# Bias-Variance Tradeoff of Graph Laplacian Regularizer

arXiv: https://arxiv.org/abs/1706.00544 · HTML: https://mlsanity.com/paper/1706.00544/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2017.

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

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Retinex-based Image Denoising / Contrast Enhancement using Gradient Graph Laplacian Regularizer](https://mlsanity.com/paper/2307.02625/) (2023)
- [Towards Bridging Review Sparsity in Recommendation with Textual Edge Graph Representation](https://mlsanity.com/paper/2508.01128/) (2025)
- [Unsupervised Graph Spectral Feature Denoising for Crop Yield Prediction](https://mlsanity.com/paper/2208.02714/) (2022)

## Abstract (arXiv)

This paper presents a bias-variance tradeoff of graph Laplacian regularizer, which is widely used in graph signal processing and semi-supervised learning tasks. The scaling law of the optimal regularization parameter is specified in terms of the spectral graph properties and a novel signal-to-noise ratio parameter, which suggests selecting a mediocre regularization parameter is often suboptimal. The analysis is applied to three applications, including random, band-limited, and multiple-sampled graph signals. Experiments on synthetic and real-world graphs demonstrate near-optimal performance of the established analysis.