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Statistical and Machine Learning Approaches for Network Analysis by Subhash C. Basak, Matthias Dehmer

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6.6 Tuning Topology Generator Parameters

The aim of this section is to examine how well the topology generators match the Skitter topology for different values of their parameters. To facilitate this comparison, grids are constructed over the possible values of the parameter spaces and various cost functions are evaluated as follows:

1. A cost function measuring the matching between the number of links in Skitter and the generated topologies

(6.20) equation

where C1 is the first cost function, θ are the model parameters (which differ for each topology generator), lt is the number of links (which is a function of the parameters), and lSkitter is the number of links in the Skitter dataset.
2. A cost function measuring the matching between the spectra of the Skitter network and of the generated topologies

(6.21) equation

where ft(λ = k) is the number of eigenvalues that fall in bin k for topology t. Note that ft(λ = k) is dependant on θ.
3. A cost function measuring the matching of the weighted spectral distributions

(6.22) equation

as defined in Equation (6.16). Here, N = 4 is used.

In addition to examining different parameter values across a grid, the optimum parameters with respect to C3(θ) are estimated ...

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