# Functional-Edged Network Modeling

arXiv: https://arxiv.org/abs/2404.00218 · HTML: https://mlsanity.com/paper/2404.00218/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 30 Mar 2024.

## Builds on (most cited first, 17 of 17)

- [Representation Learning for Dynamic Graphs: A Survey](https://mlsanity.com/paper/1905.11485/) (2019)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [Bayesian Temporal Factorization for Multidimensional Time Series Prediction](https://mlsanity.com/paper/1910.06366/) (2019)
- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Statistical clustering of temporal networks through a dynamic stochastic block model](https://mlsanity.com/paper/1506.07464/) (2015)
- [Multilinear tensor regression for longitudinal relational data](https://mlsanity.com/paper/1412.0048/) (2014)
- [Guaranteed Functional Tensor Singular Value Decomposition](https://mlsanity.com/paper/2108.04201/) (2021)
- [Spectral embedding of weighted graphs](https://mlsanity.com/paper/1910.05534/) (2019)
- [Bayesian Graphical Models for Multivariate Functional Data](https://mlsanity.com/paper/1411.4158/) (2014)
- [Temporal Graph Signal Decomposition](https://mlsanity.com/paper/2106.13517/) (2021)
- [Nonparametric and high-dimensional functional graphical models](https://mlsanity.com/paper/2103.10568/) (2021)
- [Partially Observed Dynamic Tensor Response Regression](https://mlsanity.com/paper/2002.09735/) (2020)
- [Latent Space Approaches to Community Detection in Dynamic Networks](https://mlsanity.com/paper/2005.08276/) (2020)
- [An Eigenmodel for Dynamic Multilayer Networks](https://mlsanity.com/paper/2103.12831/) (2021)
- [A New Low-Rank Tensor Model for Video Completion](https://mlsanity.com/paper/1509.02027/) (2015)
- [Latent Multimodal Functional Graphical Model Estimation](https://mlsanity.com/paper/2210.17237/) (2022)
- [Model-Based Clustering of Time-Evolving Networks through Temporal Exponential-Family Random Graph Models](https://mlsanity.com/paper/1712.07325/) (2017)

## Abstract (arXiv)

Contrasts with existing works which all consider nodes as functions and use edges to represent the relationships between different functions. We target at network modeling whose edges are functional data and transform the adjacency matrix into a functional adjacency tensor, introducing an additional dimension dedicated to function representation. Tucker functional decomposition is used for the functional adjacency tensor, and to further consider the community between nodes, we regularize the basis matrices to be symmetrical. Furthermore, to deal with irregular observations of the functional edges, we conduct model inference to solve a tensor completion problem. It is optimized by a Riemann conjugate gradient descent method. Besides these, we also derive several theorems to show the desirable properties of the functional edged network model. Finally, we evaluate the efficacy of our proposed model using simulation data and real metro system data from Hong Kong and Singapore.