Class Clustering

Description

Partition data into clusters

Details

Object of class Clustering containing clustering solution of cumulative dataset D_i. The object of class Clustering comprise of four slots. Slot Clusters contain data items of each cluster, slot Centers contain cluster centers, slot k contain the number of centers, while slot clusterMem contain cluster memberships vector.

Slots

Cluster

List of matrices, where each element of the list include data items belonging to the corresponding cluster.

Centers

Matrix of cluster centers.

k

Number of centers.

clusterMem

Numeric vector of cluster membership.

Clustering.

Description

Initialize slots of class Clustering by partitioning the dataset into k clusters.

Usage

Clusters(object, x, k)

## S4 method for signature 'Clustering,matrix,numeric'
Clusters(object, x, k)

Arguments

Details

Runs cclust function from "flexclust" package with default settings i.e. method = "kmeans", dist = "euclidean", and partition the dataset. Returns object of class Clustering.

Value

An object of class Clustering

Synthetic Datasets (Two Dimensional)

Description

A list of datasets generated at four time points containing two variables and cluster membership at each point.

Usage

Data2D

Format

A data frame

x1

X1.

x2

X2.

class

Class membership.

Synthetic Datasets (Three Dimensional)

Description

A list of datasets generated at four points containing three variables and cluster membership at each point.

Usage

Data3D

Format

A data frame

x1

X1.

x2

X2.

x3

X3.

class

Class membership.

An S4 class that contain time steps

Description

An S4 class that contain time steps

Arguments

Slots

TimeStep

Time Steps

Overlap between clusters

Description

Contains matrix of similarity indices between clusters, after clustering dynamic datasets at consecutive time points.

Slots

Overlap

A numeric matrix containing the similarity index between clusters extracted at time point t_1 and t_2. The rows of the matrix illustrate clusters extracted from first clustering \xi_1(time point t_1),whereas columns represent clusters extracted from second clustering \xi_2(time point t_2).

rx

A numeric vector containg radius of each cluster from first clustering \xi_1.

ry

A numeric vector containg radius of each cluster from second clustering \xi_2.

Centersx

A numeric vector containing centers of clusters from first clustering \xi_1.

Centersy

A numeric vector containing centers of clusters from second clustering \xi_2.

avgDisx

A numeric vector containing average distance between points in a cluster from its center in first clustering \xi_1.

avgDisy

A numeric vector containing average distance between points in a cluster from its center in second clustering \xi_2.

clusterMem

A vector of integers containing cluster membership from second clustering \xi_2.

Overlap

Description

Initialize slots of class OverLap by importing clustering solutions of dynamic datasets at two consecutive time points. Clusters at each time point should be provided as a list of matrices, where each matrix contains dataset belongs to the corresponding cluster.

Usage

Overlap(object, e1, e2)

## S4 method for signature 'OverLap,Clustering,Clustering'
Overlap(object, e1, e2)

## S4 method for signature 'OverLap,ANY,ANY'
Overlap(object, e1, e2)

Arguments

Value

Return an object of class OverLap.

Monitor Transitions in Cluster Solutions.

Description

Model and trace the evolution of clusters evolving over time in cumulative datasets. A typical call to Transition() function involves three essential pieces: the data input (listdata, listclus, overlap), choice of window swSize, and the threshold parameters. The function either receive a list of datasets arriving at time points t_1, t_2, t_3, ..., t_n respectively, list of clustering solutions extracted from cumulative datasets at successive time points, or list of objects of class OverLap (see Details).

