan and Wong (Hartigan and Wong, 1979) algorithm without imposing that the use of the euclidean distance and without imposing that the centers of the groups are calculated by averaging the points. This function allows other distances to be used and allows the centers of the groups to be calculated in different ways.

Usage

Step6(
  data,
  centers,
  grouping,
  distance,
  centers_function,
  Ic12_change,
  Ic12,
  index
)

Arguments

Value

Returns a list with:

• centers: the information of the centers updated. Matrix with dim(centers)[1] centers of dim(centers)[2] dimensions.

• IC1andIC2: the information of the IC1 and IC2 updated. Matrix. The first row contains the IC1 of each point. The second column contains the IC2 of each point. IC1 and IC2 are the closets and second closest cluster centers.

• grouping: the information of the groups updated. List. Each component of the list contains a vector with the points that belong to that group. More specifically, the list component i has a vector with the numbers of the row of the matrix data where the points belonging to group i are.

• Live_set: Vector. Contains the groups that have been modified during the Step 6.

• index: number. The information of index updated.

References

Hartigan, J. A., & Wong, M. A. (1979). Algorithm AS 136: A k-means clustering algorithm. Journal of the royal statistical society. series c (applied statistics), 28(1), 100-108.

Examples

set.seed(231)
data12=gtools::rdirichlet(10,c(1,1,4,4,20,20))
data1=t(data12)
k=3
seed=5

distance<- function(vect1, vect2){
 sqrt(sum((vect1-vect2)^2))
}

centers_function<-function(data, grouping){
 center=matrix(0,length(grouping), dim(data)[2])
 for (i in 1:(length(grouping))){

   if(length(grouping[[i]])==1){
     center[i,]=data[grouping[[i]],]
   }else{
     center[i,]=apply(data[grouping[[i]],],2,mean)
   }
 }
 return(center)
}

if(!is.null(seed)){
 set.seed(seed)
}
centers <- data1[sample(1:nrow(data1), k), ]

#We calculate the distance between each row of the data matrix and the centers
Dist_e_cent=matrix(0,dim(data1)[1],dim(centers)[1])
for (i in 1:(dim(data1)[1])){
 for (j in 1:(dim(centers)[1])){
   Dist_e_cent[i,j]=distance(data1[i,],centers[j,])
 }
}

#We obtain the IC1 and IC2 for each taxa
Ic12_change=Dist_IC1_IC2(Dist_e_cent)
Group=Ic12_change[,1]
grouping<-list()
for(i in 1:(max(Group))){
 grouping[[i]]=which(Group==i)
}


#Update the clusters centers.
centers=centers_function(data1, grouping)

Ic12=cbind(c(1,1,3,3,2,2),c(1,2,1,2,3,3))

P1=Step6(data1, centers, grouping, distance, centers_function, Ic12_change,Ic12, 0)

Add values to a vector if they are not already in it

Description

This function adds two values to a vector if the values are not already in the vector.

Usage

add_unique_numbers(vector, num1, num2)

Arguments

Value

Returns the vector with the values added if they are not alredy in the vector.

Examples

mi_vector <- c(1, 2, 3, 4, 5)
num1 <- 8
num2 <- 10

mi_vector <- add_unique_numbers(mi_vector, num1, num2)

Add one value to a vector if it is not already there

Description

This function adds one value to a vector if it is not already in the vector.

Usage

add_unique_numbers2(vector, num1)

Arguments

Value

Returns the vector with the value added if it is not already in the vector.

Examples

mi_vector <- c(1, 2, 3, 4, 5)
num1 <- 8

mi_vector <- add_unique_numbers2(mi_vector, num1)

Center of a cluster when the Relative distance is used.

Description

This function calculates the center of a group when the Relative distance is used to group.

Usage

centers_function_RelativeDistance(data, grouping)

Arguments

Value

A matrix. The row i contains the centers of the group in [[i]].

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
          matrix(runif(20,20,30), nrow = 2, ncol = 10),
          matrix(runif(20,50,70), nrow = 2, ncol = 10))

grouping=list(c(1,2), c(3,4),c(5,6))
centers_function_RelativeDistance(data, grouping)

Center of a cluster using the mean

Description

This function calculates the center of a group using the mean of its components.

Usage

centers_function_mean(data, grouping)

Arguments

Value

A matrix. The row i contains the centers of the group in [[i]].

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
          matrix(runif(20,20,30), nrow = 2, ncol = 10),
          matrix(runif(20,50,70), nrow = 2, ncol = 10))
grouping=list(c(1,2), c(3,4),c(5,6))
centers_function_mean(data, grouping)

Distance between a point and a group

Description

This function calculates the distance between the point i of the data matrix and all the components in the group num.

