Leveraging Feature Alignment in Grassmannian Manifold for Multi-Output Regression Tasks

Despite notable progress in domain adaptation for classification, regression-based domain adaptation remains challenging, particularly in terms of handling complex data structures, ensuring cross-domain generalization, and maintaining the precision and mathematical rigor required to validate model effectiveness. Unlike classification tasks, which are more resilient to variations in feature scaling, regression tasks are notably more sensitive, making their performance more vulnerable in domain adaptation scenarios. In this paper, we propose a generalized regularization technique grounded in the Grassmannian manifold to address the feature alignment problem. This approach leverages the underlying manifold structure of the data while preserving mathematical bounds, thereby enhancing the precision and efficiency of problem-solving. To demonstrate the effectiveness of the proposed algorithm, we apply it to estimate multi-output parameters in two distinct domains: 1) the Arabidopsis thaliana plant dataset, collected from a high-throughput phenotyping platform at Palacký University, and 2) the publicly available dSprites shape recognition with six adaptation tasks. These tasks are critical to advance agricultural research and address generalization challenges in multi-output regression. Accurate predictions provide deeper insights into plant growth and health, thereby supporting more effective crop management strategies. We evaluate the effectiveness of our framework by comparing it with state-of-the-art regression alignment techniques that are independent of the underlying backbone and adaptable to transfer learning tasks. Experimental results show that our framework consistently outperforms existing methods,results description. The source code will be made publicly available upon acceptance at https://github.com/lingping-fuzzy.