# Learning Label Initialization for Time-Dependent Harmonic Extension

arXiv: https://arxiv.org/abs/2205.01358 · HTML: https://mlsanity.com/paper/2205.01358/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 48 references that are in the map.
- First posted on arXiv 3 May 2022.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models](https://mlsanity.com/paper/2005.07959/) (2020)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Unifying Graph Convolutional Neural Networks and Label Propagation](https://mlsanity.com/paper/2002.06755/) (2020)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [The game theoretic p-Laplacian and semi-supervised learning with few labels](https://mlsanity.com/paper/1711.10144/) (2017)
- [Properly-weighted graph Laplacian for semi-supervised learning](https://mlsanity.com/paper/1810.04351/) (2018)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
- [Algorithms for Lipschitz Learning on Graphs](https://mlsanity.com/paper/1505.00290/) (2015)
- [Asymptotic behavior of ℓp-based Laplacian regularization in semi-supervised learning](https://mlsanity.com/paper/1603.00564/) (2016)
- [Should Graph Neural Networks Use Features, Edges, Or Both?](https://mlsanity.com/paper/2103.06857/) (2021)

## Built on by (most cited first, 1 of 1)

- [Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian](https://mlsanity.com/paper/2401.07463/) (2024)

## Abstract (arXiv)

Node classification on graphs can be formulated as the Dirichlet problem on graphs where the signal is given at the labeled nodes, and the harmonic extension is done on the unlabeled nodes. This paper considers a time-dependent version of the Dirichlet problem on graphs and shows how to improve its solution by learning the proper initialization vector on the unlabeled nodes. Further, we show that the improved solution is at par with state-of-the-art methods used for node classification. Finally, we conclude this paper by discussing the importance of parameter t, pros, and future directions.