Data integration is a topic in modern data analysis gathering great interest in both theoretical background and practical applications. It combines diverse data from disparate sources into meaningful and valuable information. There is a line of works named JIVE(Joint and Inidividual Variation Explained) that focus on the case where diverse features are gathered from a common set of experiment subjects. In this presentation, we introduce the basic framework in which JIVE captures the joint aspects of multiple datasets and recognizes the individual structure inherent to each dataset. Then we suggest an insight of the geometrical groundwork for this method: the optimization formulation for JIVE established in view of the minimization problem of the sum of distances between subspaces which have different dimensions in the data space. Finally we review some methods of manifold optimization that have been proposed to solve the optimization problems over Stiefel and Grassmann manifolds and explain the adoption of Manifold ADMM(Alternating Directions Method of Multipliers) in line with the proximal gradient method for Riemannian manifolds.