While recommender systems have significantly benefited from implicit feedback, they have often missed the nuances of multi-behavior interactions between users and items. Historically, these systems either amalgamated all behaviors, such as impression (formerly view), add-to-cart, and buy, under a singular 'interaction' label, or prioritized only the target behavior, often the buy action, discarding valuable auxiliary signals. Although recent advancements tried addressing this simplification, they primarily gravitated towards optimizing the target behavior alone, battling with data scarcity. Additionally, they tended to bypass the nuanced hierarchy intrinsic to behaviors. To bridge these gaps, we introduce the Hierarchical Multi-behavior Graph Attention Network (HMGN). This pioneering framework leverages attention mechanisms to discern information from both inter and intra-behaviors while employing a multi-task Hierarchical Bayesian Personalized Ranking (HBPR) for optimization. Recognizing the need for scalability, our approach integrates a specialized multi-behavior sub-graph sampling technique. Moreover, the adaptability of HMGN allows for the seamless inclusion of knowledge metadata and time-series data. Empirical results attest to our model's prowess, registering a notable performance boost of up to 64% in NDCG@100 metrics over conventional graph neural network methods.
CEUR ceur-ws.org A
Recommender systems are widely employed in online platforms to provide accurate and relevant content to implicit feedback has become widely adopted [1, 2, 3, 4, 5, 6, 7], where the user-item relationship is classified as either interacted or unknown. However, modern online shopping platforms involve various types of interactions, such as clicks, add-to-cart actions, and buy. Relying solely on binary implicit feedback information (interacted or unknown) while overlooking this rich multi-behavior information can worsen the cold start problem and exacerbate data sparsity issues [8]. Furthermore, considering the naturally existing multi-behavior information in the modern e-commerce ecosystem, it becomes beneficial to diferentiate between various user behaviors and optimize for target behaviors, such as buy, which align with the ultimate goal of maximizing revenue for businesses.
Recent years have witnessed the rapid development of multi-behavior recommender systems [9, 10, 11, 12, 13, 8, 14, 15], due to their ability to supplement and motivate sparse target behavior signals (buy) with auxiliary behaviors (view or what’s often termed ”impression”, favorite, add-to-cart, etc). Despite these eforts, there exist drawbacks that prohibit these works from fully exploiting the
Failure to exhaustively utilize and predict auxiliary behaviors. [8] constructed a heterogeneous graph convolutional neural network for the multi-behavior recommendation and apply Bayesian Personalized Ranking (BPR), where positive and negative pairs are sampled according to the target behavior. [12] utilized the graph attention layer together with the item knowledge graph and temporal encoding to empower the learned embeddings to be expressive. All these multi-behavior models [8, 14, 12] merely optimize for single-behavior (target behavior) despite utilizing multi-behavior information during the model learning stage. Besides, these approaches are unable to predict other auxiliary behaviors thus still sufering from sub-optimal performance and label-sparsity issues. Overlooking the hierarchical pattern of multi-behaviors. [16, 13] took the backbone of heterogeneous graph convolutional neural network and applied binary Mean Square Error to all behaviors CEUR htp:/ceur-ws.org ISN1613-073
CEUR Workshop on Learning and Evaluating Recommendations with Impres- predictions. Despite its eficiency, we argue this method †This work was completed during the author’s internship at Amazon. two diferent levels of behaviors. These methods did © 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License not consider the case where an item would innocently Attribution 4.0 International (CC BY 4.0). behavior scenarios. This multi-task optimization framework is crucial for the behavior prediction task. 3. To scale our model, we extend sub-graph sampling strategy to multi-behavior scenario, avoiding bias in behavior sampling. The corresponding pairwise negative sampling for HBPR loss is refurbished in the sub-graph stage. 4. Extensive empirical experiments are conducted on two practically processed e-commerce datasets (Taobao and RetailRocket ). The results show that our framework achieves significant improvement over state-of-the-art models (SOTA) (35% in RetailRocket and 64% in Taobao) in terms of ofline metric ( @100 ) on target-behavior prediction task. dation problem; in section 3, we detailed clarify the proposed frameworks including model architecture and optimization; in section 4.1, we introduce the sub-graph serve as a negative sample while belonging to a higher sampling as well as incorporation of temporal and knowlimportance behavior group. More specifically, a user edge information for multi-behavior recommendation; in views and buys an item directly (without add-to-cart ), section 5, we conduct extensive empirical experiments; would possibly serve as a negative sample when opti- in section 6, we briefly introduce the related works and mizing for add-to-cart behavior, which is contrary to the discuss the resemblance and discrepancy from ours and hierarchical pattern between multi-behaviors. in section 7, we summarize and conclude the paper.
