# Dimension Reduction with Locally Adjusted Graphs

arXiv: https://arxiv.org/abs/2412.15426 · HTML: https://mlsanity.com/paper/2412.15426/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 55 references that are in the map.
- First posted on arXiv 19 Dec 2024.

## Builds on (most cited first, 15 of 15)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Pervasive Label Errors in Test Sets Destabilize Machine Learning Benchmarks](https://mlsanity.com/paper/2103.14749/) (2021)
- [All-but-the-Top: Simple and Effective Postprocessing for Word Representations](https://mlsanity.com/paper/1702.01417/) (2017)
- [Understanding and Utilizing Deep Neural Networks Trained with Noisy Labels](https://mlsanity.com/paper/1905.05040/) (2019)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Visualizing Large-scale and High-dimensional Data](https://mlsanity.com/paper/1602.00370/) (2016)
- [Simple and Effective Dimensionality Reduction for Word Embeddings](https://mlsanity.com/paper/1708.03629/) (2017)
- [From t-SNE to UMAP with contrastive learning](https://mlsanity.com/paper/2206.01816/) (2022)
- [Automatic Selection of t-SNE Perplexity](https://mlsanity.com/paper/1708.03229/) (2017)
- [Hierarchical Nearest Neighbor Graph Embedding for Efficient Dimensionality Reduction](https://mlsanity.com/paper/2203.12997/) (2022)
- [A Probabilistic Graph Coupling View of Dimension Reduction](https://mlsanity.com/paper/2201.13053/) (2022)
- [Navigating the Effect of Parametrization for Dimensionality Reduction](https://mlsanity.com/paper/2411.15894/) (2024)

## Built on by (most cited first, 9 of 9)

- [The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction](https://mlsanity.com/paper/2503.09101/) (2025)
- [MAPLE: Self-Supervised Learning-Enhanced Nonlinear Dimensionality Reduction for Visual Analysis](https://mlsanity.com/paper/2601.20173/) (2026)
- [FloDR: An invertible dimensionality reduction method based on a normalising flow](https://mlsanity.com/paper/2607.26278/) (2026)
- [Language Models for Adult Service Website Text Analysis](https://mlsanity.com/paper/2507.10743/) (2025)
- [Leveraging Non-linear Dimension Reduction and Random Walk Co-occurrence for Node Embedding](https://mlsanity.com/paper/2602.24069/) (2026)
- [mlx-vis: GPU-Native Dimensionality Reduction on Apple Silicon](https://mlsanity.com/paper/2603.04035/) (2026)
- [A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2604.02535/) (2026)
- [SmartIterator: Visual Analytics Workflows for Supervising Unsupervised Data Grouping](https://mlsanity.com/paper/2605.28219/) (2026)
- [CosMAP: Contrastive Manifold Approximation and Projection for Dimensionality Reduction of Omics and Genealogical Data](https://mlsanity.com/paper/2608.11269/) (2026)

## Abstract (arXiv)

Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often involves converting the original high-dimensional data into a graph. In this graph, each edge represents the similarity or dissimilarity between pairs of data points. However, this graph is frequently suboptimal due to unreliable high-dimensional distances and the limited information extracted from the high-dimensional data. This problem is exacerbated as the dataset size increases. If we reduce the size of the dataset by selecting points for a specific sections of the embeddings, the clusters observed through DR are more separable since the extracted subgraphs are more reliable. In this paper, we introduce LocalMAP, a new dimensionality reduction algorithm that dynamically and locally adjusts the graph to address this challenge. By dynamically extracting subgraphs and updating the graph on-the-fly, LocalMAP is capable of identifying and separating real clusters within the data that other DR methods may overlook or combine. We demonstrate the benefits of LocalMAP through a case study on biological datasets, highlighting its utility in helping users more accurately identify clusters for real-world problems.