# Deep Clustering with Incomplete Noisy Pairwise Annotations: A Geometric Regularization Approach

arXiv: https://arxiv.org/abs/2305.19391 · HTML: https://mlsanity.com/paper/2305.19391/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 85 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 30 of 31)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Contrastive Clustering](https://mlsanity.com/paper/2009.09687/) (2020)
- [Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering](https://mlsanity.com/paper/1610.04794/) (2016)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Deep learning from crowds](https://mlsanity.com/paper/1709.01779/) (2017)
- [Provably End-to-end Label-Noise Learning without Anchor Points](https://mlsanity.com/paper/2102.02400/) (2021)
- [Spectral Methods meet EM: A Provably Optimal Algorithm for Crowdsourcing](https://mlsanity.com/paper/1406.3824/) (2014)
- [Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications](https://mlsanity.com/paper/1803.01257/) (2018)
- [The Why and How of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1401.5226/) (2014)
- [On Identifiability of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1709.00614/) (2017)
- [Learning from Crowds by Modeling Common Confusions](https://mlsanity.com/paper/2012.13052/) (2020)
- [Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clustering](https://mlsanity.com/paper/1608.04290/) (2016)
- [Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case](https://mlsanity.com/paper/1406.5273/) (2014)
- [A Framework for Deep Constrained Clustering -- Algorithms and Advances](https://mlsanity.com/paper/1901.10061/) (2019)
- [Crowdsourcing via Pairwise Co-occurrences: Identifiability and Algorithms](https://mlsanity.com/paper/1909.12325/) (2019)
- [Neural network-based clustering using pairwise constraints](https://mlsanity.com/paper/1511.06321/) (2015)
- [Matrix Completion via Max-Norm Constrained Optimization](https://mlsanity.com/paper/1303.0341/) (2013)
- [Anchor-Free Correlated Topic Modeling: Identifiability and Algorithm](https://mlsanity.com/paper/1611.05010/) (2016)
- [On Mixed Memberships and Symmetric Nonnegative Matrix Factorizations](https://mlsanity.com/paper/1607.00084/) (2016)
- [A Framework for Deep Constrained Clustering](https://mlsanity.com/paper/2101.02792/) (2021)
- [Deep Conditional Gaussian Mixture Model for Constrained Clustering](https://mlsanity.com/paper/2106.06385/) (2021)
- [Robust Near-Separable Nonnegative Matrix Factorization Using Linear Optimization](https://mlsanity.com/paper/1302.4385/) (2013)
- [Self-Dictionary Sparse Regression for Hyperspectral Unmixing: Greedy Pursuit and Pure Pixel Search are Related](https://mlsanity.com/paper/1409.4320/) (2014)
- [A Tensor Approach to Learning Mixed Membership Community Models](https://mlsanity.com/paper/1302.2684/) (2013)
- [Semi-crowdsourced Clustering with Deep Generative Models](https://mlsanity.com/paper/1810.11971/) (2018)
- [Crowdsourcing via Annotator Co-occurrence Imputation and Provable Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2106.07193/) (2021)
- [Memory-Efficient Convex Optimization for Self-Dictionary Separable Nonnegative Matrix Factorization: A Frank-Wolfe Approach](https://mlsanity.com/paper/2109.11135/) (2021)

## Built on by (most cited first, 5 of 5)

- [Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Software](https://mlsanity.com/paper/2402.06019/) (2024)
- [Learning From Crowdsourced Noisy Labels: A Signal Processing Perspective](https://mlsanity.com/paper/2407.06902/) (2024)
- [Angular Constraint Embedding via SpherePair Loss for Constrained Clustering](https://mlsanity.com/paper/2510.06907/) (2025)
- [Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition](https://mlsanity.com/paper/2511.04291/) (2025)
- [Uncertainty-Aware Probabilistic Constrained Clustering from Entangled Pairwise Supervision](https://mlsanity.com/paper/2608.12027/) (2026)

## Abstract (arXiv)

The recent integration of deep learning and pairwise similarity annotation-based constrained clustering -- i.e., textitdeep constrained clustering (DCC) -- has proven effective for incorporating weak supervision into massive data clustering: Less than 1% of pair similarity annotations can often substantially enhance the clustering accuracy. However, beyond empirical successes, there is a lack of understanding of DCC. In addition, many DCC paradigms are sensitive to annotation noise, but performance-guaranteed noisy DCC methods have been largely elusive. This work first takes a deep look into a recently emerged logistic loss function of DCC, and characterizes its theoretical properties. Our result shows that the logistic DCC loss ensures the identifiability of data membership under reasonable conditions, which may shed light on its effectiveness in practice. Building upon this understanding, a new loss function based on geometric factor analysis is proposed to fend against noisy annotations. It is shown that even under textitunknown annotation confusions, the data membership can still be textitprovably identified under our proposed learning criterion. The proposed approach is tested over multiple datasets to validate our claims.