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

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.