CRANFIELD UNIVERSITY Eleni Anthippi Chatzimichali ...

Linkage algorithms consist of various different algorithms such as single linkage,
complete linkage and Ward’s method. For two given clusters and , a single
linkage algorithm calculates the shortest distance between the two clusters as
described in Equation 5
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Equation 5 Single linkage algorithm
Where and are elements of the clusters and respectively.
1.4.2.2 -means Clustering
-means clustering is an unsupervised clustering technique that attempts to “minimise
the sum of point-to-centroid distances, summed over all clusters” (Arthur and
Vassilvitskii, 2007). The objective function for -means clustering is
∑ ∑‖
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Equation 6 k-means clustering algorithm
Where, is the number of clusters, is the th pattern belonging to the
th cluster,
is the centre of cluster and is the number of data points. The algorithm’s steps
can be described as follows:
1. Initially, the number of clusters is selected, for instance
2. Randomly the items are assigned to the clusters
3. A new centroid is calculated for each of the clusters (a distinct set of points
belongs to a certain centroid)
4. The distance of each item towards the centroids is calculated
5. The items are subsequently assigned to the closest centroid
6. The algorithm keeps iterating until the assignments to the clusters are stable
The algorithm’s simplicity and speed makes it an appealing technique for cluster
analysis. However, a major disadvantage of this algorithm is that it is sensitive to the
selection of the initial partitions.
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