A Hybrid Bundle Recommender System Using Modified FP-Growth and Compound Critiquing for E-Commerce

In recent years, e-commerce has become a primary channel for digital transactions. Despite continuous technological advances, significant limitations remain, particularly in delivering relevant and personalized shopping experiences [1]. One challenge stems from user behavior: customers often purchase multiple related products in a single transaction, yet most recommender systems are still limited to suggesting individual items and are not capable of identifying and recommending product bundles frequently bought together. Consequently, users are required to perform manual searches, which are time-consuming and may lead to the omission of relevant products [2-4].

Bundle recommenders address this issue by recommending a set of complementary items as a single package, improving search efficiency while supporting marketing strategies such as cross-selling and up-selling [3]. However, conventional bundle recommendation still has limitations: there is little personalization of the resulting bundles because they are often created manually without considering each user’s unique preferences [3]. Prior studies have attempted to tackle this through approaches such as collaborative bundle recommendation and personalized bundle generation [5].

However, this system still faces several unresolved challenges. First, the interaction problem is sparse: the number of user interactions with bundles is much lower than with individual products, making it difficult for systems to accurately learn user preferences [3, 6]. Second, there is the output space complexity problem: the number of possible item combinations in a bundle is extremely large, making it hard for the system to select an optimal bundle. Third, many bundle recommender systems are still static and cannot adapt to user- specific contexts and needs, which affects recommendation quality and relevance [7-10].

In addition to these technical limitations, most existing bundle recommendation systems are still static, as bundles are formed entirely based on historical transaction patterns. This condition gives rise to the problem of bundle monotony, namely, the tendency of the system to produce bundles with items that are too homogeneous, for example, coming from the same category or attribute. As a result, user exploration is limited, and the level of recommendation personalization decreases.

A conversational bundle recommender has been proposed to address these challenges [3], in which the system and user interact progressively through real-time feedback. One study adopting this approach is Bundle MCR (Multi-Round Conversational Recommendation) [3], which introduces a multi-turn interaction model between the user and the system. In this model, the system can choose to ask about user preferences or gradually recommend items in sequence [3]. The Bundle MCR framework is built on the Bundle BERT architecture and is trained using a two-stage strategy: cloze-style pre-training and reinforcement learning fine-tuning [3]. Although highly flexible and adaptive, this approach requires complex computing infrastructure and substantial resources. Compound Critiquing is one of the more adaptive innovations [11], which allows users to provide feedback on multiple attributes at once, speeding up the adjustment process and improving accuracy. For example, in the book domain, users can provide inputs such as “latest edition” or “different author” to filter recommendations based on content preferences and interaction history.

Nevertheless, the effectiveness of a recommender system still depends heavily on its ability to identify association patterns among products. A suitable approach for this is ARM, which is used to find items that frequently co-occur in users’ transaction histories. ARM has proven capable of capturing complex product relationships and is widely used in recommender systems. Common ARM algorithms include Apriori and FP-Growth [11]. Of the two, FP-Growth is known to be more efficient because it eliminates the need to generate all candidate itemsets explicitly. However, this algorithm still faces challenges in execution time and memory usage when applied to large-scale datasets [12]. The MFP-Growth algorithm was developed to overcome these limitations [12] by improving the FP-tree structure, optimizing the header table, and eliminating the need to repeatedly construct conditional subtrees, resulting in faster performance, lower memory consumption, and higher-quality association rules [12]. In addition to these technical limitations, most existing bundle recommendation systems are still static, as bundles are generated entirely based on historical transaction patterns. This creates the problem of bundle monotony, a system's tendency to generate bundles with items that are too homogeneous, such as those from the same category or attribute. As a result, user exploration is limited, and the level of recommendation personalization decreases.

This study proposes integrating MFP-Growth with Compound Critiquing to build a dynamic, efficient, and personalized bundle recommender system. MFP-Growth rapidly extracts product association patterns, while Compound Critiquing ensures the system adapts to user preferences. This combination is expected to improve recommendation relevance, accelerate search, broaden product exploration, and enhance user satisfaction on e-commerce platforms.

ARM is a core method in data mining aimed at discovering interesting relationships among items in large datasets, particularly transactional data. ARM focuses on identifying items that frequently co-occur and forming rules in the format $X \rightarrow Y$, where $X$ and $Y$ are subsets of the item universe and are disjoint $(X \cap Y=\varnothing)$ [12]. In this context, $X$ is called the antecedent, and Y is the consequent [12]. These associative rules are important for uncovering hidden patterns in data and have been widely applied across sectors such as retail, telecommunications, IoT systems, patient symptom analysis, and even transportation scheduling [12]. The two primary metrics used to evaluate such rules are:

• Support measures how often X and Y occur together in the data.

