Modeling Personalized Item Frequency Information for Next-basket Recommendation

1 INTRODUCTION

• NBR recommends items from a user's sequence of purchased baskets [45][44][46], unlike top-n recommendation and item-sequence recommendation.Flattening baskets into item sequences introduces an order among items within a basket that does not exist [p04].Source: §1 · p. 1
• Existing RNNs are a mainstream choice for sequential modeling, but cannot directly capture item-frequency information in recommendation.Modeling the relation between historical records and the recommended items is a central NBR challenge.Source: §1 · p. 1
• PIF contains more than repeated-purchase patterns: similar users may also purchase an item that the target user repeatedly buys.The paper reports that existing methods do not fully use this collaborative purchase information.Source: §1 · pp. 1–2
• The paper proposes a kNN method that directly captures both PIF patterns, considers temporal dynamics, analyzes RNNs' difficulty learning vector addition, and evaluates on four real-world datasets.These are among the paper's stated contributions.Source: §1 · p. 2

2.1 Problem Definition

• Next-basket recommendation predicts a fixed-size set of items from a user's sequence of historical baskets.Each basket is represented as a 0/1 item vector.Source: §2.1 · p. 2

2.2 Relation between PIF and Target Basket

• Collaborative purchase patterns retrieve more than half of target-basket items across four datasets, exceeding 0.8 in three, while repeated-purchase importance varies by dataset.The analysis uses 300 nearest neighbors; the authors expect RecallN to increase with more neighbors.Source: §2.2 · p. 2, Table 1 · p. 2
• Combining repeated and collaborative purchase patterns leaves only a small part of target-basket items uncovered, indicating potential for PIF in NBR.The collaborative pattern also provides signal beyond the overlap with repeated purchases.Source: §2.2 · p. 3

2.3 Existing NBR Methods

• Markov-chain methods model transitions from recent baskets, whereas RNN-based methods aggregate representations across the full history to model longer-term dependencies.Some methods use attention to select relevant items or baskets.Source: §2.3 · p. 3

2.4 Difficulty in Learning Item Frequency

• Markov-chain methods miss high-order PIF, while RNNs would need to aggregate basket vectors like vector addition for their hidden state to capture it.The section investigates whether existing methods can learn the sum of a user's basket vectors.Source: §2.4 · p. 3

2.4.1 Difficulty in Learning Vector Addition.

• Training loss converged to 4, above the zero-vector baseline's 1.6 average MSE, and remained similar after removing embeddings, changing optimizers, or doubling data.The synthetic test used 2,500 sequences of ten one-hot vectors, with two repeated items placed at the end; the RNN module followed the existing NBR aggregation structure.Source: §2.4.1 · pp. 3–4

2.4.2 Closed-form Solution for Vector Addition with RNN.

• A closed-form solution shows vanilla RNNs can represent vector addition, yet nonlinear-free training still converged around 4, suggesting optimization misses the global minimum.The authors conclude that RNN-based methods fail to capture PIF in their setting.Source: §2.4.2 · pp. 4–5
• Initializing with the closed-form solution may overcome this optimization difficulty, but its correlated weights may make learning temporal dynamics harder.The authors therefore argue that PIF should be captured carefully because RNNs have difficulty learning it.Source: §2.4.3 · p. 5

3 PROPOSED METHOD

• TIFUKNN directly uses the two patterns associated with personalized item frequency and considers temporal dynamics when selecting items.The authors propose this as a direct neighbor-based alternative to model-based methods, which they leave for future work.Source: §3 · p. 5

3.1 Integrating Temporal Dynamics

• Because item frequency cannot distinguish items with equal counts, TIFUKNN assigns smaller weights to earlier repeated purchases.The authors report that short gaps dominate, while gap distributions vary across datasets.Source: §3.1 · p. 5

3.2 Nearest Neighbors based Method

• For similarity search, historical baskets are aggregated into user vectors using hierarchical decay within and across groups, giving more weight to recent records.The method uses Euclidean distance to find the k nearest neighbors; other similarity functions are left for future work.Source: §3.2 · p. 5
• Prediction blends the target user's representation, associated with repeated purchases, and the average neighbor representation, associated with collaborative purchases; the top s entries are recommended.A hyperparameter α balances the two components.Source: §3.2 · pp. 5–6

Next-basket recommendation

• NBR predicts item sets from sequences of past baskets, unlike traditional collaborative recommendation and sequential recommendation, which use item sets and item sequences, respectively.Source: §4 · p. 6
• The related-work review identifies a lack of kNN-based NBR methods, which this paper's proposed method addresses.Source: §4 · p. 6

Difficulty in Training RNNs

• The paper presents difficulty learning vector addition as a distinct RNN training phenomenon and calls for further theoretical analysis.Source: §4 · p. 6

