# High-dimensional Clustering onto Hamiltonian Cycle

arXiv: https://arxiv.org/abs/2304.14531 · HTML: https://mlsanity.com/paper/2304.14531/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 78 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 22 of 22)

- [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)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Invariant Information Clustering for Unsupervised Image Classification and Segmentation](https://mlsanity.com/paper/1807.06653/) (2018)
- [SCAN: Learning to Classify Images without Labels](https://mlsanity.com/paper/2005.12320/) (2020)
- [Contrastive Clustering](https://mlsanity.com/paper/2009.09687/) (2020)
- [Joint Unsupervised Learning of Deep Representations and Image Clusters](https://mlsanity.com/paper/1604.03628/) (2016)
- [SPICE: Semantic Pseudo-labeling for Image Clustering](https://mlsanity.com/paper/2103.09382/) (2021)
- [SpectralNet: Spectral Clustering using Deep Neural Networks](https://mlsanity.com/paper/1801.01587/) (2018)
- [Deep Spectral Clustering using Dual Autoencoder Network](https://mlsanity.com/paper/1904.13113/) (2019)
- [Hierarchical Clustering: Objective Functions and Algorithms](https://mlsanity.com/paper/1704.02147/) (2017)
- [Improving Unsupervised Image Clustering With Robust Learning](https://mlsanity.com/paper/2012.11150/) (2020)
- [Clustering with Deep Learning: Taxonomy and New Methods](https://mlsanity.com/paper/1801.07648/) (2018)
- [N2D: (Not Too) Deep Clustering via Clustering the Local Manifold of an Autoencoded Embedding](https://mlsanity.com/paper/1908.05968/) (2019)
- [LSD-C: Linearly Separable Deep Clusters](https://mlsanity.com/paper/2006.10039/) (2020)
- [A Tighter Analysis of Spectral Clustering, and Beyond](https://mlsanity.com/paper/2208.01724/) (2022)
- [An iterative clustering algorithm for the Contextual Stochastic Block Model with optimality guarantees](https://mlsanity.com/paper/2112.10467/) (2021)
- [Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering](https://mlsanity.com/paper/2206.05553/) (2022)
- [EVNet: An Explainable Deep Network for Dimension Reduction](https://mlsanity.com/paper/2211.15478/) (2022)
- [Deep Learning with Nonparametric Clustering](https://mlsanity.com/paper/1501.03084/) (2015)
- [Order preserving hierarchical agglomerative clustering](https://mlsanity.com/paper/2004.12488/) (2020)
- [Consistent Representation Learning for High Dimensional Data Analysis](https://mlsanity.com/paper/2012.00481/) (2020)

## Built on by (most cited first, 2 of 2)

- [Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structures](https://mlsanity.com/paper/2308.09250/) (2023)
- [AIGC In China: Current Developments And Future Outlook](https://mlsanity.com/paper/2308.08451/) (2023)

## Abstract (arXiv)

Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable to simultaneously present the similarities between different clusters and outliers. This paper proposes a new framework called High-dimensional Clustering onto Hamiltonian Cycle (HCHC) to solve the above problems. First, HCHC combines global structure with local structure in one objective function for deep clustering, improving the labels as relative probabilities, to mine the similarities between different clusters while keeping the local structure in each cluster. Then, the anchors of different clusters are sorted on the optimal Hamiltonian cycle generated by the cluster similarities and mapped on the circumference of a circle. Finally, a sample with a higher probability of a cluster will be mapped closer to the corresponding anchor. In this way, our framework allows us to appreciate three aspects visually and simultaneously - clusters (formed by samples with high probabilities), cluster similarities (represented as circular distances), and outliers (recognized as dots far away from all clusters). The experiments illustrate the superiority of HCHC.