# CoreSPECT: Enhancing Clustering Algorithms via an Interplay of Density and Geometry

arXiv: https://arxiv.org/abs/2507.08243 · HTML: https://mlsanity.com/paper/2507.08243/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 11 Jul 2025.

## Builds on (most cited first, 9 of 9)

- [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)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
- [Manifold Topology Divergence: a Framework for Comparing Data Manifolds](https://mlsanity.com/paper/2106.04024/) (2021)
- [Intrinsic Dimensionality Estimation within Tight Localities: A Theoretical and Experimental Analysis](https://mlsanity.com/paper/2209.14475/) (2022)
- [Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms](https://mlsanity.com/paper/1712.06206/) (2017)
- [Large sample spectral analysis of graph-based multi-manifold clustering](https://mlsanity.com/paper/2107.13610/) (2021)
- [PECANN: Parallel Efficient Clustering with Graph-Based Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2312.03940/) (2023)

## Abstract (arXiv)

In this paper, we provide a novel perspective on the underlying structure of real-world data with ground-truth clusters via characterization of an abundantly observed yet often overlooked density-geometry correlation, that manifests itself as a multi-layered manifold structure. We leverage this correlation to design CoreSPECT (Core Space Projection based Enhancement of Clustering Techniques), a general framework that improves the performance of generic clustering algorithms. Our framework boosts the performance of clustering algorithms by applying them to strategically selected regions, then extending the partial partition to a complete partition for the dataset using a novel neighborhood graph based multi-layer propagation procedure. We provide initial theoretical support of the functionality of our framework under the assumption of our model, and then provide large-scale real-world experiments on 19 datasets that include standard image datasets as well as genomics datasets. We observe two notable improvements. First, CoreSPECT improves the NMI of K-Means by 20% on average, making it competitive to (and in some cases surpassing) the state-of-the-art manifold-based clustering algorithms, while being orders of magnitude faster. Secondly, our framework boosts the NMI of HDBSCAN by more than 100% on average, making it competitive to the state-of-the-art in several cases without requiring the true number of clusters and hyper-parameter tuning. The overall ARI improvements are higher.