# UniForCE: The Unimodality Forest Method for Clustering and Estimation of the Number of Clusters

arXiv: https://arxiv.org/abs/2312.11323 · HTML: https://mlsanity.com/paper/2312.11323/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 77 references that are in the map.
- First posted on arXiv 18 Dec 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [SpectralNet: Spectral Clustering using Deep Neural Networks](https://mlsanity.com/paper/1801.01587/) (2018)
- [Fast and Eager k-Medoids Clustering: O(k) Runtime Improvement of the PAM, CLARA, and CLARANS Algorithms](https://mlsanity.com/paper/2008.05171/) (2020)
- [Deep Density-based Image Clustering](https://mlsanity.com/paper/1812.04287/) (2018)
- [DBSCAN++: Towards fast and scalable density clustering](https://mlsanity.com/paper/1810.13105/) (2018)
- [A review of mean-shift algorithms for clustering](https://mlsanity.com/paper/1503.00687/) (2015)
- [Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms](https://mlsanity.com/paper/1712.06206/) (2017)
- [To Cluster, or Not to Cluster: An Analysis of Clusterability Methods](https://mlsanity.com/paper/1808.08317/) (2018)
- [Deep Embedded K-Means Clustering](https://mlsanity.com/paper/2109.15149/) (2021)
- [Merging K-means with hierarchical clustering for identifying general-shaped groups](https://mlsanity.com/paper/1712.08786/) (2017)
- [Global k-means++: an effective relaxation of the global k-means clustering algorithm](https://mlsanity.com/paper/2211.12271/) (2022)
- [Multi-Prototypes Convex Merging Based K-Means Clustering Algorithm](https://mlsanity.com/paper/2302.07045/) (2023)
- [The UU-test for Statistical Modeling of Unimodal Data](https://mlsanity.com/paper/2008.12537/) (2020)
- [Git: Clustering Based on Graph of Intensity Topology](https://mlsanity.com/paper/2110.01274/) (2021)
- [Mode testing, critical bandwidth and excess mass](https://mlsanity.com/paper/1609.05188/) (2016)
- [A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances Over Random Projections](https://mlsanity.com/paper/2311.16614/) (2023)

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

- [Deep Clustering Using the Soft Silhouette Score: Towards Compact and Well-Separated Clusters](https://mlsanity.com/paper/2402.00608/) (2024)
- [Hierarchical clustering with maximum density paths and mixture models](https://mlsanity.com/paper/2503.15582/) (2025)

## Abstract (arXiv)

Estimating the number of clusters k while clustering the data is a challenging task. An incorrect cluster assumption indicates that the number of clusters k gets wrongly estimated. Consequently, the model fitting becomes less important. In this work, we focus on the concept of unimodality and propose a flexible cluster definition called locally unimodal cluster. A locally unimodal cluster extends for as long as unimodality is locally preserved across pairs of subclusters of the data. Then, we propose the UniForCE method for locally unimodal clustering. The method starts with an initial overclustering of the data and relies on the unimodality graph that connects subclusters forming unimodal pairs. Such pairs are identified using an appropriate statistical test. UniForCE identifies maximal locally unimodal clusters by computing a spanning forest in the unimodality graph. Experimental results on both real and synthetic datasets illustrate that the proposed methodology is particularly flexible and robust in discovering regular and highly complex cluster shapes. Most importantly, it automatically provides an adequate estimation of the number of clusters.