Usage

Transition(
  listdata,
  swSize = 1,
  Overlap = NULL,
  listclus = NULL,
  typeind = 1,
  Survival_thrHold = 0.7,
  Split_thrHold = 0.3,
  location_thrHold = 0.3,
  density_thrHold = 0.3,
  k = NULL
)

Arguments

Details

The Transition() function apply 'MONIC' algorithm presented by Spiliopoulou et.al (2006) to trace changes in cluster solutions of dynamic data sets. The changes includes two types of transition i.e. External transition and Internal transition. External Transition consist of 'Survive', 'Split', 'Merge', 'Disappeared' and 'newly emerged' candidates, while Internal transition consist of changes in location and cohesion of the survived clusters. The listdata argument allow user to import dynamic datasets as a list of matrices or data frames, where each element of the list is a matrix containing data set at a single time point. Each dataset are clustered by 'kmeans' algorithm using default settings of cclust() function from flexclust package. The number of clusters at each time stamp can be import by k argument of the function, which is a vector of integers encompassing number of partitions in corresponding datasets of listdata argument. Once the datasets are clustered, the 'Overlap' matrices in clustering at consecutive time stamps are calculated. The Overlap matrix is calculated by using algorithm presented by Ntoutsi, I., et.al (2012). These 'Overlap' matrices are used to trace the transitions occurred in cluster solutions. Alternatively, the user can directly import list of 'Overlap' matrices between consecutive clustering. The Overlap matrix can be calculated using Overlap(obj, e1, e2) method of the package, where 'obj' is the object of class OverLap and e1, e2 are any clustering at time stamp i and j respectively. As a third option user can provide list of clusters at each data point utilizing listclus argument. Each element of the listclus is a nested list, which holds clusters at a single time stamp.

Value

Returns A list of class Monic.

References

Spiliopoulou, M., Ntoutsi, I., Theodoridis, Y., Schult, R. MONIC: modeling and monitoring cluster transitions. In: Eliassi-Rad, T., Ungar, L. H., Craven, M., Gunopulos, D. (eds.) ACM SIGKDD 2006, pp. 706-711. ACM, Philadelphia (2006).

Examples

### Example 1: typeind = 1 (listdata Argument)

d1 <- Data2D[[1]][c("X1", "X2")]
d2 <- Data2D[[2]][c("X1", "X2")]
d3 <- Data2D[[3]][c("X1", "X2")]

listdata <- list(d1, d2, d3)

p <- Transition(listdata = listdata, swSize = 1, typeind = 1, Survival_thrHold = 0.8,
                Split_thrHold = 0.3, density_thrHold = 0.3, location_thrHold = 0.3, k = c(3,3,2))

### Example 2: typeind = 3 (listclus Argument)

D1 <- d1
D2 <- merge(d1, d2, all.x = TRUE, all.y = TRUE)
D3 <- merge(D2, d3, all.x = TRUE, all.y = TRUE)

set.seed(10)
f1 <- kmeans(D1, 3)
C1 <- list()
for(i in 1:3)C1[[i]] <- D1[f1$cluster == i, ]
f2 <- kmeans(D2, 3)
C2 <- list()
for(i in 1:3)C2[[i]] <- D2[f2$cluster == i, ]
f3 <- kmeans(D3, 2)
C3 <- list()
for(i in 1:2)C3[[i]] <- D3[f3$cluster == i, ]

listclus <- list(C1, C2, C3)

p <- Transition(listclus = listclus, typeind = 3, Survival_thrHold = 0.8,
                Split_thrHold = 0.3, density_thrHold = 0.3, location_thrHold = 0.3)

### Example 3: typeind = 3 (Overlap Argument)

obj <- new("OverLap")
Overlap1 <- Overlap(obj, e1 = C1, e2 = C2)
Overlap2 <- Overlap(obj, e1 = C2, e2 = C3)

Overlap <- list(Overlap1, Overlap2)
p <- Transition(Overlap = Overlap, typeind = 2, Survival_thrHold = 0.8,
                Split_thrHold = 0.3, density_thrHold = 0.3, location_thrHold = 0.3)

External Transition Candidates

Description

Class containing candidates that adopted external transition from first clustering \xi_1, and emerged as new clusters at second clustering \xi_2.

Slots

SurvivalCanx

Vector of integers comprising Candidates that Survive from first clustering \xi_1.

SurvivalCany

Vector of integers comprising Candidates that Survive to second clustering \xi_2.

SplitCanx

Vector of integers comprising Candidates that Sliced into Various daughter Clusters from first clustering \xi_1.

SplitCany

List of integer vectors comprising Candidates that emerged as daughter clusters in second clustering \xi_2 because of Split from first clustering \xi_1.

