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arxiv: 2510.10243 · v2 · submitted 2025-10-11 · 💻 cs.DB

Efficient Mining of Low-Utility Sequential Patterns

Jian Zhu , Zhidong Lin , Wensheng Gan , Philip S. Yu This is my paper

Pith reviewed 2026-05-18 07:48 UTC · model grok-4.3

classification 💻 cs.DB
keywords low-utility sequential pattern miningsequential pattern miningutility-based data miningpruning strategiessequence utilitydata mining algorithmspattern discovery
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The pith

New algorithms mine low-utility sequential patterns faster and with less memory by extending candidates and pruning redundancies.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper formalizes low-utility sequential pattern mining as a distinct problem because high-utility methods do not transfer directly. It redefines sequence utility and introduces a sequence-utility chain to track information compactly during search. Three algorithms are developed: an exhaustive baseline plus two optimized versions that generate patterns via shrinkage or extension while applying pruning based on maximal non-mutually contained sequence sets. Experiments confirm that the extension-based version runs with lower runtime and memory use yet returns the full set of patterns. This makes low-utility pattern discovery feasible on realistic datasets where exhaustive enumeration would be too slow.

Core claim

By redefining sequence utility and employing the maximal non-mutually contained sequence set to prune candidates, the LUSPM_e algorithm discovers the complete set of low-utility sequential patterns more efficiently than baseline and shrinkage-based methods, using less runtime and memory.

What carries the argument

The maximal non-mutually contained sequence set together with extension-based generation and multiple pruning strategies that eliminate redundant subsequence checks while preserving completeness.

If this is right

  • LUSPM_e requires less runtime and memory than LUSPM_s while still returning every valid low-utility pattern.
  • The sequence-utility chain records utility values without repeated full database scans.
  • Pruning via the maximal non-mutually contained set removes many redundant generation steps in both optimized algorithms.
  • Both LUSPM_s and LUSPM_e scale to larger sequence collections than the exhaustive baseline.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The extension-plus-pruning design could be reused for other pattern tasks where low values of a measure are the objects of interest, such as rare-event detection.
  • Parallelizing the extension operations across multiple processors would likely improve speed further on very long sequence collections.
  • Domain-specific utility redefinitions for genomics or network logs could be plugged into the same chain structure with only local changes.

Load-bearing premise

The maximal non-mutually contained sequence set and associated pruning strategies correctly eliminate redundant candidates without missing any valid low-utility sequential patterns or violating the redefined utility measure.

What would settle it

On a small dataset where every possible subsequence can be exhaustively checked, LUSPM_e either reports a pattern whose utility is miscalculated or omits a pattern that meets the low-utility threshold.

Figures

Figures reproduced from arXiv: 2510.10243 by Jian Zhu, Philip S. Yu, Wensheng Gan, Zhidong Lin.

