In recent years, multi-view multi-label learning (MVML) has attracted extensive attention due to its close alignment to real-world scenarios. Information-theoretic methods have gained prominence for learning nonlinear correlations. However, two key challenges persist: first, features in real-world data commonly exhibit high-order structural correlations, but existing information-theoretic methods struggle to learn such correlations; second, commonly relying on heuristic optimization, information-theoretic methods are prone to converging to local optima. To address these two challenges, we propose a novel method called Structural Entropy Guided High-Order Correlation Learning for Multi-View Multi-Label Feature Selection (SEHFS). The core idea of SEHFS is to convert the feature graph into a structural-entropy-minimizing encoding tree, quantifying the information cost of high-order dependencies and thus learning high-order feature correlations beyond pairwise correlations. Specifically, features exhibiting strong high-order redundancy are grouped into a single cluster within the encoding tree, while inter-cluster feaeture correlations are minimized, thereby eliminating redundancy both within and across clusters. Furthermore, a new framework based on the fusion of information theory and matrix methods is adopted, which learns a shared semantic matrix and view-specific contribution matrices to reconstruct a global view matrix, thereby enhancing the information-theoretic method and balancing the global and local optimization. The ability of structural entropy to learn high-order correlations is theoretically established, and and both experiments on eight datasets from various domains and ablation studies demonstrate that SEHFS achieves superior performance in feature selection.

翻译：近年来，多视图多标签学习因其与现实场景的紧密契合而受到广泛关注。信息论方法在学习非线性相关性方面已占据重要地位。然而，两个关键挑战依然存在：首先，现实世界数据中的特征通常表现出高阶结构相关性，但现有信息论方法难以学习此类相关性；其次，信息论方法通常依赖启发式优化，容易收敛至局部最优解。为应对这两个挑战，我们提出了一种名为“面向多视图多标签特征选择的结构熵引导高阶相关性学习”的新方法。SEHFS的核心思想是将特征图转化为结构熵最小化的编码树，从而量化高阶依赖的信息代价，进而学习超越成对相关性的高阶特征相关性。具体而言，表现出强高阶冗余性的特征在编码树中被分组至单个簇内，同时最小化簇间特征相关性，从而消除簇内及簇间的冗余。此外，采用了一种基于信息论与矩阵方法融合的新框架，通过学习共享语义矩阵和视图特定贡献矩阵来重构全局视图矩阵，从而增强信息论方法并平衡全局与局部优化。结构熵学习高阶相关性的能力在理论上得以确立，并且在来自不同领域的八个数据集上的实验及消融研究均表明，SEHFS在特征选择中实现了优越的性能。