$ Support  (X \rightarrow Y)=\frac{X \cup Y}{D B}$        (1)

• Confidence reflects the strength of the rule, namely the probability of Y occurring when X occurs.

$Confidence (X \rightarrow Y)=\frac{\text { support } X \cup Y}{\text { support }(X)}$         (2)

An itemset is called frequent if its support exceeds a user- defined minimum threshold [13]. By first identifying frequent itemsets, the system then derives associative rules based on minimum support and confidence thresholds, eliminating any rules that do not meet these minima.

The proposed MFP-Growth algorithm is designed to reduce overall execution time and memory usage [16]. In conventional FP-Growth, the search proceeds by traversing the header table in descending order of item frequency, followed by scanning the current FP-tree to obtain the conditional pattern base for each item [17]. The system then repeatedly reconstructs conditional FP-trees without fully optimizing pruning strategies. Typically, pattern growth proceeds through a sequence of suffix patterns derived from frequently occurring itemsets. Figure 1 illustrates the recursive mining process in FP-Growth [12]. This recursive construction of FP-trees has been shown to require more time and memory [18]. A new structure is therefore needed to avoid these costly operations and improve processing efficiency.

Figure 1. Flowchart

The proposed MFP-tree structure is a prefix tree with an organized node layout and an address table for frequent items that consists of three parts: the first is a node list for each frequent item, while the other two store item information and the total frequency count for each node in the list. In addition, this structure preserves data relationships across itemsets.

5.1 System design

This study presents a system workflow that describes the overall operation of the proposed system. Figure 1 shows the workflow of the bundle recommender system.

Bundle recommendations are generated from users’ explicit preferences by leveraging the MFP-Growth algorithm and the Compound Critiquing technique. The process begins with collecting user transaction data and book metadata, such as ISBN, genre, publication year, price, author, and publisher. Next, MFP-Growth is used to extract association rules among items by considering metrics such as support, confidence, lift, and metadata similarity scores, producing a set of candidate bundles. The system then computes metadata similarity scores for the candidate bundles. These similarity scores serve as the basis for forming the Top N bundle recommendations.

When users receive the initial recommendations, they can provide feedback through Compound Critiquing. Users may submit more specific preferences (in the form of compound critiques), such as wanting cheaper bundles, newer editions, different authors, or specific genres. The system’s next task is to interpret these critiques, update the scores and composition of the bundles, and re-filter results based on the critiqued metadata dimensions. This makes the recommendations more dynamic and personalized. New recommendations are then generated and shown again, taking all user critiques into account. This process can be repeated iteratively until the system finds bundles that best match user needs. Finally, the system stores the interaction outcomes as preference references for future recommendation sessions. With this workflow, the system is not only reactive to purchase history but also proactive in understanding and adapting to users’ explicit preferences.

5.2 Data description

This study uses a dataset of book purchase transactions from the Amazon e-commerce platform. The dataset was chosen because it captures real user consumption patterns in selecting and buying books and enables analysis of bundle-based purchasing behavior. It serves as the basis for mining association rules, developing the recommendation model, and evaluating the system’s effectiveness.

Dataset characteristics:

• Total Transactions: 94,004 user transaction sessions

• Number of Unique Books: 101 titles

• Average Items per Transaction: 1.98

• Metadata: title, author, publisher, publication year, genre, and price

The book transaction dataset used has an average number of items per transaction of 1.98, which reflects realistic purchasing behaviours in the book domain. Even though the number of items per transaction is relatively small, joint purchasing patterns can still be identified through the accumulation of large numbers of transactions, so the Association Rule Mining-based approach remains relevant.

In addition to transaction data, the dataset includes metadata for each book. This metadata not only adds context to the modelling process, but it is also essential for Compound Critiquing. For example, attributes such as genre and price are used when users provide specific preferences like “prefer a different genre” or “prefer a lower price.” By combining transaction data with metadata, the system can apply rule- based processing while also considering content similarity, so the resulting bundle recommendations are statistically relevant and aligned with individual user preferences.

5.3 Modified FP-Growth algorithm

The implementation of the MFP-Growth algorithm follows a system design workflow that explains how the algorithm is applied in this study. Figure 2 shows the implementation process of the MFP-Growth algorithm.