Figure 1
Figure 1. Figure 1: Sequence-utility chain of sequences⟨a, b, c⟩, ⟨a, b⟩, ⟨a⟩, and ⟨g, a⟩. B. LUSPMb In order to mine low-utility sequential patterns (LUSPs) (i.e., sequences S that satisfy 0 < u(S) ≤ minUtil), a naive idea is to first mine all high-utility sequential patterns (HUSPs) and then take the complement set with respect to all possible sequences. However, this approach is impractical for two reasons. First, the util… view at source ↗
Figure 2
Figure 2. Figure 2: Shrinkage search tree of sequence ⟨a, b, c, a, d⟩ when minUtil = 4. <a,b,c,a,d> <b,c,a,d> <c,a,d> <a,d> <a> <b> <c> <d> <b,a> <b,d> <c,a> <c,d> <b,c,d> <b,a,d> <a,a> <a,a,d> <a,c> <a,c,a> <a,c,d> <a,c,a,d> <a,b> <a,b,d> <a,b,a,d> <a,b,c> <a,b,c,a> <a,b,c,d> <a,b,a> <b,c,a> <b,c> [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Extension search tree of sequence ⟨a, b, c, a, d⟩ when minUtil = 4. ≥ LBS(Q, F) > minUtil. Therefore, pruning S, F, and all their extensions is valid. Proof. Suppose F is a super-sequence and S is a subsequence of F. If LBS(S, F) > minUtil, then by Theorem 3, we have u(S) ≥ LBS(S, F) > minUtil, which means S is not a LUSP. Moreover, by Theorem 4, the utility of F also exceeds minUtil, so F is not a LUSP. F… view at source ↗
Figure 4
Figure 4. Figure 4: Time consumption analysis of LUSPMs and LUSPMe 0 1 2 3 4 5 6 1/7 2/7 3/7 4/7 5/7 6/7 1e3 LUSPMₑ LUSPMₛ 0 5 10 15 20 25 30 35 40 10 12 14 16 18 20 Memory (MB) 1e2 minutil (a) SIGN 0.0 0.5 1.0 1.5 2.0 2.5 3.0 10 12 14 16 18 20 Memory (MB) 1e2 minutil (b) Synthetic3k 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 Memory (MB) 1e2 minutil (c) Leviathan 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 20 21 22 23 24 25 Memory (MB) … view at source ↗
Figure 5
Figure 5. Figure 5: Memory consumption analysis of LUSPMs and LUSPMe example, in the Synthetic3k dataset, when minUtil = 20, the runtime of LUSPMs is approximately 7975s, whereas LUSPMe requires only 3406s, representing a reduction of about 57.3%. In the Leviathan dataset, when minUtil = 6, the runtime of LUSPMs is approximately 56319s, while LUSPMe requires 19650s, representing a reduction of about 65.1%. This is probably be… view at source ↗
Figure 6
Figure 6. Figure 6: Number of utility computations of LUSPMs and LUSPMe 0 5 10 15 20 25 30 35 40 1/7 2/7 3/7 4/7 5/7 6/7 Runtime (s) 1e2 maxLen (c) Leviathan 0 1 2 3 4 5 6 7 8 1/7 2/7 3/7 4/7 5/7 6/7 Runtime (s) 1e2 maxLen (b) Synthetic3k 0 1 2 3 4 5 6 1/7 2/7 3/7 4/7 5/7 6/7 Runtime (s) 1e2 maxLen (a) SIGN 0 1 2 3 4 5 6 1/7 2/7 3/7 4/7 5/7 6/7 1e3 LUSPMₛ LUSPMₑ 0.0 0.5 1.0 1.5 2.0 2.5 1/7 2/7 3/7 4/7 5/7 6/7 Runtime (s) 1e2 … view at source ↗
Figure 7
Figure 7. Figure 7: Runtime performance under different values of [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Memory performance under different values of [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Scalability analysis of LUSPMs and LUSPMe We generate synthetic datasets with sequences of varying lengths (ranging from 50K to 100K) by randomly sampling rows from the six datasets in Table IV as well as from the YooChoose dataset2 [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
read the original abstract

Discovering valuable insights from rich data is a crucial task for exploratory data analysis. Sequential pattern mining (SPM) has found widespread applications across various domains. In recent years, low-utility sequential pattern mining (LUSPM) has shown strong potential in applications such as intrusion detection and genomic sequence analysis. However, existing research in utility-based SPM focuses on high-utility sequential patterns, and the definitions and strategies used in high-utility SPM cannot be directly applied to LUSPM. Moreover, no algorithms have yet been developed specifically for mining low-utility sequential patterns. To address these problems, we formalize the LUSPM problem, redefine sequence utility, and introduce a compact data structure called the sequence-utility chain to efficiently record utility information. Furthermore, we propose three novel algorithm--LUSPM_b, LUSPM_s, and LUSPM_e--to discover the complete set of low-utility sequential patterns. LUSPM_b serves as an exhaustive baseline, while LUSPM_s and LUSPM_e build upon it, generating subsequences through shrinkage and extension operations, respectively. In addition, we introduce the maximal non-mutually contained sequence set and incorporate multiple pruning strategies, which significantly reduce redundant operations in both LUSPM_s and LUSPM_e. Finally, extensive experimental results demonstrate that both LUSPM_s and LUSPM_e substantially outperform LUSPM_b and exhibit excellent scalability. Notably, LUSPM_e achieves superior efficiency, requiring less runtime and memory consumption than LUSPM_s. Our code is available at https://github.com/Zhidong-Lin/LUSPM.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces the problem of low-utility sequential pattern mining (LUSPM), which has not been addressed by prior algorithms focused on high-utility patterns. It redefines sequence utility, presents a sequence-utility chain data structure, and develops three algorithms: an exhaustive baseline LUSPM_b, a shrinkage-based LUSPM_s, and an extension-based LUSPM_e. Pruning is achieved via the maximal non-mutually contained sequence set. Experiments indicate that LUSPM_s and LUSPM_e are more efficient than the baseline, with LUSPM_e requiring the least runtime and memory while returning the complete set of low-utility sequential patterns.

