We introduce an innovative and mathematically rigorous definition for computing common information from multi-view data, drawing inspiration from G\'acs-K\"orner common information in information theory. Leveraging this definition, we develop a novel supervised multi-view learning framework to capture both common and unique information. By explicitly minimizing a total correlation term, the extracted common information and the unique information from each view are forced to be independent of each other, which, in turn, theoretically guarantees the effectiveness of our framework. To estimate information-theoretic quantities, our framework employs matrix-based R{\'e}nyi's $\alpha$-order entropy functional, which forgoes the need for variational approximation and distributional estimation in high-dimensional space. Theoretical proof is provided that our framework can faithfully discover both common and unique information from multi-view data. Experiments on synthetic and seven benchmark real-world datasets demonstrate the superior performance of our proposed framework over state-of-the-art approaches.

翻译：受信息论中Gács-Körner共同信息的启发，我们提出了一种创新且数学严谨的定义，用于计算多视图数据中的共同信息。基于该定义，我们开发了一种新颖的监督式多视图学习框架，以同时捕获共同信息与各视图的独特信息。通过显式最小化总相关项，所提取的共同信息与各视图的独特信息被强制要求相互独立，这从理论上保证了我们框架的有效性。为估计信息论度量，本框架采用基于矩阵的Rényi α阶熵泛函，无需在高维空间中进行变分近似或分布估计。理论证明表明，我们的框架能够准确发现多视图数据中的共同信息与独特信息。在合成数据集及七个真实世界基准数据集上的实验表明，所提出的框架性能优于当前最先进的方法。