Package 'clusTransition' reference manual

Title:	Monitor Changes in Cluster Solutions of Dynamic Datasets
Description:	Monitor and trace changes in clustering solutions of accumulating datasets at successive time points. The clusters can adopt External and Internal transition at succeeding time points. The External transitions comprise of Survived, Merged, Split, Disappeared, and newly Emerged candidates. In contrast, Internal transition includes changes in location and cohesion of the survived clusters. The package uses MONIC framework developed by Spiliopoulou, Ntoutsi, Theodoridis, and Schult (2006)<doi:10.1145/1150402.1150491> .
Authors:	Muhammad Atif
Maintainer:	Muhammad Atif <[email protected]>
License:	GPL-3
Version:	1.0
Built:	2024-11-20 06:40:08 UTC
Source:	CRAN

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)
Clusters(object, x, k)

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

Arguments

`object`	An object of class `Clustering`.
`x`	Numeric matrix of data.
`k`	Number of centers.

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
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
Data3D

Format

A data frame

x1: X1.
x2: X2.
x3: X3.
class: Class membership.

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)
extTransitionCan(object)

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

Arguments

object

An object of class Transitioncan

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)
extTransitionCount(object)

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

Arguments

object

An object of class Transitioncount

Value

Return an object of class TransitionCount

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)
internalTransition(object)

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

Arguments

object

An object of class intTransitionCan

Value

Return an object of class intTransitionCan

Internal Transition Candidates

Description

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

Arguments

object

An object of class Transitioncan

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.

An S4 class that contain time steps

Description

An S4 class that contain time steps

Arguments

object

An object of class Transitioncan

Slots

TimeStep: Time Steps

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)
moplot(object)

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

Arguments

object

An object of class Monic

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)
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

`object`	An object of class `OverLap`
`e1`	An object of class `Clustering`, or any object that can be coerced, such as list of matrices or data frames that contain clusters from first clustering.
`e2`	An object of class `Clustering`, or any object that can be coerced, such as list of matrices or data frames that contain clusters from second clustering.

Value

Return an object of class OverLap.

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 $\xi_2$ .

Show Method for output

Description

Show Method for output

Usage

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

Arguments

object

An object of class Monic

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
)
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

`listdata`	List of numeric matrices containing datasets `d_1, d_2, ..., d_n`, or a list of objects that can be coerced to such matrices, for instance, data frames. Each element of the list contain dataset `d_i` evolving at corresponding time point `t_i`. The number of clusters in each accumulative data matrix is specified by the argument `k`.
`swSize`	Integer value (1, length(listdata)) indicating size of the sliding window. As time goes by, each window consist only objects that fall in the interval [t-swSize+1, t], while older objects are discarded. The default value of `swSize = 1` indicate landmark window model, where objects over the entire history are included i.e. [1, t]. Size of sliding window can only be provided if `listdata` arguments is choosen. If there are total `n` time stamps and a window of size `swSize` is selected then entire history would be devided into `n-swSize+2` window panes.
`Overlap`	A list of objects as produced by the `Overlap()` method. The object contains a matrix of similarity indices between clusters, and the summaries of clusters extracted at first and second clustering.
`listclus`	`listclus` is a list of nested lists containing clustering solutions $\xi_1, \xi_2, ..., \xi_n$ at time points `{t1, t2,···, tn}` respectively, and having the same length as the number of time points. The `i^th` element of `listclus` is a nested list that contain set of clusters as matrices at corresponding time point `t_i` i.e. $\xi_i = {X1, X2,···, Xki}$ . For more details, see Examples.
`typeind`	Type indicator. `typeind = 1` indicates that the raw data is provided in `listdata` argument, `typeind = 2` indicates that the `OverLap` objects are provided, whereas `typeind = 3` indicates that list of clusters are provided using `listclus` argument.
`Survival_thrHold`	A numeric value (0,1) indicating minimum threshold value for survival of clusters.
`Split_thrHold`	A numeric value (0,1) indicating minimum threshold value for split of clusters.
`location_thrHold`	A numeric value (0,1) indicating minimum threshold value for shift in location of survived clusters.
`density_thrHold`	A numeric value (0,1) indicating minimum threshold value for changes in density of Survived clusters.
`k`	Numeric Vector of length `vector("numeric", length = n-swSize+2)`. In the case of landmark window, its length is `n`, whereas in case of sliding window model its length is `n-swSize+2`, where `n` is the number of time points and `swSize` is the size of the sliding window. This argument should only be provided if `listdata` argument is chosen.

