# Generalized Clustering and Multi-Manifold Learning with Geometric Structure Preservation

arXiv: https://arxiv.org/abs/2009.09590 · HTML: https://mlsanity.com/paper/2009.09590/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2020.

## Built on by (most cited first, 7 of 7)

- [Data Augmentation of Contrastive Learning is Estimating Positive-incentive Noise](https://mlsanity.com/paper/2408.09929/) (2024)
- [boldsymbolλ-Orthogonality Regularization for Compatible Representation Learning](https://mlsanity.com/paper/2509.16664/) (2025)
- [Automated Graph Self-supervised Learning via Multi-teacher Knowledge Distillation](https://mlsanity.com/paper/2210.02099/) (2022)
- [Mitigating Negative Flips via Margin Preserving Training](https://mlsanity.com/paper/2511.08322/) (2025)
- [Multi-Scale Geometric Autoencoder](https://mlsanity.com/paper/2509.24168/) (2025)
- [Robust Multi-Manifold Clustering via Simplex Paths](https://mlsanity.com/paper/2507.10710/) (2025)
- [Spherical Interpolation for Backward-Compatible Multimodal Representations](https://mlsanity.com/paper/2609.39836/) (2026)

## Abstract (arXiv)

Though manifold-based clustering has become a popular research topic, we observe that one important factor has been omitted by these works, namely that the defined clustering loss may corrupt the local and global structure of the latent space. In this paper, we propose a novel Generalized Clustering and Multi-manifold Learning (GCML) framework with geometric structure preservation for generalized data, i.e., not limited to 2-D image data and has a wide range of applications in speech, text, and biology domains. In the proposed framework, manifold clustering is done in the latent space guided by a clustering loss. To overcome the problem that the clustering-oriented loss may deteriorate the geometric structure of the latent space, an isometric loss is proposed for preserving intra-manifold structure locally and a ranking loss for inter-manifold structure globally. Extensive experimental results have shown that GCML exhibits superior performance to counterparts in terms of qualitative visualizations and quantitative metrics, which demonstrates the effectiveness of preserving geometric structure.