Semi-supervised label distribution learning via global factorization and local constrain

In label distribution learning, properly handling samples with missing label distributions is a particularly challenging task. When dealing with unlabeled samples, leveraging correlation is especially crucial as it reveals the intrinsic patterns of data distribution and effectively reduces the model’s hypothesis space. Currently, semi-supervised label distribution learning follows the same correlation mining methods as those used under complete supervision. However, due to the lack of supervision information for some samples, these methods designed for complete supervision are insufficient in a semi-supervised context. On one hand, the absence of labels for some samples makes it difficult to mine label correlations; on the other hand, label correlations mined solely based on samples are biased, leading to imprecise label correlations due to the missing labels. To address these issues, this paper innovatively proposes two strategies for mining label correlations in semi-supervised label distribution learning: first, exploring the common correlations between known and unknown label distributions; second, using the information of known label distributions to reveal the correlations of unknown label distributions. Specifically, globally, we employ independent component analysis for matrix completion of missing sample labels, and locally, we improve the $k$-NN framework to utilize the label constraints of known label distributions to restrict the label distribution values of unknown label distributions. Based on these mined correlations, we designed a semi-supervised label distribution learning algorithm. The algorithm outperforms existing methods in 67.27 % of cases, achieving outstanding performance, and demonstrates significant statistical significance in two-sample $t$-tests.