1. Jagdish Gangolly State University of New York at Albany
Clustering
Jagdish Gangolly
State University of New York at Albany
Acc 522 Fallo, 2001 (Jagdish S. Gangolly)
12/29/2018

2. Clustering Clustering in S-Plus Objectives of Clustering Methods
Hierarchical
Partitioning (iterative-relocation)
Model-based methods
Acc 522 Fallo, 2001 (Jagdish S. Gangolly)
12/29/2018

3. Clustering in S-Plus You need to load the S-Plus cluster library
library(cluster)
Data can be either in
np matrix of measurement on each of the p variables for each object, or
nn matrix of dissimilarities where d(i,j) in the matrix represents dissimilarity between object i and object j. daisy in the library cluster constructs the dissimilarity matrix.
Acc 522 Fallo, 2001 (Jagdish S. Gangolly)
12/29/2018

4. Objectives of Clustering
To classify data set into groups that are internally cohesive and externally isolated (loosely coupled)
dataset (matrix, dataframe)
distance measure
optimisation criterion
number of clusters (partitioning)
shape of clusters, probability distribution (model-based)
Acc 522 Fallo, 2001 (Jagdish S. Gangolly)
12/29/2018

5. Clustering methods: Hierarchical I
Hierarchical Methods:
Agglomerative methods: Start with each observation forming a separate group. Observations close to each other are successively merged. The results are displayed in the form of a dendrogram
Divisive methods: Initial cluster consists of one cluster containing the whole dataset. This is successively split into ntwo smaller clusters until each cluster contains exactly a single object
Acc 522 Fallo, 2001 (Jagdish S. Gangolly)
12/29/2018

6. Clustering methods: Hierarchical II
Agglomerative Nesting:
agnes(x, diss, metric, stand, method,…)
Methods:
average (group average)
single (linkage), nearest neighbour method
complete (linkage), furthest neighbour method
ward (Ward’s method)
weighted (weighted average linkage)
Evaluation criterion: Agglomeration coefficient (AC)
Results display: Dendrogram, Banner plot
Acc 522 Fallo, 2001 (Jagdish S. Gangolly)
12/29/2018

7. Clustering methods: Hierarchical III
hclust: hierarchical clustering
hclust(dist, method, sim)
dist: distances
method:
compact (complete linkage)
average
connected (single linkage)
results displayed using plclust
Acc 522 Fallo, 2001 (Jagdish S. Gangolly)
12/29/2018

8. Clustering methods: Hierarchical IV
Divisive Analysis:
diana(x, diss, metric, stand, …)
Evaluation criterion: Divisive coefficient (DC)
Results display: Dendrogram, Banner plot
Monothetic Analysis: For binary data matrix. For each split, mona uses a single (well-chosen) variable
mona(x)
Acc 522 Fallo, 2001 (Jagdish S. Gangolly)
12/29/2018

9. Clustering methods: Partitioning Methods I
Method for dividing the set of objects into k clusters; k needs to be specified by the user.
k-means:
Partitioning among Medoids: accepts a dissimilarity matrix, minimises the sum of dissimilarities (rather than distances) and so is more robust, and displays a silhoutte plot
pam(data, k, diss, metric, stand,…)
data: matrix or dataframe
diss: T or F
metric: euclidean or manhattan
stand: T or F
Acc 522 Fallo, 2001 (Jagdish S. Gangolly)
12/29/2018

10. Clustering methods: Partitioning Methods II
Clustering large applications: Considers data subsets of fixed size to cluster very large datasets
clara(x, k, metric, stand, samples, sampsize, …)
Fanny: Fuzzy clustering.
fanny(x, k, diss, metric, stand,…)
Acc 522 Fallo, 2001 (Jagdish S. Gangolly)
12/29/2018

11. Clustering: Displays of Results
Dendrograms:
plot.agnes()
plot.diana()
plot.mona()
Print:
print.agnes()
print.diana()
print.mona()
print.pam()
print.fanny()
print.clara()
Acc 522 Fallo, 2001 (Jagdish S. Gangolly)
12/29/2018