# Deep Clustering Using the Soft Silhouette Score: Towards Compact and Well-Separated Clusters

arXiv: https://arxiv.org/abs/2402.00608 · HTML: https://mlsanity.com/paper/2402.00608/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 83 references that are in the map.
- First posted on arXiv 1 Feb 2024.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering](https://mlsanity.com/paper/1610.04794/) (2016)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (2016)
- [Joint Unsupervised Learning of Deep Representations and Image Clusters](https://mlsanity.com/paper/1604.03628/) (2016)
- [Network Representation Learning: A Survey](https://mlsanity.com/paper/1801.05852/) (2017)
- [Deep Clustering: A Comprehensive Survey](https://mlsanity.com/paper/2210.04142/) (2022)
- [ClusterGAN : Latent Space Clustering in Generative Adversarial Networks](https://mlsanity.com/paper/1809.03627/) (2018)
- [A Comprehensive Survey on Deep Clustering: Taxonomy, Challenges, and Future Directions](https://mlsanity.com/paper/2206.07579/) (2022)
- [Clustering with Deep Learning: Taxonomy and New Methods](https://mlsanity.com/paper/1801.07648/) (2018)
- [Discriminatively Boosted Image Clustering with Fully Convolutional Auto-Encoders](https://mlsanity.com/paper/1703.07980/) (2017)
- [Deep Density-based Image Clustering](https://mlsanity.com/paper/1812.04287/) (2018)
- [Strongly Augmented Contrastive Clustering](https://mlsanity.com/paper/2206.00380/) (2022)
- [Minimum adjusted Rand index for two clusterings of a given size](https://mlsanity.com/paper/2002.03677/) (2020)
- [Adversarial Deep Embedded Clustering: on a better trade-off between Feature Randomness and Feature Drift](https://mlsanity.com/paper/1909.11832/) (2019)
- [Deep Embedded K-Means Clustering](https://mlsanity.com/paper/2109.15149/) (2021)
- [Spectral Clustering via Ensemble Deep Autoencoder Learning (SC-EDAE)](https://mlsanity.com/paper/1901.02291/) (2019)
- [Revisiting Silhouette Aggregation](https://mlsanity.com/paper/2401.05831/) (2024)
- [Global k-means++: an effective relaxation of the global k-means clustering algorithm](https://mlsanity.com/paper/2211.12271/) (2022)
- [Minimum Density Hyperplanes](https://mlsanity.com/paper/1507.04201/) (2015)
- [UniForCE: The Unimodality Forest Method for Clustering and Estimation of the Number of Clusters](https://mlsanity.com/paper/2312.11323/) (2023)

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

- [Diversify and Conquer: Diversity-Centric Data Selection with Iterative Refinement](https://mlsanity.com/paper/2409.11378/) (2024)
- [Aircraft Trajectory Segmentation-based Contrastive Coding: A Framework for Self-supervised Trajectory Representation](https://mlsanity.com/paper/2407.20028/) (2024)
- [SENSE: Self-Supervised Neural Embeddings for Spatial Ensembles](https://mlsanity.com/paper/2512.11145/) (2025)
- [CVSearch: Empowering Multimodal LLMs with Cognitive Visual Search for High-Resolution Image Perception](https://mlsanity.com/paper/2605.23655/) (2026)
- [A Framework Based on Graph Cellular Automata for Similarity Evaluation in Urban Spatial Networks](https://mlsanity.com/paper/2511.00768/) (2025)
- [Ensemble of Unsupervised Deep Learning for Clustering Imbalanced Tabular Data](https://mlsanity.com/paper/2608.00346/) (2026)
- [BehaviorFormer: Discovering Behavioral Patterns via Clusterable Next-Token Prediction](https://mlsanity.com/paper/2610.16322/) (2026)

## Abstract (arXiv)

Unsupervised learning has gained prominence in the big data era, offering a means to extract valuable insights from unlabeled datasets. Deep clustering has emerged as an important unsupervised category, aiming to exploit the non-linear mapping capabilities of neural networks in order to enhance clustering performance. The majority of deep clustering literature focuses on minimizing the inner-cluster variability in some embedded space while keeping the learned representation consistent with the original high-dimensional dataset. In this work, we propose soft silhoutte, a probabilistic formulation of the silhouette coefficient. Soft silhouette rewards compact and distinctly separated clustering solutions like the conventional silhouette coefficient. When optimized within a deep clustering framework, soft silhouette guides the learned representations towards forming compact and well-separated clusters. In addition, we introduce an autoencoder-based deep learning architecture that is suitable for optimizing the soft silhouette objective function. The proposed deep clustering method has been tested and compared with several well-studied deep clustering methods on various benchmark datasets, yielding very satisfactory clustering results.