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Discovering High-utility Sequential Rules with Increasing Utility Ratio

Zhenqiang Ye, Wensheng Gan, Gengsen Huang, Tianlong Gu, Philip S. Yu

TL;DR

This work addresses the problem of discovering high-utility sequential rules that progressively increase utility as rules are expanded. It introduces the SRIU algorithm, which employs two expansion modes (left-right and right-left) guided by an e-index to choose the expansion path, and uses IPEUM-based pruning along with upper-bound strategies to aggressively prune unpromising candidates. Key contributions include novel data structures (TempTable, UTable, PUTable) and pruning rules (IPEUP, CONFP, EUREP, EULEP, LEEP, REEUP), as well as memory-efficient Roaring bitmaps and MaxIS to handle large, dense datasets. Experimental results on real and synthetic data demonstrate that SRIU achieves substantial search-space reductions, improved runtime and memory performance in many settings, and mining results with higher confidence and conviction, supporting practical applicability in domains like e-commerce and healthcare.

Abstract

Utility-driven mining is an essential task in data science, as it can provide deeper insight into the real world. High-utility sequential rule mining (HUSRM) aims at discovering sequential rules with high utility and high confidence. It can certainly provide reliable information for decision-making because it uses confidence as an evaluation metric, as well as some algorithms like HUSRM and US-Rule. However, in current rule-growth mining methods, the linkage between HUSRs and their generation remains ambiguous. Specifically, it is unclear whether the addition of new items affects the utility or confidence of the former rule, leading to an increase or decrease in their values. Therefore, in this paper, we formulate the problem of mining HUSRs with an increasing utility ratio. To address this, we introduce a novel algorithm called SRIU for discovering all HUSRs with an increasing utility ratio using two distinct expansion methods, including left-right expansion and right-left expansion. SRIU also utilizes the item pair estimated utility pruning strategy (IPEUP) to reduce the search space. Moreover, for the two expansion methods, two sets of upper bounds and corresponding pruning strategies are introduced. To enhance the efficiency of SRIU, several optimizations are incorporated. These include utilizing the Bitmap to reduce memory consumption and designing a compact utility table for the mining procedure. Finally, extensive experimental results from both real-world and synthetic datasets demonstrate the effectiveness of the proposed method. Moreover, to better assess the quality of the generated sequential rules, metrics such as confidence and conviction are employed, which further demonstrate that SRIU can improve the relevance of mining results.

Discovering High-utility Sequential Rules with Increasing Utility Ratio

TL;DR

This work addresses the problem of discovering high-utility sequential rules that progressively increase utility as rules are expanded. It introduces the SRIU algorithm, which employs two expansion modes (left-right and right-left) guided by an e-index to choose the expansion path, and uses IPEUM-based pruning along with upper-bound strategies to aggressively prune unpromising candidates. Key contributions include novel data structures (TempTable, UTable, PUTable) and pruning rules (IPEUP, CONFP, EUREP, EULEP, LEEP, REEUP), as well as memory-efficient Roaring bitmaps and MaxIS to handle large, dense datasets. Experimental results on real and synthetic data demonstrate that SRIU achieves substantial search-space reductions, improved runtime and memory performance in many settings, and mining results with higher confidence and conviction, supporting practical applicability in domains like e-commerce and healthcare.

Abstract

Utility-driven mining is an essential task in data science, as it can provide deeper insight into the real world. High-utility sequential rule mining (HUSRM) aims at discovering sequential rules with high utility and high confidence. It can certainly provide reliable information for decision-making because it uses confidence as an evaluation metric, as well as some algorithms like HUSRM and US-Rule. However, in current rule-growth mining methods, the linkage between HUSRs and their generation remains ambiguous. Specifically, it is unclear whether the addition of new items affects the utility or confidence of the former rule, leading to an increase or decrease in their values. Therefore, in this paper, we formulate the problem of mining HUSRs with an increasing utility ratio. To address this, we introduce a novel algorithm called SRIU for discovering all HUSRs with an increasing utility ratio using two distinct expansion methods, including left-right expansion and right-left expansion. SRIU also utilizes the item pair estimated utility pruning strategy (IPEUP) to reduce the search space. Moreover, for the two expansion methods, two sets of upper bounds and corresponding pruning strategies are introduced. To enhance the efficiency of SRIU, several optimizations are incorporated. These include utilizing the Bitmap to reduce memory consumption and designing a compact utility table for the mining procedure. Finally, extensive experimental results from both real-world and synthetic datasets demonstrate the effectiveness of the proposed method. Moreover, to better assess the quality of the generated sequential rules, metrics such as confidence and conviction are employed, which further demonstrate that SRIU can improve the relevance of mining results.
Paper Structure (23 sections, 3 theorems, 5 equations, 10 figures, 4 tables, 3 algorithms)

This paper contains 23 sections, 3 theorems, 5 equations, 10 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Sequential Pattern Mining
  4. High-Utility Sequential Pattern Mining
  5. Sequential Rule Mining
  6. High-Utility Sequential Rule Mining
  7. Preliminaries and Problem Formulation
  8. The SRIU Algorithm
  9. Definitions and upper bounds
  10. Data structures
  11. Additional optimization
  12. The SRIU Algorithm
  13. Complexity analysis
  14. Time complexity
  15. Space complexity
  16. ...and 8 more sections

Key Result

Theorem 1

Given any item pair $(a,b)$, a sequential rule $r$ = $\{a\} \to \{b\}$ and $r^\prime$ the expansion of $r$, there is $\textit{SEU}(r^\prime)$$\leq$$\textit{SEU}(r)$ = $\textit{IPEUM}(a,b)$.

Figures (10)

  • Figure 1: The TempTable w.r.t. $\{a\} \to \{d\}$.
  • Figure 2: The TempTable w.r.t. $\{a\} \to \{d\}$.
  • Figure 3: The PUTable w.r.t. $\{a\} \to \{d,e\}$.
  • Figure 4: The runtime usage on different thresholds with increasing utility minRatio = 0.
  • Figure 5: The consumption of memory on different thresholds with increasing utility minRatio = 0.
  • ...and 5 more figures

Theorems & Definitions (17)

  • Definition 1: Sequence database fournier2022pattern
  • Definition 2: Sequential rule fournier2014erminer
  • Definition 3: The size of a sequential rule
  • Definition 4: Confidence han2001prefixspan
  • Definition 5: Utility of item / itemset / sequential rule
  • Definition 6: Expansion of sequential rule
  • Definition 7: Utility of sequence
  • Definition 8: Sequence estimated utility, SEU zida2015efficient
  • Definition 9: Item pair estimated utility pruning map
  • Theorem 1
  • ...and 7 more