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.

`Survive`	Number of clusters survived.
`Merged`	Number of clusters merged.
`Split`	Number of clusters split.
`Died`	Number of clusters disappeared.
`new.Emerged`	Number of newly emerged clusters, which are not upshot of any external transition.
`SurvivalCanx`	A vector of integers indicating candidates from the first clustering survived to the latter time stamp
`SurvivalCany`	A vector of integers indicating candidates of second clustering, that clinch the survival candidates from first clustering.
`SplitCanx`	A vector of integers indicating candidate(s) that split into various daughter clusters from first clustering.
`SplitCany`	List of integer vector(s) designating candidates appeared, as a result of splits from first clustering.
`MergeCanx`	List of integer vector(s) designating Candidates that spliced together to form new clusters. Each element of the list gives candidates that merge together to form one.
`MergeCany`	Vector of integers designating candidates that emerged, as a result of merger of different candidates from first clustering.
`EmergCan`	Vector of integers contain Newly emerged candidates, which are not result of any external transition.
`SurvivalRatio`	The Ratio of survived clusters at second clustering to the total number of clusters at first clustering.
`AbsorptionRatio`	Ratio of number of merged clusters to total number of clusters at first clustering.
`passforwardRatio`	Sum of SurvivalRatio and AbsorptionRatio. This gives the ratio of clusters that is also present at second clustering either in the form of survival or absorption.
`Overlap`	A numeric matrix containing overlap of the two clustering. The rows of matrix indicate first clustering, while columns indicate second clustering.
`Centersx`	A matrix of cluster centers from first clustering.
`Centersx`	A matrix of cluster centers from second clustering.
`rx`	A numeric vector containing radius of each cluster from first clustering.
`ry`	A numeric vector containing radius of each cluster from second clustering.
`avgDisx`	A numeric vector containing average distance of points in a cluster from its center in first clustering.
`avgDisy`	A numeric vector containing average distance of points in a cluster from its center in second clustering.
`ShiftLocCan`	A vector of integers comprises of Survived candidates with shift in location.
`NoShiftLocCan`	A vector of integers comprises of Survived candidates with no shift in location.
`MoreCompactCan`	A Vector of integers comprises of Survived candidates, which becomes more compact.
`MoreDiffuseCan`	A Vector of integers comprises of Survived candidates, which becomes more diffuse.
`NoChangeCompactCan`	A Vector of integers comprises of Survived candidates, with no changes in compactness.
`Location.diff`	A numeric vector containing Distance between the centers of survived clusters.
`Compactness.diff`	A numeric vector containing Difference between compactness of survived clusters.
`Cluster_Tracex`	A vector containing result of each cluster from first clustering.
`Cluster_Tracey`	A Vector representing result of each cluster from second clustering.
`clusterMem`	A vector of integers (from 1 to k) indicating the point to which cluster it is allocated from second clusterig.

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)


### 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 $\xi_1$ .

Package 'clusTransition'

Help Index

Class Clustering

Description

Details

Slots

Clustering.

Description

Usage

Arguments

Details

Value

Synthetic Datasets (Two Dimensional)

Description

Usage

Format

Synthetic Datasets (Three Dimensional)

Description

Usage

Format

External Transition Candidate.

Description

Usage

Arguments

Value

External Transition Count

Description

Usage

Arguments

Value

Internal Transition Candidates.

Description

Usage

Arguments

Value

Internal Transition Candidates

Description

Arguments

Slots

An S4 class that contain time steps

Description

Arguments

Slots

plot Method for output

Description

Usage

Arguments

Overlap

Description

Usage

Arguments

Value

Overlap between clusters

Description

Slots

Show Method for output

Description

Usage

Arguments

Monitor Transitions in Cluster Solutions.

Description

Usage

Arguments

Details

Value

References

Examples

External Transition Candidates

Description

Slots

External Transition Count

Description

Slots