Session Line Graph Channel in Recommendations

• Session Line Graph Channel is a neural graph modeling approach that builds a line graph from session hypergraphs, capturing inter-session overlaps using metrics like Jaccard similarity.
• The method employs an Importance Extraction Module with self-attention to denoise session embeddings, thus enhancing the quality of feature representations.
• Integrating this channel into multi-channel architectures like GraphFusionSBR and DHCN yields significant improvements in recommendation accuracy, particularly for sparse, short sessions.

A session line graph channel is a neural graph modeling approach that constructs a line graph over session-based data, where each node represents an entire session (modeled as a hyperedge in a session hypergraph), and edges indicate overlap (typically, shared items) between sessions. The session line graph channel enables explicit modeling of inter-session relationships, complementing traditional item- or hyperedge-level graph neural approaches and enhancing the representational capacity for session-based recommendation tasks.

1. Mathematical Definition and Construction

Given a session hypergraph $G_h = (V, E)$, where $V$ is the set of all items and $E = \{e_1, e_2, \dots, e_M\}$ is the set of sessions (each hyperedge $e_p$ is the set of items in session $p$), the session line graph $G_\ell = \mathcal{L}(G_h) = (V_\ell, E_\ell)$ is constructed as:

• $V_\ell = \{v_{e_p} : e_p \in E\}$, i.e., one node per session.
• $(v_{e_p}, v_{e_q}) \in E_\ell$ iff $e_p \cap e_q \neq \emptyset$.

Edge weights reflect session overlap, e.g., via Jaccard similarity:

$W_{pq} = \frac{|e_p \cap e_q|}{|e_p \cup e_q|}$

The line graph adjacency matrix $A \in \mathbb{R}^{M \times M}$ is constructed with $A_{pq}=W_{pq}$ if $e_p \cap e_q \neq \emptyset$ and $A_{pq}=0$ otherwise. Self-loops are added to form $\widehat{A} = A + I_M$, and the degree matrix $\widehat{D}$ is computed row-wise.

Session-level features are typically initialized by attention-weighted pooling over item embeddings within each session (see Section 3), then propagated according to the standard GCN layer-wise update:

$$\Theta_\ell^{(l+1)} = \widehat{D}^{-1} \widehat{A} \Theta_\ell^{(l)}$$

for $L$ layers, followed by layer averaging:

$$\Theta_\ell = \frac{1}{L+1} \sum_{l=0}^{L} \Theta_\ell^{(l)}$$

The row $\theta_{\ell,p}$ in $\Theta_\ell$ gives the final line graph representation for session $p$ (He et al., 13 Jan 2026).

2. Motivation and Role in Session-Based Recommendation

Session-based recommender systems typically lack persistent user IDs, relying on anonymous, short user-event sequences. Item-graph or hypergraph methods capture intra-session signals, but largely neglect cross-session dependencies such as frequent co-occurrence patterns of item sequences across different sessions. The session line graph channel provides an explicit mechanism for leveraging correlations among sessions, i.e., inter-session dynamics, by:

• Modeling session similarity structure via shared items.
• Smoothing and propagating information between similar sessions.
• Enabling contrastive or mutual-information objectives between channels, facilitating more robust representations under data sparsity conditions.

Integrating the line graph channel, as in GraphFusionSBR and DHCN, demonstrably increases next-item prediction performance, especially on datasets with frequent short sessions and sparse data (Xia et al., 2020, He et al., 13 Jan 2026).