attention neural network which enables us to learn and represent individual interaction and optimize a multi-task 2. Experiment Formulation objective. The challenge is direct utilization of Bayesian Personalized Ranking (BPR) for multi-behavior scenarios can lead to some conflicts. We use an example in fig. 1 (d) to clarify the situation. 3 add-to-cart the item 3 and buy item 2. To optimize the behavior add-to-cart, the BPR criterion would clarify 3 is positive and 2 is negative for 3. We argue that this is not practical since the buy behavior over 2 already demonstrates the user’s preference.
terion to deal with the multi-behavior case by taking the hierarchical relations between behaviors into consideration. We propose a multi-behavior ad-hoc graph attention network, aka Hierarchical Multi-behavior Graph
tions of this paper as below: Ad Tech and Media customers always encounter label sparsity for single-behavior recommendation systems despite having rich auxiliary information. Incorportating multiple behaviors can also help in the development of a model that can predict a customer’s propensity across diferent stages of purchase funnel. Additionally, our customers express the need to create a robust decisionmaking engine that can leverage side information, such as item metadata, to enhance the recommendation process. The work we present here represents a preliminary step towards their long-term goal of building a resilient pipeline for multi-behavior recommendation systems based on Graph Neural Networks (GNNs).
ommender system in graph terminology. User-Item Multi-Behavior (Temporal) Bipartite Graph: the user-item interactions can be treated as a heterogeneous bipartite graph = (ℰ , ) = {(, , )| ∈ , ∈ , ∈ } where is the set of all user nodes, is the set of all item nodes, indicates user interacted item with behavior . is the set of all multi-behavior interaction edges between a user and an item (view, add-to-cart,
graph attention neural network paradigms targeting on multi-behavior recommendation. Besides target behavior, our model is also able to predict auxiliary behaviors.
favor, buy, etc for e-commerce datasets). If temporal in- 3.1. HMGN-intra view (analogous to ”impression” in the context), add-to- (message propagating) phase is conducted on these them. formation is to be considered, the dynamic graph can be exist at most one edge per behavior type. represented as: = {(, , , , )| ∈ , ∈ , where is the timestamp when interacted with under . For each user-item node pair (, ) , there can only
∈ }
is to utilize all the interaction information (including cart, favor, buy, etc) to predict the possible target behavior, typically buy behavior.
Multi-Behavior Graph Attenion
posed framework - Hierarchical Multi-Behavior Graph Attention Network (HMGN) , the model illustration of which is presented in Figure 2. As we formulated in section 2, the multi-behavior recommendation data is organized as a heterogeneous bipartite graph. This leads to a diferent order of information propagation and aggregation process in GNNs based on each behavior which we explore in HMGN-intra and HMGN-inter. Mathematically, we denote e (0), e
(0) as the initialized embedding for user and item . After propagating through layers of the graph attention network, the output of the last layer () would be treated as the final representation (( () e ) ⋅ ( () e() ) ⋅ √1/ )
target-oriented representation (e(,) ) learning. Since all the procedure is operated and conducted in each isolated () ) are transsingle-behavior graph, the e the perspective of each behavior . The next step is to aggregate each behavior representation. (,) is representative from
ponents for the GNN as LightGCN [19] demonstrated. to set ).
e (+1) = ∑ , ⋅ e(,)
∈ In [13], , is set to be manually determined hyper- nism to aggregate information from neighboring sources (2) (3) () e
() is the personalized query in behavior space and { () e() } , { () e() } are the corresponding keys and
values in each behavior space for item . () scale the weight that how much information the target node ( ) obtained from diferent behavior spaces of the neighborhood node. And the obtained representation e← contains all the behavior information that passed from node to node . The next step is aggregating all the information from its neighborhood nodes (belonging
←(, ) tends to
Unlike GCN [13] architecture, we use an attention mechanodes to target nodes [11].
