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.

翻译：近年来，各机构间数据的积累使得机密数据分析技术备受关注，该技术通过在多机构间共享数据的同时保护敏感信息来提高分析精度。在这些方法中，数据协同分析（Data Collaboration Analysis, DCA）因其在计算成本和通信负载方面的效率而受到关注，它能够在保护机密信息的同时促进不同机构间的数据共享与分析。然而，现有用于确定必要协同函数的优化问题面临挑战，例如协同表示的最优解往往是零矩阵，以及推导解的过程难以理解。本研究通过将矩阵分割为列向量来构建优化问题，并提出了一种基于广义特征值问题的求解方法，从而解决了这些问题。此外，我们展示了通过加权和针对特定情境选择高效算法来更有效地构建协同函数的方法。使用真实数据集的实验表明，我们提出的协同函数优化问题的构建与求解方法在预测精度上优于现有方法。