**C(Y) Algorithm (Node-Based Version)**

*Inputs*: The graph G(N, E), cost vector c(e), e ∈ E, initial Yo value for Y.

Edges are ordered so that the costs satisfy c(e(1)) ≤ c(e(2)) ≤ … ≤ c(e(|E|)).

Set Y = Yoand sLast = |E|.

#### **Begin Outer Loop**

While Y < Large

*Initialization(A)*. Set Ynext = Large, K = {1, …, n}, and for each k ∈ K let L(k) = k,

Nk = {k}, E<sup>k</sup> = ∅, and MinCostB(k) = Large.

*Initialization(B)*. Let i′ = p(1) and i″ = q(1) and select e(1) (= (i′, i″)) by identifying k′ = L(i′) and k″ = L(i″) and absorbing Nk″ into Nk′ to create the cluster Nk′: = Nk′∪ N<sup>k</sup> ″= {i′, i″} with edge set Ek′ = e(1). Set MinCostB(k′) = c(e(1)) and set K: = K \ {k″}. Finally, initialize the edge index s by setting s = 1.

It is possible to combat drift and also take advantage of the different features of the C(W) and C(Y) algorithms by joining these algorithms to create an algorithm C(Z) that incorporates the

Let α be a nonnegative weight applied to the edge selection criterion of C(W) and let β = 1 – αbe a nonnegative weight applied to the edge selection criterion of C(Y). We construct Algorithm C(Z) so that it will be the same as C(W) if α = 1 and will be the same as C(Y) if α = 0 (β = 1).

For notational convenience, we refer to the value MinCost(k) of the C(W) algorithm as

MinCostC(i) = α∙MinCostA(k) + β∙MinCostB(i), for k = L(i).

To apply this criterion, we create values MinCostC(i′) and MinCostC(i″) for nodes i′ = p(s) and

) + β ∙ MinCostB(i′

), MinCostC(i″))

)

A Class of Parametric Tree-Based Clustering Methods http://dx.doi.org/10.5772/intechopen.76406 145

″= {i′, i″} with edge set Ek′

) = α ∙ MinCostA(k′

MinCost evaluation criteria of both C(W) and C(Y) simultaneously.

MinCostA(k). Then the MinCost evaluation criterion of C(Z) is given by.

MinCostC(i″) = α ∙ MinCostA(k″) + β ∙ MinCostB(i″)

*Inputs*: The graph G(N, E), cost vector c(e), e ∈ E, initial Zo value for Z.

Edges are ordered so that the costs satisfy c(e(1)) ≤ c(e(2)) ≤ … ≤ c(e(|E|)).

L(i″) and absorb Nk″ into Nk′ to create the cluster Nk′: = Nk′∪ N<sup>k</sup>

*Initialization(A)*. Set Znext = Large, K = N (= {1, …, n}), and for each k ∈ K let.

= e(1). Set MinCostA(k′) = c(e(1)) and MinCostB(i) = c(e(1)) for i = i′ and i″. Set.

*Initialization(B)*. Let i′ = p(1) and i″ = q(1) and select e(1) (= (i′, i″)).Set k′ = L(i′) and k″ =

= ∅, and MinCostA(k) = MinCostB(k) = MinCostC(k) = Large.

i″ = q(s), and for k′ = L(i′) and k″ = L(i″), given by

Associated with the foregoing values, we define

MinCostC0 = Min(MinCostC(i′

We state the C(Z) algorithm by reference to these definitions.

MinCostC(i′

**C(Z) Algorithm.**

Set Z = Zo and sLast = |E|

L(k) = k, N<sup>k</sup> = {k}, E<sup>k</sup>

K: = K \ {k″} and s = 1.

**Begin Outer Loop**

While Z < Large