Significance. This research opens up a new direction in utility-based sequential pattern mining by targeting low-utility patterns, relevant for applications like intrusion detection and genomic analysis. The provision of open code supports reproducibility. If the pruning strategies are proven sound, the efficiency improvements could make LUSPM practical for large datasets.

major comments (2)
  1. [§3.4 (Maximal Non-Mutually Contained Sequence Set and Pruning)] §3.4 (Maximal Non-Mutually Contained Sequence Set and Pruning): The pruning strategies rely on the assumption that the redefined utility allows safe elimination of candidates using maximal non-mutually contained sequences. The manuscript should include a detailed proof or empirical verification that no low-utility pattern is discarded by these strategies, as this is central to both the completeness claim and the efficiency advantages reported for LUSPM_e.
  2. [§5 (Experiments)] §5 (Experiments): While outperformance is claimed, the section should specify the exact datasets, utility thresholds, number of runs for timing, and include statistical significance tests to substantiate the scalability and efficiency claims.
minor comments (2)
  1. [Abstract] Abstract: Consider adding one or two example datasets or typical utility threshold values to give readers a concrete sense of the experimental setup.
  2. [§2 (Related Work)] §2 (Related Work): Ensure all citations to high-utility SPM papers are up to date and include a brief comparison table if space allows.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the constructive feedback on our manuscript. We address each major comment below and will revise the manuscript to strengthen the presentation of our contributions.

read point-by-point responses

  1. Referee: §3.4 (Maximal Non-Mutually Contained Sequence Set and Pruning): The pruning strategies rely on the assumption that the redefined utility allows safe elimination of candidates using maximal non-mutually contained sequences. The manuscript should include a detailed proof or empirical verification that no low-utility pattern is discarded by these strategies, as this is central to both the completeness claim and the efficiency advantages reported for LUSPM_e.

    Authors: We agree that a formal proof is necessary to rigorously establish the soundness of the pruning strategies. In the revised manuscript, we will add a detailed proof in §3.4 showing that the maximal non-mutually contained sequence set combined with the redefined sequence utility preserves all low-utility patterns. The proof will be based on the anti-monotonicity of the utility measure with respect to sequence containment and the definition of the maximal set. We will also include a brief empirical verification using small synthetic datasets to illustrate that no valid patterns are lost. revision: yes

  2. Referee: §5 (Experiments): While outperformance is claimed, the section should specify the exact datasets, utility thresholds, number of runs for timing, and include statistical significance tests to substantiate the scalability and efficiency claims.

    Authors: We appreciate this suggestion for improving experimental transparency. In the revised §5, we will explicitly name all datasets (with their key characteristics), report the precise utility thresholds used in each experiment, state that timings are averaged over 5 independent runs, and add statistical significance tests (paired t-tests with p-values) to support the efficiency comparisons between LUSPM_b, LUSPM_s, and LUSPM_e. revision: yes

Circularity Check

0 steps flagged

Algorithmic construction with external validation; no derivation reduces to inputs by construction

full rationale

The paper formalizes LUSPM, redefines sequence utility, introduces the sequence-utility chain data structure, and proposes three algorithms (LUSPM_b baseline, LUSPM_s via shrinkage, LUSPM_e via extension) plus pruning over the maximal non-mutually contained sequence set. These steps are constructive definitions and algorithmic procedures whose completeness and efficiency claims are supported by experimental comparisons on runtime/memory rather than by any equation or parameter that is fitted to the target output and then renamed as a prediction. No self-citation chain, uniqueness theorem, or ansatz is invoked to force the central result; the work remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claims rest on the assumption that low-utility patterns can be defined by inverting or redefining the standard utility measure from high-utility SPM without introducing new fitted constants; no explicit free parameters, axioms, or invented entities are described in the provided abstract.

pith-pipeline@v0.9.0 · 5830 in / 1177 out tokens · 39441 ms · 2026-05-18T07:48:02.226471+00:00 · methodology

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