Contributions

The main contributions of present research are the following:

1. Hyperscale Hybrid Architecture: It offers a progressive approach to compute Louvain community detection with SVD, making the change to local factorization of matrices. This solves the problem of data sparsity by forming more dense user clusters.
2. Strength of Interpretability: As opposed to black-box GNN models, the proposed approach can give transparent, communal explanations behind recommendations (e.g., peer-group influence).
3. Scalable Performance: It is shown that the user space partitioning limits the dimensionality load on SVD and competitive accuracy (RMSE 0.9966) is achieved with reduced computational overhead than deep learning baselines.

Organization of the paper

The remainder of this paper is organized as follows: Section 2 reviews related literature on the topics of collaborative filtering and community detection. Section 3 elaborates the methodology framework, mathematical equations, theoretical assumptions and complexity analysis. Section 4 describes the proposed hybrid architecture, hyperparameter finding and experimental configuration. Section 5 contains the findings of the experiment and a comparative discussion. Finally, section 6 concerns the conclusion of the research and gives the direction of the future research.

Related work

Recommendation systems development has weakened as a result of the integration of graph-based approaches, community detection applications, as well as the SVD method of matrix factorization. Detailed analysis has shown that the graph-based recommender systems are meaningful since they generate key information using graph representations to form powerful recommendations and enhance readability [1].

Graph-based recommenders have been regarded as transparent to research the effects of graph structures on trust in a recommendation, such as detecting communities and modeling nodes [12].Some of the publications suggest that the methodologies of graph learning can be used to address the issue of data sparsity and cold-start successfully. [4,13].

The division process that the community detection algorithms perform on the sets of users forms unique groups, which results in better individualized recommendation outputs. There are three most popular community detection algorithms: Louvain, Leiden, and Label Propagation helping extensive network applications [2,11]. The Louvain method has been one of the favorite strategies to create the best-quality community structures, and hence it is adopted in several practical cases of the real world contexts as well [9,14]. The last memory efficient advances have boosted the scalability of such algorithms in large scale database operations [15].

Recommender systems that appeal combine collaborative and content based methods and are being popular because they offer high accuracy and diversity on the system. Study of SVD in collaborative filtering has grown because the algorithm identifies concealed patterns in user-item data matrices. The study of SVD in collaborative filtering has been broadened since the algorithm detects hidden patterns in matrices of user-item data sets. Hybrid recommendation systems derive the advantages of two methods to address sparsity constraints and overfitting and enhance user-specific recommendations. SVD based systems predict user preference with a robust performance by incorporating bias terms, which execute user, and item based methods of behaving in their selection process of a product or service [6,7].

Graph neural networks (GNNs) form a core field of graph representations that combine the information of each node in a manner that allows training suggestions. [9,16,17]. The studies mainly explore the methods used to simulate the interaction of the users with various items. As an example, Multi-Behavior GNN (MB-GNN) is an improvement to representation learning by processing the various types of interaction, including clicks and purchases [10].

Concluding remarks on research gap

The gaps in literature, through which the effectiveness of the balance between the interpretability and sparsity management could be achieved, are identified. As SVD can help to scale and GNNs can help to improve accuracy, not many combined models can use the modularity of community detection to explicitly clean up the interaction matrix first before factorization. The proposed work aims at bridging this gap by proposing a sequential framework that would use community detection, not only to regularize the data, but also to pre-process the data in order to generate dense, homogenous sub-matrices where simpler factorization is possible.

Singular Value Decomposition (SVD)

Singular Value Decomposition (SVD) is a classical element of collaborative filtering, and it provides an excellent mathematical backbone to identify latent variables used to predict user-item interactions. The user-item interaction data is represented by a matrix, R. SVD solves the problem of sparsity by breaking down the matrix R into three components of the form of U, and V^T as below mathematical expression:

(1)

Here, U is an m × k matrix capturing latent features of users, is a k × k diagonal matrix including singular values, and V^T is a k × n matrix representing latent features of items.

The optimization process finds minimal squared differences between user ratings predictions and actual values. The optimization includes the following formula:

(2)

where symbolizes the collection of user-item interactions, r_u,i is the actual rating, and is the predicted rating computed as:

(3)

Louvain community-detection method

The core function of the Louvain algorithm involves user preference cluster discovery. The strength of network division is quantified through Modularity Q, defined as [14,15]:

(4)

where w_ij represents the weight of the edge between nodes i and j, k_i and k_j represent degrees, and is 1 if nodes are in the same community.