The implementation of the MFP-Growth algorithm begins by converting the binary-encoded DataFrame into a list of transactions and applying a minimum support (min_support) threshold for each item, which is the minimum frequency an item must reach to be considered relevant. The system then checks whether the support count of each item meets the min_support value. Items that do not meet the threshold are discarded, while those that do are prioritized according to a chosen order, for example, by highest frequency. Next, an MFP-tree structure is constructed. This is a modified version of the FP-tree that stores transaction data compactly while preserving associations among items. MFP-Growth then extracts purchasing patterns using a bottom-up approach, starting from more specific patterns and moving toward more general ones. In the following stage, the system builds a header table that lists items along with node-link pointers to their corresponding nodes in the MFP-tree, enabling traversal without rebuilding conditional FP-trees. This process yields frequent patterns that can be used as the basis for generating product bundle recommendations.

Figure 2. Process Modified FP-Growth algorithm

The implementation of the MFP-Growth algorithm for generating bundle recommendations begins by converting the list of transactions into a DataFrame (df) and computing the number of transactions (total_rows). In line 2, the algorithm converts the minimum support ratio (for example, 0.01) into an absolute minimum transaction count. Next, items are filtered using the criterion support ≥ min_support. Line 6 starts the iteration over each frequent item as the initial prefix (a 1-itemset). For each item, the system retrieves its occurrence count and appends the itemset together with its support ratio to the results list. In line 9, the system builds a projected database that retains only items whose support meets the minimum; within each projected transaction, only the portion after the prefix is kept, and any subsequent duplicate occurrences are ignored to reduce the search space when extending itemsets. The system then performs recursive mining to discover longer itemsets. Finally, it returns the resulting set of itemsets, typically as a table of itemsets with their support values.

In this study, FP-Growth was used as a comparative baseline. FP-Growth was chosen because MFP-Growth is a direct extension of the FP-Growth algorithm, allowing for a fair evaluation of the improvements in efficiency and quality of the proposed association rules.

Other approaches, such as deep learning-based methods, were not used as baselines because they require significantly different data structures, learning models, and computational resources. Furthermore, the primary focus of this study was improving the efficiency and adaptability of the Association Rule Mining-based bundle recommendation system, as well as ease of interpretation of the results, which are not the primary focus of deep learning approaches. Therefore, using FP- Growth as a baseline was deemed appropriate for evaluating the methodological contributions of MFP-Growth in an objective and controlled manner.

5.4 Generating bundle recommendation

This section outlines the workflow used to construct bundle recommendations. Figure 3 shows the bundle construction workflow.

The Generate Bundle Recommender stage is performed after MFP-Growth produces association rules among book items, yielding a set of candidate bundles. Each candidate bundle is then assigned a metadata score based on similarity across attributes such as genre, publication year, author, publisher, and price, ensuring that recommendations are not only statistically relevant but also context aware. The resulting similarity scores are ranked using a combined score that merges association strength with the metadata score, producing the Initial Bundle Recommender as the Top N bundles. This initial set then serves as the basis for the Compound Critiquing stage, where users can provide feedback to iteratively refine the recommendations for greater personalization.

Figure 3. Generating bundle recommender

5.5 Compound Critiquing

The developed bundle recommender integrates Compound Critiquing to enable two-way interaction between users and the system. After the initial recommendations are generated using the MFP-Growth algorithm, users can provide explicit feedback on various aspects of a bundle, such as price, publication year, author, publisher, or genre. This mechanism is iterative: each round of feedback filters out irrelevant items, adjusts the recommendations while preserving valid association rules, and produces new alternatives until the user’s preferences are satisfied.

The critiquing criteria include:

1. Price, with the cheaper and same price rules, using a ±20% tolerance margin to ensure fair comparisons.

2. Author, with options to retain or switch the author.

3. Publication Year, using weighted median, sigmoid scaling, and variance-based penalties to ensure temporal fit.

4. Publisher, to maintain or broaden publisher variety.

5. Genre, with a 40% overlap threshold to distinguish exploration from continuity.

In this study, 11 critiquing types are available, each reflecting a user preference over a specific attribute:

1. "cheaper" – Want an item at a lower price

2. "same_price" – Want an item at the same price

3. "latest" – Want an item with a more recent publication year

4. "older" – Want an older or classic item

5. "same_genre" – Want an item in the same genre

6. "same_author" – Want an item by the same author

7. "same_publisher" – Want an item by the same publisher

8. "same_year" – Want an item with the same publication year

9. "another_author" – Want a different author

10. "another_publisher" – Want a different publisher

11. "another_genre" – Want a different genre