The previous recommendation system applied the matrix factorization collaborative filtering (MFCF) technique to only single domains. Due to data sparsity, this approach has a limitation in overcoming the cold-start problem. Thus, in this study, we focus on discovering latent features from domains to understand the relationships between domains (called domain coherence). This approach uses potential knowledge of the source domain to improve the quality of the target domain recommendation. In this paper, we consider applying MFCF to multiple domains. Mainly, by adopting the implicit stochastic gradient descent algorithm to optimize the objective function for prediction, multiple matrices from different domains are consolidated inside the cross-domain recommendation system (CDRS). Additionally, we design a conceptual framework for CDRS, which applies to different industrial scenarios for recommenders across domains. Moreover, an experiment is devised to validate the proposed method. By using a real-world dataset gathered from Amazon Food and MovieLens, experimental results show that the proposed method improves 15.2% and 19.7% in terms of computation time and MSE over other methods on a utility matrix. Notably, a much lower convergence value of the loss function has been obtained from the experiment. Furthermore, a critical analysis of the obtained results shows that there is a dynamic balance between prediction accuracy and computational complexity.
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