Singular Value Decomposition (SVD)

Singular Value Decomposition (SVD) is a classical element of collaborative filtering, and it provides an excellent mathematical backbone to identify latent variables used to predict user-item interactions. The data of interaction between the user and the item are represented in a form of a matrix, R. SVD resolves the sparsity issue by decomposing the matrix R into three terms, namely X, and , as follows in the mathematical expression:

(5)

Here, X is an m × p matrix capturing latent features of users, is a p × p diagonal matrix including singular values, and Y^T is a p × n matrix representing latent features of items.

The optimization process identifies small squared differences between the prediction of the user ratings and the actual ones. The optimization contains the following formula:

(6)

with the representation of the set of interactions between users and items in the form of the shortcut , and the real rating on the interaction between a user and item denoted by r_x,i, the predicted rating denoted by , and calculated as follows:

(7)

Louvain community-detection method

The core function of the Louvain algorithm involves user preference cluster discovery. The strength of network division is quantified through Modularity Q, defined as [14,15]:

(8)

where p_i and p_j denote degrees, w_ij is the weight of the edge between nodes i and j, and is 1 if nodes are in the same community.

Assumptions and theoretical constraints

The proposed hybrid system will be performed based on certain theoretical assumptions that SVD and Louvain algorithms should work with appropriately:

1. Low-Rank Assumption: It is assumed that the user-item interaction matrix is low-rank () user preferences can be well modeled by a few latent variables.
2. Homophily Assumption Homophily assumption: Louvain method is premised on the fact that the users within the same community are statistically important with regard to their taste preferences compared to the who were not a part of the community.
3. Identifiability with SVD: To achieve unique reconstruction of the rating matrix (up to permutation), one assumes that the singular values are distinct and that intra-community sub-matrices, while not fully dense, are sufficiently connected to ensure convergence during Stochastic Gradient Descent (SGD).

Computational complexity analysis

One of the main strengths of the suggested strategy is scalability. It is a complexity that comprises two parts:

• Louvain Algorithm:Community detector has time bound of , where N is the number of users. It is an amazing invention with sparse graphs.
• Local SVD: Standard global SVD has a complexity of , where p is latent dimensions, |R| is the number of ratings, and I is iterations. By partitioning users into C communities, C independent SVDs are performed on smaller matrices. While the total operations remain proportional, the convergence time is reduced because the sub-matrices are denser and more homogenous, requiring fewer iterations I to minimize error.

The proposed method is much lighter in terms of memory and floating-point operations as compared to GNN-based methods (e.g., NGCF) which scale at .

Hyperparameter tuning

To ensure optimal performance (Equations 4 and 5), a Grid Search strategy was employed for hyperparameter optimization.

• Learning Rate (): Values were explored in the range {0.001, 0.005, 0.01, 0.02}. It was observed that led to divergent loss, while resulted in slow convergence. The optimal value was identified as 0.005.
• Regularization (): Tests were conducted for . Values lower than 0.02 caused overfitting on the training communities, while reduced predictive accuracy by penalizing latent features too heavily. The value was selected for the reported results.

Comparative analysis and discussion

To assess the significance of the obtained RMSE (0.9966), a comparison was made against standard values reported in literature. The hybrid SVD-Louvain approach outperforms standard memory-based CF and performs competitively with basic matrix factorization baselines.

Fig 6 visualizes the performance gap. Although GNN-based methods achieve slightly lower RMSE (approx 0.92) [17], this difference arises because the proposed method prioritizes interpretability (clear community-based explanations) and computational efficiency (local factorization on denser sub-matrices) over marginal accuracy gains from black-box GNN architectures, which require substantially higher resources on sparse datasets like Netflix. Consequently, the proposed method (RMSE 0.9966) significantly outperforms isolated SVD (typically 1.05) [6] while retaining strong interpretability. This trade-off is quantified in Table 3.

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Table 3. Comparison of Proposed Hybrid Method vs. SVD and GNN Benchmarks.

https://doi.org/10.1371/journal.pone.0346579.t003

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Fig 6. RMSE Performance Comparison: Isolated SVD vs. GNN vs. Proposed Method.

https://doi.org/10.1371/journal.pone.0346579.g006

Discussion on diversity and personalization

Although the key measures are error-based (RMSE/MAE), implicitly, the hybrid architecture of the architecture increases the diversity of the recommendations. The localization of collaborative filtering to local communities eliminates the so-called popularity bias (popular globally crowd out unpopular items in the globally popular item list). In smaller, niche communities, like “Indie Horror Fans” users get recommendations tailored to the interests of their group, instead of generic blockbusters, which in itself enhances the catalog coverage and diversity of personalization than a global SVD model.