BiMMSBM

A Python library for implementing Mixed-Membership Stochastic Block Models (MMSBM) with metadata integration for bipartite network analysis and link prediction.

Overview

This library provides tools for finding membership factors and connection probabilities in bipartite networks by incorporating node metadata. It implements the Mixed-Membership Stochastic Block Model (MMSBM) to find the most plausible parameters that fit a dataset of links between nodes, with the ability to leverage user metadata for improved link prediction.

Features

• Bipartite network analysis with metadata integration
• Bayesian inference using Expectation Maximization (EM) algorithm
• Adaptive metadata importance through hyperparameters
• High-performance implementation with optional Numba acceleration

Installation of requirements

bash pip install -r requirements.txt

Requirements

• Python >= 3.5
• Required packages:
  • pandas
  • numpy
• Optional but highly recommended:
  • numba (for performance optimization)

Usage

The library can be used for link prediction in bipartite complex networks where you have: - Two types of nodes (e.g., users and items, politicians and bills) - Labeled links representing ratings, votes, preferences, or connections - Optional node metadata/attributes

Basic Example

```python import pandas as pd import BiMMSBM as sbm

Create a sample dataset

dfpoliticians = pd.DataFrame({ "legislator": ["Pedro", "Santiago", "Alberto", "Yolanda"], "Party": ["PSOE", "VOX", "PP", "Sumar"], "Moviespreferences": ["Action|Drama", "Belic", "Belic|Comedy", "Comedy|Drama"] })

Initialize nodes layer with 9 groups

politicians = sbm.nodeslayer(9, "legislator", dfpoliticians)

Add exclusive metadata (Party)

lambdaparty = 100 parties = politicians.addexclusivemetadata(lambdaparty, "Party")

Add inclusive metadata (Movie preferences)

lambdamovies = 0.3 Taumovies = 6 movies = politicians.addinclusivemetadata(lambdamovies, "Moviespreferences", Tau_movies)

Dataframe of bills

df_bills =pd.DataFrame( {"bill":["A", "B", "C","D"], "Year":[2020, 2020, 2021, 2022]})

Number of groups

K = 2

Creating the bills layer

bills = sbm.nodeslayer(K,"bill",dfbills)

Dataframe of votes

df_votes =pd.DataFrame( {"legislator":["Pedro","Pedro","Pedro","Santiago","Santiago","Santiago", "Alberto", "Alberto", "Alberto", "Yolanda", "Yolanda", "Yolanda"], "bill":["A", "B", "D", "A","C", "D", "A", "B", "C", "B","C", "D",], "votes":["Yes","No","No", "No","Yes","Yes", "No","No","Yes", "Yes","No","No"]})

Creating the BiNet object

votes = sbm.BiNet(dfvotes,"votes",nodesa=bills,nodesb=politicians) #Fitting the model ## Initialize the EM algorithm by generating the parameters votes.initEM()

## Running the EM algorithm for 100 iterations and check the convergence every 10 steps for i in range(100): votes.EM_step() if i % 10 == 0: converges = votes.converges() print(f"Iteration {i} - Convergence: {converges}") if converges: break

#Getting the accuracy print(f"Accuracy: {votes.get_accuracy()}") ```

How It Works

The Link Prediction Problem

The library solves the link prediction problem in bipartite complex networks using the Mixed-Membership Stochastic Block Model. This model assumes that: - Nodes belong to a superposition of groups - Connection probabilities depend on the groups to which nodes belong

Metadata Integration

The model can be extended to handle multipartite complex networks by incorporating metadata bipartite networks. Each metadata network is described using a MMSBM, allowing for: - Full metadata correlation - Partial metadata correlation - No metadata correlation

The importance of each metadata type is controlled by a hyperparameter:

Documentation

• Full documentation: https://oscarcapote.github.io/BiMMSBM/index.html
• Tutorial: See Tutorial.ipynb
• Example usage: See Example.ipynb

References

1. Accurate and scalable social recommendation using mixed-membership stochastic block models
2. Node Metadata Can Produce Predictability Crossovers in Network Inference Problems

License

This project is licensed under the GNU General Public License v3.0 - see the LICENSE file for details.

The GNU GPL is a free, copyleft license that ensures the software remains free and open source. It requires that any derivative works must also be distributed under the same license terms.

Author

Oscar Fajardo Fontiveros