*this information is copied from: Metodološki zvezki, Vol. 2, No. 2, 2005, 173-193 (Hierarchical Clustering with Concave Data Sets Matej Francetič, Mateja Nagode, and Bojan Nastav1)*

# Nearest neighbour

The nearest neighbour method measures distance between clusters as the distance between two points in the clusters nearest to each other. It tends to cause clusters to merge, even when they are naturally distinct, as long as proximity between their outliers is short (Wolfson et al, 2004: 610). The effect of the algorithm that it tends to merge clusters is sometimes undesirable because it prevents the detection of clusters that are not well separated. On the other hand, the criteria might be useful to detect outliers in the data set (Mucha and Sofyan, 2003). This method turns out to be unsuitable when the clusters are not clearly separated but it is very useful when detecting chaining structured data (chaining effect).

# Furthest neighbour

This method proceeds like the nearest neighbour method except that at the crucial step of revising the distance matrix, the maximum instead of the minimum distance is used to look for the new item (Mucha and Sofyan, 2003). That means that this method measures the distance between clusters through the distance between the two points in the clusters furthest from one another. Furthest neighbour results in separate clusters, even if the clusters fit together naturally, by maintaining clusters where outliers are far apart (Wolfson et al, 2004: 610). This method tends to produce very tight clusters of similar cases.

# Centroid method

The centroid is defined as the centre of a cloud of points (Joining Clusters: Clustering Algorithms). Centroid linkage techniques attempt to determine the ‘centre’ of the cluster. One issue is that the centre will move as clusters are merged. As a result, the distance between merged clusters may actually decrease between steps, making the analysis of results problematic. This is not the issue with single and complete linkage methods (Wolfson et al, 2004: 610). A problem with the centroid method is that some switching and reversal may take place, for example as the agglomeration proceeds some cases may need to be switched from their original clusters (Joining Clusters: Clustering Algorithms).

# Median method

This method is similar to the previous one. If the sizes of two groups are very different, then the centroid of the new group will be very close to that of the larger group and may remain within that group. This is the disadvantage of the centroid method. For that reason, Gover (1967) suggests an alternative strategy, called the median method, because this method could be made suitable for both similarity and distance measures (Mucha and Sofyan, 2003). This method takes into consideration the size of a cluster, rather than a simple mean (Schnittker, 2000: 3).

# Linkage between groups

The distance between two clusters is calculated as the average distance between all pairs of objects in the two different clusters. This method is also very efficient when the objects form naturally distinct ‘clumps’, however, it performs equally well with elongated, ‘chain’ type clusters (Cluster Analysis).

# Linkage within groups

This method is identical to the previous one, except that in the computations the size of the respective clusters (i.e. the number of objects contained in them) is used as a weight. Thus, this method should be used when the cluster sizes are suspected to be greatly uneven (Cluster Analysis).

# Ward's method

The main difference between this method and the linkage methods is in the unification procedure. This method does not join groups with the smallest distance, but it rather joins groups that do not increase a given measure of heterogeneity by too much. The aim of Ward’s method is to unify the groups such that variation inside these groups does not increase too drastically. This results in clusters that are as homogenous as possible (Mucha and Sofyan, 2003). Ward’s method is based on the sum-of-squares approach and tends to create clusters of similar size. The only method to rely on analysis of variance, its underlying basisis closer to regression analysis than the other methods. It tends to produce clearly defined clusters (Wolfson et al, 2004: 610).