Usage

d_i_other_group(data, i, distance, FHW_output, num)

Arguments

Value

Returns a vector. The component j contains the distance between the point in the row i of the data matrix and the point j of the group num.

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
         matrix(runif(20,20,30), nrow = 2, ncol = 10),
         matrix(runif(20,50,70), nrow = 2, ncol = 10))
k=3
seed=5


FHW_output=Hartigan_and_Wong(data,
                            Euclideandistance,
                            k,
                            centers_function_mean,
                            init_centers_random,
                            seed=seed,
                            10)

d_i_other_group(data, 1, Euclideandistance, FHW_output,2)

Finding the component in the list that contains a value

Description

This function finds in which component of the list lista the number valor is.

Usage

encontrar_componente(lista, valor)

Arguments

Value

Returns a number. Return the number of the component of list that contains the number valor.

Examples

mi_lista <- list(
a = c(1, 2, 3),
b = c(6,7,8,9),
c = c(4,5)
)

valor=7

encontrar_componente(mi_lista, valor)

Initializing the centers

Description

This function initializes the cluster centers following the procedure described in the ‘Additional Comments’ section of Hartigan and Wong (1979), without restricting the method to the use of Euclidean distance.

Usage

init_centers_hw(data, distance, k, centers_function)

Arguments

Value

Returns a matrix where each row is the center of a group.

References

Hartigan, J. A., & Wong, M. A. (1979). Algorithm AS 136: A k-means clustering algorithm. Journal of the royal statistical society. series c (applied statistics), 28(1), 100-108.

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
          matrix(runif(20,20,30), nrow = 2, ncol = 10),
          matrix(runif(20,50,70), nrow = 2, ncol = 10))
k=3
seed=5

centr=init_centers_hw(data, Euclideandistance,k,centers_function_mean)

Initializing the centers

Description

This function initializes the centers of the groups randomly.

Usage

init_centers_random(data, distance, k, centers_function)

Arguments

Value

Returns a matrix where each row is the center of a group.

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
          matrix(runif(20,20,30), nrow = 2, ncol = 10),
          matrix(runif(20,50,70), nrow = 2, ncol = 10))
k=3
seed=5

centr=init_centers_random(data, EuclideanDistance,k,centers_function_mean)

K-Medoids

Description

This function apply the K-Medoids with any distance to different number of groups and calculates quality metrics as Silhouette.

Usage

kmedois_distance(data, distance, KK = 10, index = "DaviesBouldin", k = NULL)

Arguments

Value

Returns a list with:

• Number_of_groups: Number of groups took into account to cluster.

• Output_of_grouping: list with the centers and the clusters.

• Quality: vector with the Silhouette index, Davies Bouldin Index, the Dunn index, the Within Cluster Sum (WCS) and the time (in seconds) that the algorithm needs to be executed. The WCS is equal to the sum of the distance of each point to the center of its group.

Examples

set.seed(451)
data=rbind(matrix(runif(20,1,5), nrow = 2, ncol = 10),
          matrix(runif(20,20,30), nrow = 2, ncol = 10),
          matrix(runif(20,50,70), nrow = 2, ncol = 10))

kmedois_distance(data, RelativeDistance, KK=4, index="Silhouette", k=NULL)

kmedois_distance(data, RelativeDistance, k=2)

Sum of the distance between the points in a group and a given center.

Description

This function calculates the sum of the distance between the points in a group and a given center of the group. The function calculates these values for all groups and then adds them together. The user can choose which distance to choose.

Usage

to_minimize(inicenters_v, data, grouping, distance)

Arguments

Value

Returns a number. First this function calculates the distance between each point of a group and its given center and sum these values. Then, the function sum the values obtained for each group. This is the output.

Examples

grouping=list(c(1,2,3),c(4,5),c(6,7))
set.seed(451)
data=t(gtools::rdirichlet(10, c(1,1,1,4,4,9,9)))
inicenters=runif(dim(data)[2]*length(grouping), 0.1, 0.9)
inicenters_v=as.vector(inicenters)
to_minimize(inicenters_v, data, grouping, Euclideandistance)

Vector to list

Description

This function returns a list. The component of the list i contains the positions of the vector that are equal to i.

Usage

vector_a_lista(clustering_vector)

Arguments

Value

Returns a list. The component of the list i contains the positions of the vector that are equal to i.

Examples

 vect=c(1,1,1,1,1,2,2,2,2,2,3,3,3,3,3)
 vector_a_lista(vect)