# Sampling-enabled scalable manifold learning unveils the discriminative cluster structure of high-dimensional data

arXiv: https://arxiv.org/abs/2401.01100 · HTML: https://mlsanity.com/paper/2401.01100/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 74 references that are in the map.
- First posted on arXiv 2 Jan 2024.

## Builds on (most cited first, 11 of 11)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [TriMap: Large-scale Dimensionality Reduction Using Triplets](https://mlsanity.com/paper/1910.00204/) (2019)
- [Data-driven discovery of intrinsic dynamics](https://mlsanity.com/paper/2108.05928/) (2021)
- [Interpreting the Curse of Dimensionality from Distance Concentration and Manifold Effect](https://mlsanity.com/paper/2401.00422/) (2023)
- [Supervised Dimensionality Reduction for Big Data](https://mlsanity.com/paper/1709.01233/) (2017)
- [Landmark Diffusion Maps (L-dMaps): Accelerated manifold learning out-of-sample extension](https://mlsanity.com/paper/1706.09396/) (2017)
- [MeanCut: A Greedy-Optimized Graph Clustering via Path-based Similarity and Degree Descent Criterion](https://mlsanity.com/paper/2312.04067/) (2023)

## Built on by (most cited first, 3 of 3)

- [Reasoning emerges from constrained inference manifolds in large language models](https://mlsanity.com/paper/2605.08142/) (2026)
- [Geospatial foundation-model embeddings improve population estimation unevenly across space and scale](https://mlsanity.com/paper/2605.01650/) (2026)
- [On a joint simultaneous learning of relevant feature subsets and subspaces in regression-like problems](https://mlsanity.com/paper/2607.28080/) (2026)

## Abstract (arXiv)

As a pivotal branch of machine learning, manifold learning uncovers the intrinsic low-dimensional structure within complex nonlinear manifolds in high-dimensional space for visualization, classification, clustering, and gaining key insights. Although existing techniques have achieved remarkable successes, they suffer from extensive distortions of cluster structure, which hinders the understanding of underlying patterns. Scalability issues also limit their applicability for handling large-scale data. We hence propose a sampling-based Scalable manifold learning technique that enables Uniform and Discriminative Embedding, namely SUDE, for large-scale and high-dimensional data. It starts by seeking a set of landmarks to construct the low-dimensional skeleton of the entire data, and then incorporates the non-landmarks into the learned space based on the constrained locally linear embedding (CLLE). We empirically validated the effectiveness of SUDE on synthetic datasets and real-world benchmarks, and applied it to analyze single-cell data and detect anomalies in electrocardiogram (ECG) signals. SUDE exhibits distinct advantage in scalability with respect to data size and embedding dimension, and has promising performance in cluster separation, integrity, and global structure preservation. The experiments also demonstrate notable robustness in embedding quality as the sampling rate decreases.