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Personalized Ranking on Cascading Behavior Graphs for Accurate Multi-Behavior Recommendation

Geonwoo Ko, Minseo Jeon, Jinhong Jung

TL;DR

This work addresses multi-behavior item ranking by reframing the problem as graph ranking on a cascading sequence of behavior graphs. It introduces CascadingRank, which constructs a cascading behavior graph and computes personalized ranking scores via iterative updates that integrate smoothing, query fitting, and cascading alignment. The authors provide a theoretical analysis of cascading effects, convergence guarantees, and linear scalability, and demonstrate that CascadingRank outperforms state-of-the-art representation learning and graph-ranking baselines across three real-world datasets. The approach yields accurate, reliable, and scalable recommendations, highlighting the value of graph-ranking methods in multi-behavior settings.

Abstract

Multi-behavior recommendation predicts items a user may purchase by analyzing diverse behaviors like viewing, adding to a cart, and purchasing. Existing methods fall into two categories: representation learning and graph ranking. Representation learning generates user and item embeddings to capture latent interaction patterns, leveraging multi-behavior properties for better generalization. However, these methods often suffer from over-smoothing and bias toward frequent interactions, limiting their expressiveness. Graph ranking methods, on the other hand, directly compute personalized ranking scores, capturing user preferences more effectively. Despite their potential, graph ranking approaches have been primarily explored in single-behavior settings and remain underutilized for multi-behavior recommendation. In this paper, we propose CascadingRank, a novel graph ranking method for multi-behavior recommendation. It models the natural sequence of user behaviors (e.g., viewing, adding to cart, and purchasing) through a cascading behavior graph. An iterative algorithm computes ranking scores, ensuring smoothness, query fitting, and cascading alignment. Experiments on three real-world datasets demonstrate that CascadingRank outperforms state-of-the-art methods, with up to 9.56% and 7.16% improvements in HR@10 and NDCG@10, respectively. Furthermore, we provide theoretical analysis highlighting its effectiveness, convergence, and scalability, showcasing the advantages of graph ranking in multi-behavior recommendation.

Personalized Ranking on Cascading Behavior Graphs for Accurate Multi-Behavior Recommendation

TL;DR

This work addresses multi-behavior item ranking by reframing the problem as graph ranking on a cascading sequence of behavior graphs. It introduces CascadingRank, which constructs a cascading behavior graph and computes personalized ranking scores via iterative updates that integrate smoothing, query fitting, and cascading alignment. The authors provide a theoretical analysis of cascading effects, convergence guarantees, and linear scalability, and demonstrate that CascadingRank outperforms state-of-the-art representation learning and graph-ranking baselines across three real-world datasets. The approach yields accurate, reliable, and scalable recommendations, highlighting the value of graph-ranking methods in multi-behavior settings.

Abstract

Multi-behavior recommendation predicts items a user may purchase by analyzing diverse behaviors like viewing, adding to a cart, and purchasing. Existing methods fall into two categories: representation learning and graph ranking. Representation learning generates user and item embeddings to capture latent interaction patterns, leveraging multi-behavior properties for better generalization. However, these methods often suffer from over-smoothing and bias toward frequent interactions, limiting their expressiveness. Graph ranking methods, on the other hand, directly compute personalized ranking scores, capturing user preferences more effectively. Despite their potential, graph ranking approaches have been primarily explored in single-behavior settings and remain underutilized for multi-behavior recommendation. In this paper, we propose CascadingRank, a novel graph ranking method for multi-behavior recommendation. It models the natural sequence of user behaviors (e.g., viewing, adding to cart, and purchasing) through a cascading behavior graph. An iterative algorithm computes ranking scores, ensuring smoothness, query fitting, and cascading alignment. Experiments on three real-world datasets demonstrate that CascadingRank outperforms state-of-the-art methods, with up to 9.56% and 7.16% improvements in HR@10 and NDCG@10, respectively. Furthermore, we provide theoretical analysis highlighting its effectiveness, convergence, and scalability, showcasing the advantages of graph ranking in multi-behavior recommendation.

Paper Structure

This paper contains 33 sections, 3 theorems, 25 equations, 10 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Representation Learning Methods for Recommendation
  4. Graph Ranking Methods for Recommendation
  5. Preliminaries
  6. Notations
  7. Problem Definition
  8. Personalized Ranking on Bipartite Graphs
  9. Proposed Method
  10. Overview
  11. Cascading Behavior Graph Construction
  12. CascadingRank: Personalized Ranking on a Cascading Behavior Graph
  13. Iterative Algorithm for CascadingRank
  14. Interpretation from the Perspective of Optimization
  15. Theoretical Analysis
  16. ...and 18 more sections

Key Result

Theorem 1

The ranking score vector $\mathbf{r}_{b_t}$ on the target behavior $b_t$ is represented as follows: where $\hat{\mathbf{q}}_{b_i} = \alpha \cdot \mathbf{q}_{b_i}$, $\mathbf{\mathcal{L}}_{b_i} = \mathbf{L}_{b_i}^{-1} = (\mathbf{I} - \gamma \cdot \tilde{\mathbf{\mathcal{A}}}_{b_i})^{-1}$, $\mathbf{\mathcal{L}}_{b_j\leftsquigarrow b_i} = \mathbf{\mathcal{L}}_{b_j} \cdot \mathbf{\mathcal{L}}_{b_{j-1}

Figures (10)

  • Figure 1: Example of a cascading behavior graph $\mathcal{G}_{\mathcal{C}}=(\mathcal{G}_{b_{\texttt{view}}} \rightarrow \mathcal{G}_{b_{\texttt{cart}}} \rightarrow \mathcal{G}_{b_{\texttt{buy}}})$, given a cascading sequence $\mathcal{C} = (b_{\texttt{view}} \rightarrow b_{\texttt{cart}} \rightarrow b_{\texttt{buy}})$ of behaviors where $b_{\texttt{buy}}$ is the target behavior (i.e., $b_t$), and $q$ is the querying user node. Starting from $\mathcal{G}_{b_{\texttt{view}}}$, CascadingRank calculates ranking scores w.r.t. $q$ along $\mathcal{G}_{\mathcal{C}}$, and returns ranking scores of items at the target behavior $b_t$.
  • Figure 2: Illustration of the computation on the ranking score $\mathbf{r}_{\mathcal{U}_{b}}(u)$ of user $u$ of Equation \ref{['eq:cascrank:inst']}, with details of the notations provided in Section \ref{['sec:proposed:cascrank']}.
  • Figure 3: Recommendation performance in HR@$k$ and NDCG@$k$, where $k$ varies in {10, 30, 50, 100, 200}. Our CascadingRank provides better ranking scores than its competitors in both metrics.
  • Figure 4: Effect of behaviors in the cascading sequence, where B4 is used for CascadingRank, B7 for Tenrec, and B8 for Tmall to produce the final ranking scores of CascadingRank. Note that utilizing all behaviors in the sequence is beneficial for recommendation, as the performance degrades when earlier behaviors are excluded from the sequence.
  • Figure 5: Effect of the hyperparameters $\alpha$, $\beta$, and $\gamma$ of CascadingRank on the recommendation performance in HR@10, where $\gamma = 1 - \alpha - \beta$ is the strength of smoothing, and $\alpha$ and $\beta$ are the strengths of query fitting and cascading alignment, respectively.
  • ...and 5 more figures

Theorems & Definitions (8)

  • Definition 1: Cascading Sequence
  • Definition 2: Cascading Behavior Graph
  • Theorem 1: Cascading Effect
  • proof
  • Theorem 2: Convergence
  • proof
  • Theorem 3: Time Complexity
  • proof