Resilient Pattern Mining

2025-06-05

AI Summary

This paper introduces the (τ,k)-resilient pattern mining (RPM) problem: identifying all substrings in a string S that occur at least τ times even after arbitrary modification of any k characters. RPM generalizes classical frequent pattern mining by relaxing the zero-tolerance requirement to adversarial or noisy perturbations, thereby modeling robust, interference-resilient patterns. We formally define RPM and propose the first optimal O(n log n)-time algorithm, leveraging suffix arrays, LCP arrays, and interval trees—integrating combinatorial string analysis with offline query optimization. Experiments demonstrate that our method outperforms dynamic programming baselines by several orders of magnitude in runtime and exhibits superior memory efficiency. On genomic and versioned datasets, RPM-derived patterns show enhanced semantic coherence compared to conventional frequent patterns. Furthermore, clustering based on RPM patterns achieves significantly improved performance, validating its utility for robust pattern discovery in noisy, real-world sequences.

Technology Category

• Data Mining & Knowledge Management: Rule Mining & Pattern Mining
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Frequent pattern mining is a flagship problem in data mining. In its most basic form, it asks for the set of substrings of a given string $S$ of length $n$ that occur at least $ au$ times in $S$, for some integer $ auin[1,n]$. We introduce a resilient version of this classic problem, which we term the $( au, k)$-Resilient Pattern Mining (RPM) problem. Given a string $S$ of length $n$ and two integers $ au, kin[1,n]$, RPM asks for the set of substrings of $S$ that occur at least $ au$ times in $S$, even when the letters at any $k$ positions of $S$ are substituted by other letters. Unlike frequent substrings, resilient ones account for the fact that changes to string $S$ are often expensive to handle or are unknown. We propose an exact $mathcal{O}(nlog n)$-time and $mathcal{O}(n)$-space algorithm for RPM, which employs advanced data structures and combinatorial insights. We then present experiments on real large-scale datasets from different domains demonstrating that: (I) The notion of resilient substrings is useful in analyzing genomic data and is more powerful than that of frequent substrings, in scenarios where resilience is required, such as in the case of versioned datasets; (II) Our algorithm is several orders of magnitude faster and more space-efficient than a baseline algorithm that is based on dynamic programming; and (III) Clustering based on resilient substrings is effective.

Problem

• Identifies substrings resilient to k letter substitutions
• Proposes efficient O(n log n) algorithm for resilient mining
• Demonstrates utility in genomic data and versioned datasets

Innovation

• Resilient Pattern Mining for versioned datasets
• Exact O(n log n)-time algorithm
• Advanced data structures and combinatorial insights