# a-TMFG: Scalable Triangulated Maximally Filtered Graphs via Approximate Nearest Neighbors

arXiv: https://arxiv.org/abs/2603.09564 · HTML: https://mlsanity.com/paper/2603.09564/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 10 of 10)

- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [A Review on Graph Neural Network Methods in Financial Applications](https://mlsanity.com/paper/2111.15367/) (2021)
- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
- [Network Filtering for Big Data: Triangulated Maximally Filtered Graph](https://mlsanity.com/paper/1505.02445/) (2015)
- [Locally Linear Embedding and its Variants: Tutorial and Survey](https://mlsanity.com/paper/2011.10925/) (2020)
- [Learning Clique Forests](https://mlsanity.com/paper/1905.02266/) (2019)
- [Agglomerative Likelihood Clustering](https://mlsanity.com/paper/1908.00951/) (2019)
- [Parallel Filtered Graphs for Hierarchical Clustering](https://mlsanity.com/paper/2303.05009/) (2023)
- [Faster Parallel Triangular Maximally Filtered Graphs and Hierarchical Clustering](https://mlsanity.com/paper/2408.09399/) (2024)

## Abstract (arXiv)

The traditional Triangular Maximally Filtered Graph (TMFG) construction requires pre-computation and storage of a dense correlation matrix; this limits its applicability to small and medium-sized datasets. Here we identify key memory and runtime complexity challenges when using TMFG at scale. We then present the Approximate Triangular Maximally Filtered Graph (a-TMFG) algorithm. This is a novel approach to scaling the construction of artificial graphs from data inspired by TMFG. The method employs k-Nearest Neighbors Graphs (kNNG) for initial construction, and implements a memory management strategy to search and estimate missing correlations on-the-fly. This provides representations to control combinatorial explosion. The algorithm is tested for robustness to the parameters and noise, and is evaluated on datasets with millions of observations. This new method provides a parsimonious way to construct graphs for use-cases where graphs are used as input to supervised and unsupervised learning but where no natural graph exists.