[Paper Review] FS^3: A Sampling based method for top-k Frequent Subgraph Mining

Tanay Kumar Saha, Mohammad Al Hasan|arXiv (Cornell University)|Sep 2, 2014

Data Mining Algorithms and Applications3 citations

TL;DR

FS³ is a sampling-based method for top-k frequent subgraph mining that uses Markov Chain Monte Carlo (MCMC) sampling over fixed-size subgraphs, prioritizing those with higher frequency through a scoring function. It efficiently identifies the most frequent induced subgraphs in large graphs—achieving high precision (e.g., 54.2% pr@500) in under 1 hour—without solving computationally expensive subgraph isomorphism problems, enabling scalability where traditional methods fail.

ABSTRACT

Mining labeled subgraph is a popular research task in data mining because of its potential application in many different scientific domains. All the existing methods for this task explicitly or implicitly solve the subgraph isomorphism task which is computationally expensive, so they suffer from the lack of scalability problem when the graphs in the input database are large. In this work, we propose FS^3, which is a sampling based method. It mines a small collection of subgraphs that are most frequent in the probabilistic sense. FS^3 performs a Markov Chain Monte Carlo (MCMC) sampling over the space of a fixed-size subgraphs such that the potentially frequent subgraphs are sampled more often. Besides, FS^3 is equipped with an innovative queue manager. It stores the sampled subgraph in a finite queue over the course of mining in such a manner that the top-k positions in the queue contain the most frequent subgraphs. Our experiments on database of large graphs show that FS^3 is efficient, and it obtains subgraphs that are the most frequent amongst the subgraphs of a given size.

Motivation & Objective

• Address the scalability limitations of existing frequent subgraph mining (FSM) algorithms that rely on subgraph isomorphism and exhaustive enumeration, which become infeasible for large graphs.
• Develop a method that efficiently identifies the most frequent induced subgraphs of a given size without requiring complete enumeration of the subgraph space.
• Overcome the computational infeasibility of exact FSM methods on large biological and social networks, such as protein-protein interaction (PPI) networks.
• Provide a probabilistic, scalable alternative to exact FSM that maintains high rank correlation between estimated and actual subgraph support.
• Enable fast, approximate mining of top-k frequent subgraphs suitable for downstream tasks like graph classification and indexing.

Proposed method

• Employ Markov Chain Monte Carlo (MCMC) sampling over the space of fixed-size induced subgraphs, using a target distribution based on subgraph scoring functions $ s_1(G) $ and $ s_2(G) $ to favor potentially frequent subgraphs.
• Use a finite-size priority queue to maintain the top-k most frequently sampled subgraphs, dynamically updating based on sampling frequency.
• Generate canonical codes for subgraphs to enable efficient isomorphism checking during sampling and queue insertion.
• Introduce a stopping criterion based on Gelman-Rubin diagnostics, measuring Jaccard distance between multiple sampling chains to detect convergence.
• Apply a scoring function that estimates subgraph frequency based on local neighborhood statistics, reducing reliance on full subgraph isomorphism checks.
• Optimize performance by minimizing canonical code generation and queue insertion overhead, which are negligible compared to sampling time.

Experimental results

Research questions

• RQ1 Can a sampling-based approach outperform exact FSM algorithms in terms of runtime and scalability on large graphs?
• RQ2 Does MCMC sampling with a non-uniform target distribution (based on $ s_1 $ or $ s_2 $) improve the precision of top-k frequent subgraph recovery compared to uniform sampling?
• RQ3 How does the size of the priority queue affect the accuracy and memory usage of the top-k subgraph recovery?
• RQ4 Can a convergence-based stopping criterion (Gelman-Rubin diagnostics) effectively determine when sufficient sampling has been performed?
• RQ5 How robust is the performance of FS³ across different graph datasets with varying subgraph space complexity?

Key findings

• On the PS dataset, FS³ achieved a pr@500 of 54.2% within 70 minutes using the $ s_2 $ scoring function, significantly outperforming uniform sampling (52.3% pr@500) under the same time.
• For subgraph size 8 on the PS dataset, FS³ achieved over 90% pr@500 within 10 minutes on the Mutagen dataset, indicating strong performance on smaller subgraph spaces.
• The Kendall Tau correlation between estimated and actual subgraph support was consistently high (e.g., 55.4 at 2.0 target distribution), showing strong rank correlation.
• Runtime increased almost linearly with subgraph size $ p $, and sampling time dominated execution, with queue insertion being negligible.
• Performance remained stable across different $ k $ values (100 to 500), with precision and Kendall Tau values showing minimal variation, indicating robustness to $ k $.
• The Gelman-Rubin diagnostic showed diminishing Jaccard distance between chains over iterations, confirming convergence and validating the stopping criterion.