[Paper Review] Enhancing Stability and Assessing Uncertainty in Community Detection through a Consensus-based Approach

Fabio Morea, Domenico De Stefano|arXiv (Cornell University)|Aug 6, 2024

Data-Driven Disease Surveillance5 citations

TL;DR

The paper introduces Consensus Community Detection (CCD), a framework that enhances stability, quantifies node-level uncertainty, detects outliers, and mitigates input-ordering bias for any community detection algorithm.

ABSTRACT

Complex data in social and natural sciences find effective representation through networks, wherein quantitative and categorical information can be associated with nodes and connecting edges. The internal structure of networks can be explored using unsupervised machine learning methods known as community detection algorithms. The process of community detection is inherently subject to uncertainty as algorithms utilize heuristic approaches and randomised procedures to explore vast solution spaces, resulting in non-deterministic outcomes and variability in detected communities across multiple runs. Moreover, many algorithms are not designed to identify outliers and may fail to take into account that a network is an unordered mathematical entity. The main aim of our work is to address these issues through a consensus-based approach by introducing a new framework called Consensus Community Detection (CCD). Our method can be applied to different community detection algorithms, allowing the quantification of uncertainty for the whole network as well as for each node, and providing three strategies for dealing with outliers: incorporate, highlight, or group. The effectiveness of our approach is evaluated on artificial benchmark networks.

Motivation & Objective

• Motivate the need for stable and interpretable community detection results amid algorithmic randomness and fuzziness in networks.
• Propose a general CCD framework that can be applied to any existing community detection algorithm to quantify uncertainty and improve reliability.
• Address key challenges: result validity, variability across runs, outlier handling, and input-ordering bias.
• Provide a mechanism to represent results with uncertainty at the node level and to facilitate interpretation of community structure.

Proposed method

• Run multiple stochastic partitions using the target algorithm on permuted versions of the network.
• Prune partitions that diverge from the majority based on a similarity score and a quantile threshold.
• Construct a co-occurrence matrix from the remaining partitions and recursively identify communities as blocks with assigned uncertainty coefficients γ.
• Output a partition with community labels and node-level uncertainty γ in [0,1], where γ=0 indicates stable co-occurrence and higher γ indicates residual variability.
• Introduce a quantile threshold q for selecting partitions and a threshold p for defining blocks in the co-occurrence matrix.

Figure 1: Variability of results of selected community detection algorithms on a LFR benchmark network with a nominal mixing parameter $\mu=0.40$ . Top: distribution of the number of communities. Middle: similarity between pairs of partitions. Bottom: scatterplot modularity and similarity.

Experimental results

Research questions

• RQ1 How can uncertainty be quantified and incorporated into community detection results?
• RQ2 Can a consensus-based procedure improve stability of partitions produced by different algorithms or runs?
• RQ3 How should outliers be identified and handled in the context of community detection?
• RQ4 How does input-ordering bias affect outcomes and how can it be mitigated?
• RQ5 What is the relationship between node-level uncertainty γ and network topology (e.g., centrality or core structure)?

Key findings

• CCD significantly enhances stability over single trials as the number of iterations t increases, approaching a plateau specific to each algorithm.
• CCD provides a node-level uncertainty coefficient γ, enabling identification of nodes with inconsistent community assignments (e.g., potential outliers).
• CCD reduces input-ordering bias in most algorithms and offers a framework compatible with existing methods for improved reliability.
• The approach yields interpretable representations of community structure with an explicit uncertainty measure, demonstrated on benchmarks such as Karate, RC, and LFR networks.
• Uncertainty γ increases non-linearly with the mixing parameter μ across LFR benchmarks, with different algorithms showing distinct patterns of uncertainty.

Figure 2: Three alternative strategies to manage outliers: incorporate (left), highlight as single-node communities (center), or group into an outliers’ community (right). The top row shows the network; the bottom row shows a graph of the communities, labeled with the number of nodes in each communi