MergeCanx

List of integer vectors comprising Candidates from first clustering \xi_1 that are merged. Each slot of list indicates the clusters that merge together from first clustering.

MergeCany

Vector of integers comprising Candidates that emerged in second clustering \xi_2 because of merging various clusters from first clustering \xi_1.

EmergCan

Newley emerged candidates which are not a result of any external transition from first clustering \xi_1.

Cluster_Tracey

Vector of Cluster Trace from second clustering \xi_2.

External Transition Count

Description

Trace cluster solutions of dynamic datasets at consecutive time points and counts the clusters that experiences external transition. External transition includes Survive, Split, Merge, newly emerged, and Died candidates.

Slots

Survive

Number of candidates survive from first clustering \xi_1.

Split

Number of candidates from first clustering \xi_1 that split into several daughter clusters at second clustering \xi_2.

Merge

Number of candidates from first clustering \xi_1 that merge toghter at second clustering \xi_2.

Died

Number of candidates from first clusterin \xi_1 that disapeared at second clustering \xi_2.

SurvivalRatio

Ratio of survive clusters to total number of clusters from first clusering \xi_1.

AbsorptionRatio

Ratio of Merged clusters to total number of clusters from first clusering \xi_1.

passforwardRatio

Sum of SurvivalRatio and AbsorptionRatio.

Survival_thrHold

Threshold for survival of clusters.

Split_thrHold

Threhold for split of clusters.

Cluster_Tracex

Vector containing each cluster result from first clustering \xi_1.

External Transition Candidate.

Description

This S4 method trace cluster solutions of dynamic dataset, and identify the candidates that experience external transition from first clustering and emerged at second clustering.

Usage

extTransitionCan(object)

## S4 method for signature 'TransitionCan'
extTransitionCan(object)

Arguments

Value

Return an object of class TransitionCan

External Transition Count

Description

Trace cluster solutions of dynamic datasets and count the number of clusters that experiences external transition from first clustering. The external transition includes survived, split into various daughters, spliced into one, disappeared, and newly emerged candidates.

Usage

extTransitionCount(object)

## S4 method for signature 'TransitionCount'
extTransitionCount(object)

Arguments

Value

Return an object of class TransitionCount

Internal Transition Candidates

Description

Class containing results of Internal Transition of survived clusters from first clustering \xi_1.

Arguments

Slots

Location.diff

Vector of integers containing difference in location (= Distance bw cluster centers/min(rx,ry)).

Compactness.diff

Vector of integers containing Change in density of survived clusters (d(rx, ry)).

Location_thrHold

Minimum value of threshold for shift in location.

Density_thrHold

Minimum value of threshold for change in density.

ShiftLocCan

Vector of integers containing Survived candidates with shift in their location.

NoShiftLocCan

Vector of integers containing Survived candidates with no Shift in their Location.

MoreCompactCan

Vector of integers containing Survived Candidates Which becomes more compact.

MoreDiffuseCan

Vector of integers containing Survived Candidates Which becomes more diffuse.

NoChangeCompactCan

Vector of integers containing Survived candidates with no change in compactness.

Internal Transition Candidates.

Description

This method identify internal transition of the survived clusters, obtained from 'extTransitionCan()' method.

Trace clustering solutions of cumulative datasets and identify the survived clusters experiencing Internal transitions. Internal transition includes the change in location and density of the survived candidates.

Usage

internalTransition(object)

## S4 method for signature 'intTransitionCan'
internalTransition(object)

Arguments

Value

Return an object of class intTransitionCan

plot Method for output

Description

This method plot 3 barplot and 1 line graph. The first stack barplot shows SurvivalRatio and AbsorptionRatio, second barplot shows number of newly emerged clusters at each time stamp, third barplot shows number of disapeared clusters at each time stamp. The line graph shows passforward Ratio and Survival Ratio.

Usage

moplot(object)

## S4 method for signature 'Monic'
moplot(object)

Arguments

Show Method for output

Description

Show Method for output

Usage

## S4 method for signature 'Monic'
show(object)

Arguments