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A longstanding challenge in data science is to effectively quantify systems of interest by integrating information from heterogeneous datasets, a problem known as multiview learning. In this talk, I will present recent advancements in this direction, focusing on novel algorithms based on convolutions of diffusion maps or kernel embeddings. Within the common manifold framework, the proposed algorithm can be interpreted through its spectral connection to limiting Laplacian or integral operators. Additionally, we demonstrate that the method is robust against high-dimensional noise via the analysis of the underlying kennel random matrices. This talk is based on several joint works, primarily with Hau-Tieng Wu (NYU Courant).