• The experiments ask whether the proposed methods outperform state-of-the-art NBR methods.Source: §5 · p. 6
• The study evaluates temporal dynamics and the contribution of each TIFU-KNN component to target-basket prediction.Source: §5 · p. 6
• The experiments examine how hyperparameters affect performance and whether each TIFU-KNN factor brings benefits.Source: §5 · p. 6

5.1.1 Data sets.

• The experiments use Dunnhumby, ValuedShopper, Instacart, and TaFeng transaction data, with preprocessing that removes customers with fewer than three baskets.Dunnhumby uses a 50k-user sample; Instacart and TaFeng retain items accounting for more than 95% of purchases.Source: §5.1.1 · pp. 6–7

5.1.2 Evaluation Protocol.

• Recall and NDCG evaluate predicted next baskets, with NDCG computed on the top-s sorted item list.The data are partitioned across users into five folds, with four for training and one for testing; 10% of training users are reserved for validation.Source: §5.1.2 · p. 7

5.1.3 Compared Methods.

• Baselines include global and personalized top-frequency methods, userKNN, RepeatNet, FPMC, DREAM, SHAN, and Sets2Sets.The compared methods represent frequency-based, collaborative-filtering, sequential, and NBR approaches.Source: §5.1.3 · p. 7
• The methods' hyperparameters are tuned by grid search, and the proposed method's search covers neighbor count, time-decay ratios, fusion weight, and group count.The search ranges vary by parameter and, for group count, by dataset.Source: §5.1.3 · p. 7, §5.1.4 · p. 7, Table 3 · p. 7

5.2 Performance Comparison (RQ1)

• TIFU-KNN outperforms other methods on ValuedShopper, Instacart, and TaFeng; on Dunnhumby, it has slightly better recall while Sets2Sets has better NDCG.The authors attribute the Dunnhumby exception to more unseen patterns in that dataset.Source: Table 4 · p. 8, §5.2 · p. 8
• Top-n frequency has reasonable recall but is nearly worst overall, indicating that shared popular items do not capture users' distinct items.Source: §5.2 · p. 8
• Personalized top-n frequency is competitive across datasets, supporting the importance of target users' repeated-purchase patterns in prediction.Source: §5.2 · p. 8
• Personalized top-n frequency surpasses existing NBR methods other than Sets2Sets by a large margin on ValuedShopper, Instacart, and Dunnhumby.It also outperforms Sets2Sets on ValuedShopper and Instacart; the authors suggest Sets2Sets' learned coefficients do not perfectly balance its PIF and RNN components.Source: §5.2 · p. 8
• UserKNN and RepeatNet perform worse than Sets2Sets; RepeatNet can outperform methods without repeat modeling when repeats matter, except on TaFeng.The authors note that RepeatNet also introduces a non-existing order among items within each basket.Source: §5.2 · p. 8

5.3 Effectiveness of Temporal Dynamics (RQ2)

• RecallP∩N measures the amount of unseen patterns using items shared by the repeated-purchase and collaborative-purchase components.The weights rb and rд are set to the same ratio for this analysis.Source: §5.3 · p. 8
• With ratio = 1, the method usually has the largest number of unseen patterns, while temporal dynamics help reduce them by finding better neighbors.The analysis uses RecallP∩N, based on items appearing in both the repeated-purchase and collaborative-purchase components, to quantify unseen patterns.Source: §5.3 · pp. 8–9
• The analysis represents the absence of temporal dynamics with ratio = 1.Source: §5.3 · p. 9

5.4 Effectiveness of Different Components (RQ3)

• The target user’s repeated-purchase pattern dominates the prediction.Source: §5.4 · p. 9
• The collaborative-purchase pattern provides discriminative information that further improves prediction.Source: §5.4 · p. 9
• The full TIFU-KNN combination achieves the best performance, supporting the use of the target user’s and most similar users’ personalized item frequencies together.Source: Table 5 · p. 9, §5.4 · p. 9

5.5 Sensitivity of the Hyperparameters (RQ4)

• Both time-decayed weights rb and rд should be below 1 for best performance, supporting the two-level decay design over a single decay weight.Source: §5.5 · p. 9
• Parameters selected on the validation set are close to the test-set optimal configuration.Source: §5.5 · p. 9
• All hyperparameters require suitable values to achieve the best performance.The reported recall is on the Instacart test set with predicted basket size s = 20.Source: §5.5 · p. 9

6 CONCLUSION

• The proposed kNN method generally outperforms state-of-the-art deep-learning methods, with the paper linking this advantage to RNN difficulty in approximating vector addition.Source: §6 · p. 9
• The authors call for more theoretical analysis of RNNs’ vector-addition difficulty and an optimizer with a theoretical guarantee of finding the global optimum.They distinguish this difficulty from vanishing and exploding gradient problems.Source: §6 · p. 9
• Future work could test whether other commonly used functions challenge deep models and investigate additional PIF or item-frequency patterns, including global, local, and inverse item frequency.Source: §6 · p. 9