Advanced Data Analytics Using Python_ With Machine Learning, Deep Learning and NLP Examples ( 2023)

Chapter 4
Unsupervised Learning: Clustering
Bottom-Up Approach
The bottom-up clustering method is called agglomerative hierarchical
clustering. In this approach, each input object is considered as a separate
cluster. In each iteration, an algorithm merges the two most similar clusters
into only a single cluster. The operation is continued until all the clusters
merge into a single cluster. The complexity of the algorithm is O(n^3).
In the algorithm, a set of input objects, I = {I 1 ,I 2 ,….,I n }, is given. A set
of ordered triples is <D,K,S>, where D is the threshold distance, K is the
number of clusters, and S is the set of clusters.
Some variations of the algorithm might allow multiple clusters with
identical distances to be merged into a single iteration.
Algorithm
Input: I={I 1 ,I 2 ,…., I n }
Output: O
fori = 1 to n do
Ci ← {Ii};
end for
D ← 0;
K ← n;
S ← {C1,....., Cn};
O ← <d, k, S>;
repeat
Dist ← CalcultedMinimumDistance(S);
D ← ∞;
Fori = 1 to K–1 do
Forj = i+1 to Kdo
ifDist(i, j)< Dthen
D← Dist(i, j);
u ← i;
v ← j;
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