Multi-omic data integration analyzes a vast amount of biological data and contributes to understanding the biological processes underlying organisms. Multiple machine learning techniques have been proposed to solve this task, including extensions of the joint Non-negative Matrix Factorization (jNMF) method, such as the Multi-project and Multi-profile jNMF (M&M-jNMF). This method jointly factorizes input matrices from two projects into low-rank matrices which have clustering properties. However, the M&M-jNMF method does not capture the non-linear patterns of the data. This paper proposes an extension of the M&M-jNMF approach using projections into high-dimensional spaces through kernel functions; therefore, we propose the M&M-KjNMF method. We compared the standard M&M-jNMF and M&M-KjNMF methods using three different omic profiles of the lung adenocarcinoma data. As M&M-jNMF, we used data from experimental and observational data source. We evaluated the performance of both methods by comparing the cophenetic coefficient, AUC, and biological score. We found that M&M-KjNMF outperforms M&M-jNMF. The new proposed method enables the identification of molecule co-modules enriched in pathways tightly related to lung cancer emergence and progression.