# Restricted Boltzmann Machine Assignment Algorithm: Application to solve many-to-one matching problems on weighted bipartite graph

## TL;DR

This paper introduces an iterative unsupervised learning algorithm based on Restricted Boltzmann Machines to solve perfect matching problems in weighted bipartite graphs, demonstrating its potential through real-world application.

## Contribution

It presents a novel RBM-based iterative algorithm for solving many-to-one matching problems on weighted bipartite graphs, with demonstrated real-world applicability.

## Key findings

- Successfully maximizes energy function for optimal matching
- Demonstrates effectiveness on real-world bipartite graph problem
- Provides a new approach to combinatorial optimization using RBMs

## Abstract

In this work an iterative algorithm based on unsupervised learning is presented, specifically on a Restricted Boltzmann Machine (RBM) to solve a perfect matching problem on a bipartite weighted graph. Iteratively is calculated the weights $w_{ij}$ and the bias parameters $\theta = ( a_i, b_j) $ that maximize the energy function and assignment element $i$ to element $j$. An application of real problem is presented to show the potentiality of this algorithm.