3. Initial Feature Construction and Denoising

A defining component in state-of-the-art session line graph channels is the initial session embedding mechanism, notably the Importance Extraction Module (IEM) in GraphFusionSBR (He et al., 13 Jan 2026). For a session $p$ with $t$ items and corresponding hypergraph item embeddings $X_h^{(0)} = [x_1^{(0)},...,x_t^{(0)}]^T$:

1. Query/key projections and similarity computation:

$$Q = W_q X_h^{(0)},\quad K = W_k X_h^{(0)},\quad C = \sigma(QK^T)/\sqrt{d}$$

2. Importance weights:

$$\alpha_i = \frac{1}{t-1} \sum_{j \neq i} C_{ij}, \quad \beta = \operatorname{softmax}(\alpha)$$

3. Session summary:

$$\theta_{\ell,p}^{(0)} = \sum_{i=1}^t \beta_i x_i^{(0)}$$

This self-attentive denoising accentuates informative clicks, reducing noise from uninformative item transitions. Ablation studies confirm its effect: removal degrades performance (e.g., P@20 on Tmall drops from 40.21 to 39.92) (He et al., 13 Jan 2026).

4. Cross-Channel Mutual Information Objectives

Session line graph channel representations complement hypergraph-based intra-session descriptors. In leading systems, these two session-level representations are aligned via mutual information maximization, typically a contrastive InfoNCE-style loss. For session $p$, with $\theta_{h,p}$ from the hypergraph channel and $\theta_{\ell,p}$ from the line-graph channel:

• Construct positive pairs $(\theta_{h,p}, \theta_{\ell,p})$ and negative pairs by row-wise shuffling of one channel.
• Loss:

$$\mathcal{L}_s = -\log \sigma(f_D(\theta_{h,p}, \theta_{\ell,p})) - \log \sigma(1 - f_D(\tilde{\theta}_h, \theta_{\ell,p}))$$

with $f_D(u, v) = u^T v$ and $\sigma$ the sigmoid (Xia et al., 2020).

GraphFusionSBR employs a more elaborate InfoNCE structure, with positives and negatives sampled by prediction top-k (He et al., 13 Jan 2026). The total loss function combines the recommendation loss, the self-supervised mutual information loss, and (if present) a knowledge-graph auxiliary loss.

5. Integration in Multi-Channel Architectures

The session line graph channel operates alongside other channels, each providing complementary information. In GraphFusionSBR, the architecture consists of:

• Knowledge graph channel for external or side information.
• Hypergraph channel for high-order, intra-session relationships.
• Line graph channel for inter-session dependency modeling.

The final recommendation only uses the knowledge-graph and hypergraph representations:

$$z_i = (\theta_h \| \theta_k)^T (x_{h,i} \| x_{k,i})$$

with the line-graph channel interacting through the mutual information loss for joint co-training. All channels are trained end-to-end, and the inclusion of the line-graph channel with mutual information regularization yields consistent performance improvements (He et al., 13 Jan 2026).

6. Empirical Findings and Comparative Performance

Session line graph channels have been empirically validated across multiple large-scale benchmarks. In DHCN, the inclusion of the line-graph channel yields relative improvements of 5–12% in P@20 and MRR@20 over prior SOTA GNN-based session models, with an additional 2–3% gain from self-supervised channel integration, the effect being more pronounced in short-session, sparse datasets (Xia et al., 2020).

In GraphFusionSBR, removal of the IEM or the contrastive loss consistently degrades performance. The optimal number of positives/negatives for contrastive learning is typically $K=5$, with larger values introducing noise. The contrastive loss's weight is dataset-dependent, with larger values (up to 1.0) benefiting long-tailed or high-variance session distributions (He et al., 13 Jan 2026).

7. Extensions and Generalization

The session line graph channel concept generalizes naturally to settings that demand explicit modeling of pairwise or higher-order item transitions within and across sessions. In DGTN, an extension is proposed where the line-graph is instantiated at the item transition level, allowing propagation over edge/transition nodes in both intra- and inter-session modes. These transition embeddings can be aggregated or integrated alongside traditional item-graph features, enabling fine-grained modeling of bigram or skip-gram dynamics in user navigation (Zheng et al., 2020).

A plausible implication is that future multi-channel graph neural architectures may incorporate multiple graph views (item, hypergraph, line-graph, knowledge-graph) and fuse them via design-principled objectives such as mutual information maximization or multi-view contrastive learning, to address the complex heterogeneity in observed user-session data.