<p>In recent years, recommender systems have become vital for personalizing user experiences across various online platforms. Collaborative filtering is one of the most effective techniques for generating personalized recommendations. However, it needs to handle data sparsity and cold-start problems. Cross-domain recommender systems have emerged to alleviate these issues, leveraging transfer learning to exploit knowledge from related domains. Despite several attempts, effective knowledge transfer remains a challenging and open problem in recommender systems. This paper investigates non-negative matrix factorization techniques, specifically standard non-negative matrix factorization, orthogonal non-negative matrix factorization, non-smooth non-negative matrix factorization, and deep non-negative matrix factorization integrated with transfer learning within a cross-domain recommender systems framework. Our approach involves leveraging data from source domains to enhance recommendations in target domains, thereby addressing the data sparsity problem. We employ these non-negative matrix factorization techniques to capture latent factors across domains, facilitating better knowledge transfer and recommendation accuracy. We conduct extensive experiments on cross-domain datasets to validate our proposed methods. The results demonstrate that non-smooth non-negative matrix factorization significantly outperforms other methods with transfer learning in terms of accuracy metrics such as RMSE and MAE. These findings underscore the effectiveness of non-smooth non-negative matrix factorization in cross-domain recommender systems and its potential to improve user experience by delivering more precise suggestions for items.</p>