# Connectome Smoothing via Low-rank Approximations

arXiv: https://arxiv.org/abs/1609.01672 · HTML: https://mlsanity.com/paper/1609.01672/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2016.

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

- [Online Change Point Detection for Weighted and Directed Random Dot Product Graphs](https://mlsanity.com/paper/2201.11222/) (2022)
- [Clustered Graph Matching for Label Recovery and Graph Classification](https://mlsanity.com/paper/2205.03486/) (2022)
- [Detection of Model-based Planted Pseudo-cliques in Random Dot Product Graphs by the Adjacency Spectral Embedding and the Graph Encoder Embedding](https://mlsanity.com/paper/2312.11054/) (2023)
- [Weighted Random Dot Product Graphs](https://mlsanity.com/paper/2505.03649/) (2025)

## Abstract (arXiv)

In statistical connectomics, the quantitative study of brain networks, estimating the mean of a population of graphs based on a sample is a core problem. Often, this problem is especially difficult because the sample or cohort size is relatively small, sometimes even a single subject. While using the element-wise sample mean of the adjacency matrices is a common approach, this method does not exploit any underlying structural properties of the graphs. We propose using a low-rank method which incorporates tools for dimension selection and diagonal augmentation to smooth the estimates and improve performance over the naive methodology for small sample sizes. Theoretical results for the stochastic blockmodel show that this method offers major improvements when there are many vertices. Similarly, we demonstrate that the low-rank methods outperform the standard sample mean for a variety of independent edge distributions as well as human connectome data derived from magnetic resonance imaging, especially when sample sizes are small. Moreover, the low-rank methods yield "eigen-connectomes", which correlate with the lobe-structure of the human brain and superstructures of the mouse brain. These results indicate that low-rank methods are an important part of the tool box for researchers studying populations of graphs in general, and statistical connectomics in particular.