Agglomerative Clustering Algorithm

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Agglomerative hierarchical clustering

Agglomerative clustering is one of the most common types of hierarchical clustering used to group similar objects in clusters. Agglomerative clustering is also known as AGNES (Agglomerative Nesting). In agglomerative clustering, each data point act as an individual cluster and at each step, data objects are grouped in a bottom-up method. Initially, each data object is in its cluster. At each iteration, the clusters are combined with different clusters until one cluster is formed.

Agglomerative hierarchical clustering algorithm

  • Determine the similarity between individuals and all other clusters. (Find proximity matrix).
  • Consider each data point as an individual cluster.
  • Combine similar clusters.
  • Recalculate the proximity matrix for each cluster.
  • Repeat step 3 and step 4 until you get a single cluster.

Let’s understand this concept with the help of graphical representation using a dendrogram.



With the help of the given demonstration, we can understand that how the actual algorithm work. Here no calculation has been done below all the proximity among the clusters are assumed.


Step 1:

Consider each alphabet (P, Q, R, S, T, V) as an individual cluster and find the distance between the individual cluster and all other clusters.


Step 2:

Now, merge the comparable clusters in a single cluster. Let’s say cluster Q and Cluster R are similar to each other so that we can merge them in the second step. Finally, we get the clusters [ (P), (QR), (ST), (V)]


Step 3:

Here, we recalculate the proximity as per the algorithm and combine the two closest clusters [(ST), (V)] together to form new clusters as [(P), (QR), (STV)]


Step 4:

Repeat the same process. The clusters STV and PQ are comparable and combined together to form a new cluster. Now we have [(P), (QQRSTV)].


Step 5:

Finally, the remaining two clusters are merged together to form a single cluster [(PQRSTV)]

 

                OR,


Agglomerative Clustering Algorithm

- More popular hierarchical clustering technique

Basic algorithm

- Compute the proximity matrix

- Let each data point be a cluster

- Repeat

- Merge the two closest clusters

- Update the proximity matrix

- Until only a single cluster remains


Note:

Key operation is the computation of the proximity of two clusters

Different approaches to defining the distance between clusters distinguish the different algorithms

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