Pattern Recognition, 4th Edition

13.2. Agglomerative Algorithms

Let g(Cⁱ, C^j) be a function defined for all possible pairs of clusters of X. This function measures the proximity between Cⁱ and C^j. Let t denote the current level of hierarchy. Then, the general agglomerative scheme may be stated as follows:

Generalized Agglomerative Scheme (GAS)

• R Initialization:
  • Choose R⁰ = {Cⁱ = {xⁱ], i = 1,…, N} as the initial clustering.
  • t = 0.
• Repeat:
  • t = t + 1
  • Among all possible pairs of clusters (C^r,C^s) in R^t−1 find the one, say (Cⁱ, C^j), such that(13.1)
  • Define C^q = Cⁱ ∪ C^j and produce the new clustering R^t = (R^t-1 − {Cⁱ,C^j} ∪ {C^q}.
• Until all vectors lie in a single cluster. ...