[Paper Review] AMOS: An Automated Model Order Selection Algorithm for Spectral Graph Clustering

Pin‐Yu Chen, Thibaut Gensollen+1 more|arXiv (Cornell University)|Sep 21, 2016

Complex Network Analysis Techniques24 references3 citations

TL;DR

AMOS is an automated model order selection algorithm for spectral graph clustering that incrementally tests clusterings using statistical reliability metrics under the random interconnection model, achieving minimal model order with guaranteed clustering reliability. It outperforms existing methods on real-world datasets across multiple external and internal clustering metrics.

ABSTRACT

One of the longstanding problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. In this paper, we propose AMOS, an automated model order selection algorithm for SGC. Based on a recent analysis of clustering reliability for SGC under the random interconnection model, AMOS works by incrementally increasing the number of clusters, estimating the quality of identified clusters, and providing a series of clustering reliability tests. Consequently, AMOS outputs clusters of minimal model order with statistical clustering reliability guarantees. Comparing to three other automated graph clustering methods on real-world datasets, AMOS shows superior performance in terms of multiple external and internal clustering metrics.

Motivation & Objective

• Address the longstanding model order selection problem in spectral graph clustering—automatically determining the correct number of clusters.
• Provide statistical guarantees for clustering reliability in spectral graph clustering under the random interconnection model (RIM).
• Develop an automated algorithm that identifies the minimal number of clusters while ensuring high clustering quality.
• Overcome the limitations of heuristic or optimization-based approaches that lack theoretical justification for eigenvector selection.
• Enable robust, reliable, and automated clustering on real-world graphs without requiring ground-truth cluster counts.

Proposed method

• Incrementally increase the number of clusters from 2 up to a maximum, applying spectral graph clustering at each step.
• Use the random interconnection model (RIM) to model inter-cluster connections as independent Bernoulli or bounded-weight random variables.
• Estimate clustering reliability via multi-stage statistical hypothesis tests based on the largest inter-cluster edge weight ratio.
• Apply a confidence interval test on the maximum inter-cluster weight ratio to assess whether the current clustering is statistically reliable.
• Use the condition $\prod_{i<j} F_{ij}(\widehat{t}_{\text{LB}} / \widehat{\overline{W}}_{ij}, \widehat{p}_{ij}) \geq 1 - \alpha'$ to validate reliability, where $F_{ij}$ combines normal and indicator functions.
• Terminate at the smallest $K$ for which the clustering passes all reliability tests, ensuring minimal model order with statistical confidence.

Experimental results

Research questions

• RQ1 What is the minimal number of clusters that yields a statistically reliable clustering under the random interconnection model?
• RQ2 How can spectral graph clustering be automatically configured without prior knowledge of the true number of clusters?
• RQ3 Can statistical hypothesis testing be used to validate clustering reliability in a principled way for spectral clustering?
• RQ4 How does AMOS compare to existing automated clustering methods in terms of external and internal clustering metrics?
• RQ5 Does the proposed method maintain high performance across diverse real-world graph structures with varying cluster configurations?

Key findings

• AMOS achieved the highest normalized mutual information (NMI) on the IEEE RTS dataset, with a score of 0.89, outperforming Louvain (0.74), NB (0.75), and ST (0.73).
• On the Hibernia dataset, AMOS achieved the best Rand Index (RI) of 1.0 and F-measure of 0.94, surpassing all other methods.
• For the Cogent dataset, AMOS identified 4 clusters and achieved the lowest normalized cut (NC) of 0.036, outperforming NB (0.073) and ST (0.148).
• On the Minnesota road network, AMOS selected 46 clusters and achieved the best conductance (C) of 0.074, compared to Louvain (0.290) and NB (0.186).
• In the Facebook network, AMOS achieved the lowest F-measure (0.004) and conductance (0.006), indicating strong performance despite high complexity.
• Across all datasets, AMOS achieved the best or comparable performance on the majority of clustering metrics, demonstrating robustness and reliability.