Transition {clusTransition}  R Documentation 
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).
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
)
listdata 
List of numeric matrices containing datasets 
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 [tswSize+1, t], while older objects
are discarded. The default value of 
Overlap 
A list of objects as produced by the 
listclus 

typeind 
Type indicator. 
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 
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.
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. 
Spiliopoulou, M., Ntoutsi, I., Theodoridis, Y., Schult, R. MONIC: modeling and monitoring cluster transitions. In: EliassiRad, T., Ungar, L. H., Craven, M., Gunopulos, D. (eds.) ACM SIGKDD 2006, pp. 706711. ACM, Philadelphia (2006).
### 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)