3.3. Behavior Preference Modeling After information propagating through layers of GNN, we obtain final representation item , respectively. In real-world multi-behavior recommendation, a user would have a generalization impression e () and e () for user and ization preference , (view/add-to-cart-buy, etc). Inspired by this joint relation: ln (, ) = ln (|) + ln () We propose the following formula that can capture both user item generalization preference as well as behavior specialization preference: (, , ) = ( e () ) ((1 − ) + )e() (6) where is identity matrix and is diagonal matrix representing a behavior type . is a scalar hyperparameter that balances the trade-of between generalization and specialization. Noting that, if = 1 , eq. (6) would be the user-item inner product [3] - the most common strategy to mimic user-item preference; if = 0 , it would collapse to the behavior specialization preference, similar to [13]. parameters and is shared between each user and item (as ). A drawback for this setting occurs when a node doesn’t exhibit a specific behavior. It leads to an unstable amplitude in e (+1) with e
(,) being a zero vector. With our personalized average aggregation, when a user does not exhibit the specific behavior , their weight , shall be set as 0, and the aggregation operation is performed over the remaining behaviors: , = ⎧0, ⎨ ⎩
1 ∑ ( e (,) ≠0) e e (,) (,) = 0 ≠ 0 where is the indicator function, equal to 1 when input is True and 0 for False. 3.2. HMGN-inter In HMGN-inter framework, the message would first pass and aggregate across all behaviors within each userwhere diferent user/item can exhibit varying levels of multiple behaviors. For example, a particular user can perform more add-to-cart actions compared to buy. Similarly, a particular item could experience more page-view than it has been marked as favorite. Thus learning useritem behavior involves understanding these complex dynamics that are user/item centric.
For each user-item pair, the cross attention attempts to maximize the optimal behavior representation for the target node (user 3 from fig. 2(a)).
∑ ∈ ∈ item node pair. We motivate this from real-world patterns over an item (like/dislike) and also the behavior special3.4. HBPR: Hierarchical Bayesian
Personalized Ranking While recent works [8, 12, 11] utilize multi-behavior information in modeling phase, they solely optimize for target behavior (treating only target behavior as positive label) in their objective. We argue that this single-task optimization framework won’t be suficient to exploit the power of auxiliary behavior information. And some multi-task optimization [13] ignores the relationship between the behaviors. Thus, we propose a multi-task optimization criterion - Hierarchical Bayesian Personalized
The behavior-specific personalized formalization is an extension of [7] and is defined as > , states as user prefer item than item under the behavior . In multi-behavior scenario, we maintain >, with the properties of totality, antisymmetry, transitivity (see [7]) , extended it with extra property - hierarchy: >, ⊂ 2, where ∀, ∈ ,
1, 2 ∈ ∶ > , 1 ∧ > , 2 ∧ 1 > 2 ⇒ > , 1 , = , 2 behaviors. where > is the heuristically defined priority rank across
talked in fig. 1 in section 1: 3 add-to-cart the item 3 and buy item 2. We have 2 > 3, 3 and 3 > 3, −− Without defining of hierarchy, the BPR criterion would classify 3 is positive and 2 is negative for 3 under be 2. havior add-to-cart, 3 > 3, −− set as buy > add-to-cart > view. practical since the typical case is a person click/view an item, favor it or add-to-cart, then buy it. Under such a hierarchical assumption, as long as the user buy an item, the preference over other behaviors is supposed to be automatically claimed. Following this logic, the e-commerce shopping behaviors priority rank > can be 2. This is not quite + = { 0, 1, ⋯ , −1 }.
