Label distribution learning with structured manifold subspace

• We introduce a high-order correlation metric for label distribution that adaptively attenuates large error terms. This metric is inherently insensitive to outliers and noise, providing a more robust encoding of the correlations within real-valued label distributions. • We propose a maximum correlation entropy regularization that integrates label distribution learning (LDL) with label subspace clustering for mutual enhancement. This approach promotes a more compact and accurate output space. • We provide a theoretical proof that the learned correlation matrix satisfies the block-diagonal property under the assumption of independent subspaces. • Experiments conducted on commonly used benchmark datasets, and the results of multiple metrics demonstrate the effectiveness of our method. In recent years, label distribution learning (LDL) has been proposed to solve the label ambiguity problem. To alleviate the overwhelming output space of LDL, most of the existing methods explore label correlations at a global or local level through common low-rank assumptions. However, the real-valued label description degrees have more complex correlations, making the low-rank assumption usually not hold. To tackle this issue, the proposed method leverages the label distribution manifold with structured subspaces, aiming for a more compact and accurate output space while preserving the high rank of the label distribution matrix. Specifically, a robust high-order correlation measure for label distributions is defined. Then, we simultaneously infer model parameters and conduct the label subspace clustering through the maximum correlation entropy (MCE) regularization to achieve mutual enhancement. It is further proven that the resulting label correlation matrix exhibits a block-diagonal structure under the assumption of independent subspaces. Extensive experiments on widely used benchmark datasets demonstrate the clear advantages of our proposed algorithm over state-of-the-art LDL methods. The code is accessible at https://github.com/yan-yp/LDL-MCE .