best_fit_optim {netcom}

Empirical parameterization

Description

Helper function to find the best fitting version of a mechanism by searching across its parameter space

Usage

best_fit_optim(
  parameter,
  process,
  network,
  net_size,
  net_kind,
  mechanism_kind,
  resolution,
  resolution_min,
  resolution_max,
  reps,
  power_max,
  connectance_max,
  divergence_max,
  mutation_max,
  cores,
  directed,
  method,
  cause_orientation,
  DD_kind,
  DD_weight,
  max_norm,
  best_fit_kind = "avg",
  verbose = FALSE
)

Arguments

parameter

The parameter being tested for its ability to generate networks alike the input 'network'.

process

Name of mechanism. Currently only "ER", "PA", "DD", "DM" "SW", and "NM" are supported. Future versions will accept user-defined network-generating functions and associated parameters. ER = Erdos-Renyi random. PA = Preferential Attachment. DD = Duplication and Divergence. DM = Duplication and Mutation. SW = Small World. NM = Niche Model.

network

The network being compared to a hypothesized 'process' with a given 'parameter' value.

net_size

Number of nodes in the network.

net_kind

If the network is an adjacency matrix ("matrix") or an edge list ("list").

mechanism_kind

Either "canonical" or "grow" can be used to simulate networks. If "grow" is used, note that here it will only simulate pure mixtures made of a single mechanism.

resolution

The first step is to find the version of each process most similar to the target network. This parameter sets the number of parameter values to search across. Decrease to improve performance, but at the cost of accuracy.

resolution_min

= The minimum parameter value to consider. Zero is not used because in many processes it results in degenerate systems (e.g. entirely unconnected networks). Currently process agnostic. Future versions will accept a vector of values, one for each process.

resolution_max

The maximum parameter value to consider. One is not used because in many processes it results in degenerate systems (e.g. entirely connected networks). Currently process agnostic. Future versions will accept a vector of values, one for each process.

reps

The number of networks to simulate for each parameter. More replicates increases accuracy by making the estimation of the parameter that produces networks most similar to the target network less idiosyncratic.

power_max

The maximum power of attachment in the Preferential Attachment process (PA).

connectance_max

The maximum connectance parameter for the Niche Model.

divergence_max

The maximum divergence parameter for the Duplication and Divergence/Mutation mechanisms.

mutation_max

The maximum mutation parameter for the Duplication and Mutation mechanism.

cores

The number of cores to run the classification on. When set to 1 parallelization will be ignored.

directed

Whether the target network is directed.

method

This determines the method used to compare networks at the heart of the classification. Currently "DD" (Degree Distribution) and "align" (the align function which compares networks by the entropy of diffusion on them) are supported. Future versions will allow user-defined methods.

cause_orientation

The orientation of directed adjacency matrices.

DD_kind

A vector of network properties to be used to compare networks.

DD_weight

Weights of each network property in DD_kind. Defaults to 1, which is equal weighting for each property.

max_norm

Binary variable indicating if each network property should be normalized so its max value (if a node-level property) is one.

best_fit_kind

How to aggregate the stochastic replicates of the process + parameter combination.

verbose

Defaults to TRUE. Whether to print all messages.

Details

Note: Currently each process is assumed to have a single governing parameter.

Value

A number measuring how different the input network is from the parameter + process combination.

References

Langendorf, R. E., & Burgess, M. G. (2020). Empirically Classifying Network Mechanisms. arXiv preprint arXiv:2012.15863.

Examples

# Import netcom
library(netcom)

# Adjacency matrix
size <- 10
network <- matrix(sample(c(0,1), size = size^2, replace = TRUE), nrow = size, ncol = size)

# Calculate how similar the input network is to Small-World networks with 
# a rewiring probability of 0.28.
best_fit_optim(
     parameter = 0.28, 
     process = "SW", 
     network = network, 
     net_size = 12, 
     net_kind = "matrix", 
     mechanism_kind = "grow", 
     resolution = 100, 
     resolution_min = 0.01, 
     resolution_max = 0.99, 
     reps = 3, 
     power_max = 5, 
     connectance_max = 0.5, 
     divergence_max = 0.5, 
     mutation_max = 0.5, 
     cores = 1, 
     directed = TRUE, 
     method = "DD", 
     cause_orientation = "row", 
     DD_kind = c(
         "in", "out", "entropy_in", "entropy_out", 
         "clustering_coefficient", "page_rank", "communities"
     ), 
     DD_weight = 1, 
     max_norm = FALSE,
     verbose = FALSE
)