  In recent years, the accumulation of data across various institutions has
garnered attention for the technology of confidential data analysis, which
improves analytical accuracy by sharing data between multiple institutions
while protecting sensitive information. Among these methods, Data Collaboration
Analysis (DCA) is noted for its efficiency in terms of computational cost and
communication load, facilitating data sharing and analysis across different
institutions while safeguarding confidential information. However, existing
optimization problems for determining the necessary collaborative functions
have faced challenges, such as the optimal solution for the collaborative
representation often being a zero matrix and the difficulty in understanding
the process of deriving solutions. This research addresses these issues by
formulating the optimization problem through the segmentation of matrices into
column vectors and proposing a solution method based on the generalized
eigenvalue problem. Additionally, we demonstrate methods for constructing
collaborative functions more effectively through weighting and the selection of
efficient algorithms suited to specific situations. Experiments using
real-world datasets have shown that our proposed formulation and solution for
the collaborative function optimization problem achieve superior predictive
accuracy compared to existing methods.
