# Localized Iterative Methods for Interpolation in Graph Structured Data

arXiv: https://arxiv.org/abs/1310.2646 · HTML: https://mlsanity.com/paper/1310.2646/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2013.

## Built on by (most cited first, 4 of 4)

- [Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction](https://mlsanity.com/paper/2403.19800/) (2024)
- [Online Filtering over Expanding Graphs](https://mlsanity.com/paper/2301.06898/) (2023)
- [Kernel-based Joint Multiple Graph Learning and Clustering of Graph Signals](https://mlsanity.com/paper/2310.19005/) (2023)
- [Randomized Space-Time Sampling for Affine Graph Dynamical Systems](https://mlsanity.com/paper/2509.16818/) (2025)

## Abstract (arXiv)

In this paper, we present two localized graph filtering based methods for interpolating graph signals defined on the vertices of arbitrary graphs from only a partial set of samples. The first method is an extension of previous work on reconstructing bandlimited graph signals from partially observed samples. The iterative graph filtering approach very closely approximates the solution proposed in the that work, while being computationally more efficient. As an alternative, we propose a regularization based framework in which we define the cost of reconstruction to be a combination of smoothness of the graph signal and the reconstruction error with respect to the known samples, and find solutions that minimize this cost. We provide both a closed form solution and a computationally efficient iterative solution of the optimization problem. The experimental results on the recommendation system datasets demonstrate effectiveness of the proposed methods.