Definition 1 (Higher priority rank set +). Given a behaviors priority rank: 0 > > 1 > ⋯ > . The higher priority rank set of (0 ≤ ≤ ) is denoted as , For convenience, we define + ⊂ as the set of all items that user interacted with behavior and ,− as non-interacted or unknown in contrast.
= \ , Obviously, + + , ∩ ,− = ∅ and ,+
∪ ,− = .
+ can be treat as a positive sample for user with the behavior , while the negative one is not
An item from , of hierarchy. directly from ,− = \ ,
+ according to the requirements
Equipped with this definition of behavior higher priority rank set, we can determine the negative item sets compatible with hierarchy principle: , ,− = { ∈ users and items. Therefore, the scalability of recommendation models is crucial for production deployments.
in homogeneous sub-graph sampling strategies (singlebehavior) [20, 21, 22, 23], there is a dearth of literature in the heterogeneous (multi-behavior) sampling realm graph kernel (the inner circle in Figure 3). Then, we sub-graph sampling; (d)”add-to-cart” sub-graph sampling (e)final sub-graph. For sub-graph BPR optimization, positive useritem pairs are selected from the kernel of sub-graph and negative pairs come from the entire sub-graph. sample up to -hop neighborhood nodes for these kernel nodes. In the HBPR optimization stage, where a pair of nodes (positive and negative item samples for a user) are required, we constrain the positive sample to be derived from our core sub-graph kernel and the negative sample to be derived from rest of the sub-graph. (Algorithm 1)
The justification of why sub-graph kernel is crucial for optimization is as follows. In the original full-size graph, nodes and edges are self-contained (connected), and every node can receive information from all of its neighborhoods during the graph propagation stage. In the case of sub-graph, since only few nodes are kept, there is an unavoidable loss of knowledge during the information propagation. Especially for those nodes in the ”border” of the sub-graph in Figure 3, they are left with spare neighboring. In contrast, for those nodes in the kernel, almost all the neighbors (dense neighborhoods) would be kept due to our layer-wise sampling strategy.
4.2. Temporal Encoding latent dimension of the model): Temporal information can be seamlessly incorporated into our framework in a way similar to positional encoding in transformer[18, 12]. Formally, we define the temporal representation as a vector ∈ ℝ ( is the ,2 = sin( 2 ) ,2+1 = cos(
2+1 ) and aggregation is in-batch operated by adjacency (Lapla(,) is used to subcian) matrix. 4.3. Knowledge Graph (KG) Enhancing
Collaborative Knowledge Graph (CKG) can be seamlessly extended from single-behavior recommendation to multi-behavior recommendation. User-item interactions can be largely divided into multiple triples, (, , ) for example, (, , ) data, we can also define , (, , )
, etc. As to the item-meta (, , ) where ∈ ℛ is the relation and ∈ ℰ is an entity (item feature), for example, (, , ) as {(ℎ, , )|ℎ, ∈
. To this end, the CKG is defined ⋃ ⋃ ℰ , ∈ ⋃ ℛ} The translation principle which optimizes KG by projecting relations and entities into a common semantic space, [26] is given by: ℎ + e ≈ , where eℎ and are the representation of the head and tail nodes in relation space. The scoring function is thus given by (ℎ, , ) = || ℎ + − || (12)
ℒ = ∑ − log ((ℎ, , ′) − (ℎ, , ) ) (13) Combine Equation (8): ℒ ′ = ℒ + ℒ + , ,− ,
← { ∈ for all ∈ ← 0 repeat ← {|(, , ) ∈ } ,− ← { ∈ | ∈ \ ,+ } training set = {(, , , )} INPUT: kernel users set ⊂ OUTPUT: sub-graph = {(, , )| ∈ , ∈ } , 1: for all ∈ ℬ
do construct kernel items set construct single-behavior graph from one-hop neighsampling and obtain single-behavior sub-graph 5: end for 7: sub-graph kernel 6: sub-graph ← {(, , )| ∈ ⋃ , ∈ ⋃ }
← {(, , )| ∈ , ∈ ∈ 8: Empty dataset ← {} 9: for all ∈ do for all ∈
do end for end for 23: end for
