This paper introduces a novel Functional Graph Convolutional Network (funGCN) framework that combines Functional Data Analysis and Graph Convolutional Networks to address the complexities of multi-task and multi-modal learning in digital health and longitudinal studies. With the growing importance of health solutions to improve health care and social support, ensure healthy lives, and promote well-being at all ages, funGCN offers a unified approach to handle multivariate longitudinal data for multiple entities and ensures interpretability even with small sample sizes. Key innovations include task-specific embedding components that manage different data types, the ability to perform classification, regression, and forecasting, and the creation of a knowledge graph for insightful data interpretation. The efficacy of funGCN is validated through simulation experiments and a real-data application.

翻译：本文提出了一种新颖的功能图卷积网络（funGCN）框架，该框架融合功能数据分析与图卷积网络，以应对数字健康与纵向研究中多任务和多模态学习的复杂性。随着健康解决方案在改善医疗保健与社会支持、确保健康生活以及促进各年龄段福祉方面的重要性日益提升，funGCN提供了一种统一方法来处理多实体的多变量纵向数据，并确保在小样本量下仍具有可解释性。其关键创新包括：管理不同数据类型的任务特定嵌入组件、支持分类、回归与预测的能力，以及构建用于深度解释数据的知识图谱。通过仿真实验与真实数据应用验证了funGCN的有效性。