# Towards Robust Nonlinear Subspace Clustering: A Kernel Learning Approach

arXiv: https://arxiv.org/abs/2501.06368 · HTML: https://mlsanity.com/paper/2501.06368/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 70 references that are in the map.
- First posted on arXiv 10 Jan 2025.

## Builds on (most cited first, 12 of 12)

- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [Robust and Efficient Subspace Segmentation via Least Squares Regression](https://mlsanity.com/paper/1404.6736/) (2014)
- [Subspace Clustering by Block Diagonal Representation](https://mlsanity.com/paper/1805.09243/) (2018)
- [MT2ST: Adaptive Multi-Task to Single-Task Learning](https://mlsanity.com/paper/2406.18038/) (2024)
- [Twin Learning for Similarity and Clustering: A Unified Kernel Approach](https://mlsanity.com/paper/1705.00678/) (2017)
- [Kernel Sparse Subspace Clustering on Symmetric Positive Definite Manifolds](https://mlsanity.com/paper/1601.00414/) (2016)
- [A Robust Spectral Clustering Algorithm for Sub-Gaussian Mixture Models with Outliers](https://mlsanity.com/paper/1912.07546/) (2019)
- [Enhanced Latent Multi-view Subspace Clustering](https://mlsanity.com/paper/2312.14763/) (2023)
- [Nonlinear subspace clustering by functional link neural networks](https://mlsanity.com/paper/2402.02051/) (2024)
- [Kernel Correlation-Dissimilarity for Multiple Kernel k-Means Clustering](https://mlsanity.com/paper/2403.03448/) (2024)
- [Wormhole: Concept-Aware Deep Representation Learning for Co-Evolving Sequences](https://mlsanity.com/paper/2409.13857/) (2024)

## Abstract (arXiv)

Kernel-based subspace clustering, which addresses the nonlinear structures in data, is an evolving area of research. Despite noteworthy progressions, prevailing methodologies predominantly grapple with limitations relating to (i) the influence of predefined kernels on model performance; (ii) the difficulty of preserving the original manifold structures in the nonlinear space; (iii) the dependency of spectral-type strategies on the ideal block diagonal structure of the affinity matrix. This paper presents DKLM, a novel paradigm for kernel-induced nonlinear subspace clustering. DKLM provides a data-driven approach that directly learns the kernel from the data's self-representation, ensuring adaptive weighting and satisfying the multiplicative triangle inequality constraint, which enhances the robustness of the learned kernel. By leveraging this learned kernel, DKLM preserves the local manifold structure of data in a nonlinear space while promoting the formation of an optimal block-diagonal affinity matrix. A thorough theoretical examination of DKLM reveals its relationship with existing clustering paradigms. Comprehensive experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed method.