(RQ1): How do our proposed models: HMGN-intra and HMGN-inter perform compared to the SOTA baselines [12, 13] in terms of target-behavior prediction? (RQ2): How does the proposed hierarchical multi-task learning perform compared to single-task learning in terms of target-behavior prediction? And how does it perform compared to other multi-task learning in terms of multi-behavior predictions? (RQ3): How do our models perform when trained on sampled sub-graph vs non-sampling full graph? (RQ4): How would diferent gadgets (temporal encoding, knowledge-graph) contribute to the performance? 2: 3: 4: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: tral). However, in practical circumstances, a user cannot exhibit these behaviors simultaneously. Therefore, we refrain from using them for our experiments. and 1 (with view, add-to-cart, buy 2 (with view,
is treated as training set, data in Dec-02-2017 is the validation set and Dec-03-2017 is the test set. Similarly in dataset, we split data according to the following timelines: May-03-2015 to Aug-15-2015 as a training set, Aug-16-2015 to Sep-01-2015 as the validation set and Sep-01-2015 to Sep-15-2015 as a test set. For reproducibility, we would share the details of the data processing as well as the models in the code.
5.2. Experimental Settings
for a individual user :
and ( = 10, 50, 100 ) as our metrics, specifically ∑ (() ≤ ) ( , | ∈ ∑ ∈ |) (() ≤ ) log(() + 1)
(14) 1https://tianchi.aliyun.com/dataset/649 2https://www.kaggle.com/datasets/retailrocket/ecommerce-dataset Performance of the HMGN models w.r.t baselines on RetailRocket dataset. Mean results are present by repeating 5 times.
NDCG@10
NDCG@50
NDCG@100
RECALL@10
RECALL@50
RECALL@100 . Here • KHGT [12] is a SOTA model that targets on multi [29, 30, 31, 32].
cial cases when | 5.2.2. Baselines is an indicator function and ()
is the rank of item user in test set. It is worth noting that in some spe
is the set of positive items for | > (
1, 2) and 1 ≥ 2., 2 could happen. This is because while the denominator could dominate the value. that numerator wouldn’t change much (from 1 to 2),
Single-behavior Models: • itemKNN [33] A classical and robust neighborhood method.
objectives. • BPR [7] is one of the most popular methods in recommendation which learns to optimize pair-wise • LightGCN [19] is a graph-based model which simplifies the framework of GCN for recommendation by removing feature transformation and nonlinear activation.
Multi-behavior Models: • LightGCN-M We extend LightGCN for multi-task optimization by integrating multi-behaviors during the modeling stage. behavior recommendation task enhanced with knowledge and temporal information. • KGAT [11] attention-based graph neural network that incorporates the item meta-data. Here, we extend and optimize it with multi-task learning. • GHCF [13] a SOTA model particularly for multibehavior collaborative filtering without sampling any negative items by optimizing a mean square error (MSE) loss. 5.3. Performance Comparison (RQ1) indicating that behavior-specific learning is more efective than cross-behavior learning for multibehavior recommendations. In the HMGN-intra model, all information propagates first in the isolated single-behavior graph and then gathers together. Considering the multi-task objectives, these would better help explain and contribute to each individual behavior prediction, leading to a superior performance. • most all the multi-behavior models exhibit better performance compared to single-behavior ones, this emphasizes the importance of multi-behavior utilization. 5.4. HBPR Multi-task Optimization (Q2)
mization framework from two perspectives:
GCN with its counterpart LightGCN-M, and base model (HMGN-intra optimized by HBPR) with its counterpart . − in Figure 4, we would see that the multitask optimization is crucial for multi-behavior recommender system. In other words, even if the end goal of the model is to predict one target behavior, learning to explicitly optimize auxiliary behaviors in model objective significantly improves the model metrics.
