A new network model that combines latent factors and sparse graphs

Overview • Quickstart • Acknowledgements

Overview

• Model Description : Our paper proposes a combined model, which integrates the latent factor model and the logistic regression model, for the network data. It is noticed that neither a latent factor model nor a logistic regression model alone is sufficient to capture the structure of the data. The proposed model has a latent (i.e., factor analysis) model to represent the main technological trends (a.k.a., factors), and adds a sparse component that captures the remaining ad hoc dependence.

• Paper link: "Latent Factor + Sparse Matrix logistic regression model for network data"

• Main functions for model selection

  1. ADMM_Optim : Main function for making inference for model parameters. Takes adjacency matrix and tuning parameters of models (gamma,delta) as input parameters. Gives the estimated alpha, matrices M, L and S as output of the function.
  2. Model_Sel : Given the adjacency matrix of the network data and the ranges of grids for gamma and delta to search over, the function gives: (1) a pair of indices (gamma, delta) that minimizes AIC over the given grid. (2) a pair of indices (gamma, delta) that minimizes BIC over the given grid. (3) the number of non-zero entries of the estimated S for each point on the grid. (4) the rank of the estimated L for each point on the grid.
  3. CV : Code for Network Cross-validation. Refer Section 6.2. of the paper for detailed explanation of the procedure. Takes the adjacency matrix of the network data, a pair of tuning parameters (gamma, delta) and the number of K iterations for the averaged mis-classifation rate of edges. Gives the K averaged mis-classification rate as output.
  4. Eval_func : Code for evaluation of the selected model. Given the adjacency matrix of the network data, and selected model parameters (gamma, delta) through AIC, BIC or Heuristic Network Cross-validation, the function gives: (1) the rank of estimated L matrix. (i.e. K) (2) K clustered nodes by applying k-means algorithm on K eigen-vectors of estimated L matrix. (3) the number of non-zero entries on upper-triangular part of the estimated S matrix. (4) a list of pairs of nodes which create the ad-hoc edges of the selected model.

• Codes for Simulations and Real Data analysis : We made a simple demonstration on how our model can be applied to a network data by using aforementioned functions. A famous Zachary Karate Club Network data is analzyed here.

  1. Simulation1 : Code for reproducing results presented in Section 6.1. of the paper.
  2. Simulation2 : Code for reproducing results presented in Section 6.2. of the paper.
  3. Polblog : Code for reproducing results presented in Section 7.1. of the paper.
  4. Citation_network : Code for reproducing results presented in Section 7.2. of the paper.

• Data References