DM7 - Community Detection

It is a probabilistic generative model used primarily for overlapping community detection, assuming edges are generated based on the shared communities of two nodes.

The probability of an edge existing increases as the nodes share more communities, typically modeled as a noisy-OR function.

It introduces a continuous, non-negative community membership strength parameter ($F_{ij}$) for each node, allowing for efficient gradient-based optimization.

$p(i,j)=1-\exp (-F_i\cdot F_j^{\top })$.

By maximizing the log-likelihood of the observed graph using block coordinate ascent.

It can efficiently detect both overlapping and non-overlapping communities in near-linear time while handling arbitrary, non-convex cluster shapes.

The tendency of modularity-based algorithms to fail to detect small communities, instead artificially merging them into larger ones if the total number of edges in the network is very large.

The Modularity Matrix ($B$), where entries are $B_{ij}=A_{ij}-\frac{d_i{d}_j}{2m}$.