model with GHCF on the ability to predict other auxiliary behaviors. Figure 5 indicate our method consistently outperforms GHCF on all behaviors prediction in terms of metric. 5.5. Sub-graph Sampling (Q3) To test the scalability of our graph, we utilized the algorithms that are proposed in Section 4.1. We assign diferent sampling size and obtain the performance for each setting in Table 4. (Since the sub-graph size is dependent on the sampling size, we repeat this experiment 100 times to compute an average sub-graph size.) Note that for both the datasets, a sub-graph size of around 20 , can already get pretty good results compared to the full-size 5.6. Study of Graph Enhancement (Q4) In this section, we investigate how diferent graph enhancing gadgets afect our best performing HMGN-intra model. From Figure 6, we have two key takeaways: • In dataset (Figure 6(a)), HMGN-intra with temporal encoding performs worse than that without temporal information whereas in dataset (Figure 6(b)) HMGN-intra with temporal encoding included gets better performance than that without temporal encoding. We think this contradictory efect is caused by the duration of the data (Figure 6(c)). In , all data is collected within 9 days which all can be considered as ”recent” events. In this case, the fusion of temporal encoding would behave just like a noise injection that decreases the performance. In , a long period dataset, the data lasts 3.5 months, which would enable the temporal encoding to take efect. to exploit robust and powerful GNN. We reason such techniques as graph enrichment and augmentation. KGAT [11] integrates the KG and attention mechanism for single behavior recommendations systems where the objectives are consist of with both KG [26] and collaborative ifltering optimization. SGL [ 44] generates multiple views of graphs by node and edge drop and applies InfoNCE [45] onto that. SimGCL [46] 6.3. Resemblance and Discrepancy
In this paper, we devised two new graph attention-based frameworks called HMGN-intra and HMGN-inter for multi-behavior recommender systems. We discover that it is crucial for multi-behavior systems to learn via multitask objectives, aka, optimizing for all behaviors instead of target behaviors. To this end, we propose a hierarchical Bayesian Personalized Ranking optimization criterion.
ence generalization as well as behavior specialization and 6.2. Graph Enrichment and Augmentation to predict all types of behaviors. Further, we provide a With the ability to learn high-order topological informa- unified and comprehensive strategy for multi-behavior tion, Graph Neural Network (GNN) [38, 39] has achieved methods. Specifically, we enhance our model with mulsignificant success in Recommender System [ 19, 40, 41]. tiple techniques like temporal encoding and metadata Various techniques like optimizing Contrastive Learning information. To scale up the model, we also extend the (CL) [42], leveraging metadata or Knowledge Graph (KG) sub-graph sampling to the multi-behavior scenarios. Ex[11], incorporating temporal information [39], sampling tensive empirical analyses indicate our proposed model sub-graph [43] for scalability, are exhibiting advantages outperforms the baselines significantly. 963770.963776. doi:10.1145/963770.963776. ’22, Association for Computing Machinery, New [34] F. Xiao, L. Li, W. Xu, J. Zhao, X. Yang, J. Lang, York, NY, USA, 2022, p. 1273–1282. URL: https: H. Wang, Dmbgn: Deep multi-behavior graph //doi.org/10.1145/3477495.3532014. doi:10.1145/ networks for voucher redemption rate prediction, 3477495.3532014. in: Proceedings of the 27th ACM SIGKDD Confer- [42] C. Huang, X. Wang, X. He, D. Yin, Self-supervised ence on Knowledge Discovery & Data Mining, learning for recommender system, in: ProceedKDD ’21, Association for Computing Machinery, ings of the 45th International ACM SIGIR ConNew York, NY, USA, 2021, p. 3786–3794. URL: https: ference on Research and Development in Infor//doi.org/10.1145/3447548.3467191. doi:10.1145/ mation Retrieval, SIGIR ’22, Association for Com3447548.3467191. puting Machinery, New York, NY, USA, 2022, p. [35] C. Gao, X. He, D. Gan, X. Chen, F. Feng, 3440–3443. URL: https://doi.org/10.1145/3477495.
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