## Monday, 29 August 2011

Dendrograms are often used for displaying relationships among clusters. A dendrogram shows the multidimensional distances between objects in a tree-like structure. Objects which are closest to each other in the multidimensional data space are connected by a horizontal line, forming a cluster which can be regarded as a "new" object. The new cluster and the remaining original data are again searched for the closest pair, and so on. The distance of the particular pair of objects (or clusters) is reflected in the height of the horizontal line. The dendrogram can also be represented in horizontal format.
Depending upon the motive of making the cluster and our convenience of decision making we decide where to cut the dendrogram. We decide the position of cutting the dendrogram intuitively also.

Interpretations of Dendrogram
The results of the cluster analysis are shown by a dendrogram, which lists all of the samples
and indicates at what level of similarity any two clusters were joined.  The x-axis is some

measure of the similarity or distance at which clusters join and dierent programs use dierent measures on this axis.  In the dendrogram shown above, samples 1 and 2 are the most
similar and join to form the ﬁrst cluster, followed by samples 3 and 4.  The last two clusters to
form are 1-2-3-4 and 5-9-6-7-8-10.  Clusters may join pairwise, such as the joining of 1-2 and 3-
4.  Alternatively, individual samples may be sequentially added to an existing cluster, such as
the join of 6 with 5-9, followed by the join of 7.  Such sequential joining of individual samples
is known as chaining.

Determining the number of groups in a cluster analysis is often the primary goal.  Although
objective methods have been proposed, their application is somewhat arbitrary.  Typically, one
looks for natural groupings deﬁned by long stems, such as the one to the right of cluster 1-2-3-
4.  Some have suggested that all clusters be deﬁned at a consistent level of similarity, such that
one would draw a line at some chosen level of similarity and all stems that intersect that line
would indicate a group.  The strength of clustering is indicated by the level of similarity at
which elements join a cluster.  In the example above, elements 1-2-3-4 join at similar levels, as
do elements 5-9-6-7-8-10, suggesting the presence of two major clusters in this analysis

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Ashutosh Pratap Singh (13011)

Operations Goup 1