Statistical and Machine Learning Approaches for Network Analysis

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)

where C₁ is the first cost function, θ are the model parameters (which differ for each topology generator), l_t is the number of links (which is a function of the parameters), and l_Skitter 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)

where f_t(λ = k) is the number of eigenvalues that fall in bin k for topology t. Note that f_t(λ = k) is dependant on θ.

3. A cost function measuring the matching of the weighted spectral distributions

(6.22)

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 ...