# Generalizing the Convolution Operator to extend CNNs to Irregular Domains

arXiv: https://arxiv.org/abs/1606.01166 · HTML: https://mlsanity.com/paper/1606.01166/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2016.

## Built on by (most cited first, 2 of 2)

- [Predicting the traffic flux in the city of Valencia with Deep Learning](https://mlsanity.com/paper/2210.01630/) (2022)
- [Establishing a real-time traffic alarm in the city of Valencia with Deep Learning](https://mlsanity.com/paper/2309.02010/) (2023)

## Abstract (arXiv)

Convolutional Neural Networks (CNNs) have become the state-of-the-art in supervised learning vision tasks. Their convolutional filters are of paramount importance for they allow to learn patterns while disregarding their locations in input images. When facing highly irregular domains, generalized convolutional operators based on an underlying graph structure have been proposed. However, these operators do not exactly match standard ones on grid graphs, and introduce unwanted additional invariance (e.g. with regards to rotations). We propose a novel approach to generalize CNNs to irregular domains using weight sharing and graph-based operators. Using experiments, we show that these models resemble CNNs on regular domains and offer better performance than multilayer perceptrons on distorded ones.