# Twin Learning for Similarity and Clustering: A Unified Kernel Approach

arXiv: https://arxiv.org/abs/1705.00678 · HTML: https://mlsanity.com/paper/1705.00678/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2017.

## Built on by (most cited first, 14 of 14)

- [Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view](https://mlsanity.com/paper/2102.07943/) (2021)
- [Towards Clustering-friendly Representations: Subspace Clustering via Graph Filtering](https://mlsanity.com/paper/2106.09874/) (2021)
- [COIN: Co-Cluster Infomax for Bipartite Graphs](https://mlsanity.com/paper/2206.00006/) (2022)
- [STERLING: Synergistic Representation Learning on Bipartite Graphs](https://mlsanity.com/paper/2302.05428/) (2023)
- [Joint Multi-view Unsupervised Feature Selection and Graph Learning](https://mlsanity.com/paper/2204.08247/) (2022)
- [Multiple Kernel Clustering with Dual Noise Minimization](https://mlsanity.com/paper/2207.06041/) (2022)
- [Adaptive Attribute and Structure Subspace Clustering Network](https://mlsanity.com/paper/2109.13742/) (2021)
- [Deep Contrastive Graph Learning with Clustering-Oriented Guidance](https://mlsanity.com/paper/2402.16012/) (2024)
- [A Unified Framework for Fair Spectral Clustering With Effective Graph Learning](https://mlsanity.com/paper/2311.13766/) (2023)
- [Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithms](https://mlsanity.com/paper/2103.10656/) (2021)
- [Leachable Component Clustering](https://mlsanity.com/paper/2208.13217/) (2022)
- [Revealing and Utilizing In-group Favoritism for Graph-based Collaborative Filtering](https://mlsanity.com/paper/2404.17598/) (2024)
- [Towards Robust Nonlinear Subspace Clustering: A Kernel Learning Approach](https://mlsanity.com/paper/2501.06368/) (2025)
- [Scalable Robust Bayesian Co-Clustering with Compositional ELBOs](https://mlsanity.com/paper/2504.04079/) (2025)

## Abstract (arXiv)

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.