# Edge-enhancing Filters with Negative Weights

arXiv: https://arxiv.org/abs/1509.02491 · HTML: https://mlsanity.com/paper/1509.02491/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2015.

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

- [A Method for Handling Negative Similarities in Explainable Graph Spectral Clustering of Text Documents -- Extended Version](https://mlsanity.com/paper/2504.12360/) (2025)

## Abstract (arXiv)

In [DOI:10.1109/ICMEW.2014.6890711], a graph-based denoising is performed by projecting the noisy image to a lower dimensional Krylov subspace of the graph Laplacian, constructed using nonnegative weights determined by distances between image data corresponding to image pixels. We~extend the construction of the graph Laplacian to the case, where some graph weights can be negative. Removing the positivity constraint provides a more accurate inference of a graph model behind the data, and thus can improve quality of filters for graph-based signal processing, e.g., denoising, compared to the standard construction, without affecting the costs.