Orthogonal and spherical quaternion features for weakly supervised learning with label confidence optimization

Weakly supervised learning (WSL) addresses the challenge of incomplete or noisy labels, but current methods often fail to capture the complexities introduced by weak labels in feature extraction, revealing the limitations of neural networks in modeling the intricate relationships between features and labels. To address these issues, we introduce the Orthogonal and Spherical Quaternion Neural Network (OSQNN), which utilizes quaternion feature embedding with an orthogonal constraint to map real-valued features into quaternion space. This approach improves the understanding of feature-label relationships by overcoming the challenge of embedding real-world data into quaternion spaces. OSQNN maps quaternion features onto a sphere and estimates label reliability through nearest neighbors, maintaining a coherent geometric structure in feature distributions. Furthermore, quaternion convolutions are transformed into parallel grouped real-valued convolutions, enhancing processing efficiency without sacrificing the benefits of quaternion-based computations. Additionally, we propose the Label Confidence Guided Expectation-Maximization (LCGEM) algorithm, integrated into OSQNN, to more effectively capture the complex relationships between weak labels and feature distributions. Experimental results across eight datasets demonstrate the superiority of OSQNN. For instance, in SSL on CIFAR10 (20% labeled data) and CIFAR100, it achieved 91.06% and 69.16% accuracy respectively; in NSL with 40% incorrect labels on CIFAR10 and CIFAR100, the accuracies were 80.84% and 51.98%, showing its high accuracy and robustness. The ablation study highlights the role of the orthogonal constraint and spherical feature mapping in improving performance, while t-SNE visualization confirms the ability of OSQNN to learn discriminative feature representations.