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Functional Graph Convolutional Networks: A unified multi-task and multi-modal learning framework to facilitate health and social-care insights

Tobia Boschi, Francesca Bonin, Rodrigo Ordonez-Hurtado, Cécile Rousseau, Alessandra Pascale, John Dinsmore

Abstract

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.

Functional Graph Convolutional Networks: A unified multi-task and multi-modal learning framework to facilitate health and social-care insights

Abstract

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.
Paper Structure (25 sections, 5 equations, 4 figures, 5 tables, 1 algorithm)

This paper contains 25 sections, 5 equations, 4 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work.
  3. Methodology
  4. Assumptions on longitudinal features.
  5. Embedding modules
  6. Longitudinal features.
  7. Categorical features.
  8. Scalar features.
  9. Selection of $\mathbf{k_{graph}}$ and $\mathbf{k_{gcn}}$.
  10. Knowledge Graph estimation
  11. Graph Convolutional Network
  12. Input.
  13. Training.
  14. Mapping back to original features.
  15. Simulation experiments
  16. ...and 10 more sections

Figures (4)

  • Figure 1: funGCN architecture. Embedding modules are discussed in Subsection \ref{['subsec:embeddings']}, the knowledge graph estimation in Subsection \ref{['subsec:kg_estimation']}, and the GCN module in Subsection \ref{['subsec:gcn']}.
  • Figure 2: Simulation results. For each investigated scenario $(p=20, 50, 100, 500)$, dots represent the average over 80 replications (20 for each target), and the width of the interval indicates the standard deviation. The $y$-$axis$ for regression and forecast are inverted: higher values correspond to better performance in all the panels.
  • Figure 3: SHARE results. Boxplots generated from the distribution obtained from a total of 260 replications for regression and forecasting tasks, and 80 replications for classification -- encompassing 20 replications for each target. The dots and the lines indicate the means and medians of the distributions, respectively. The $y$-$axis$ for regression and forecast are inverted: higher values correspond to better performance in all the panels.
  • Figure 4: SHARE knowledge graph. Graph constructed considering all the $1,518$ subjects with $k_{graph} = 3$ and pruning parameter $\theta =0.5$. Each node represents a feature, while different colors refer to different modalities. The nodes' diameter and edges' width are proportional to the connections’ number and strength, respectively.