# Nonlinear mixture model motivated subspace clustering

arXiv: https://arxiv.org/abs/2606.29261 · HTML: https://mlsanity.com/paper/2606.29261/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 37 references that are in the map.
- First posted on arXiv 28 Jun 2026.

## Builds on (most cited first, 7 of 7)

- [Subspace Clustering by Block Diagonal Representation](https://mlsanity.com/paper/1805.09243/) (2018)
- [Sparse Regularization via Convex Analysis](https://mlsanity.com/paper/1803.06765/) (2018)
- [Is an Affine Constraint Needed for Affine Subspace Clustering?](https://mlsanity.com/paper/2005.03888/) (2020)
- [Self-Representation Based Unsupervised Exemplar Selection in a Union of Subspaces](https://mlsanity.com/paper/2006.04246/) (2020)
- [Scalable and Robust Sparse Subspace Clustering Using Randomized Clustering and Multilayer Graphs](https://mlsanity.com/paper/1802.07648/) (2018)
- [Leveraging Union of Subspace Structure to Improve Constrained Clustering](https://mlsanity.com/paper/1608.02146/) (2016)
- [A Data Mining Approach Combining K-Means Clustering with Bagging Neural Network for Short-term Wind Power Forecasting](https://mlsanity.com/paper/1709.05261/) (2017)

## Abstract (arXiv)

We derive the linear union-of-subspaces (UoS) model for subspace clustering (SC) from the nonlinear mixture model (NMM) used in blind source separation (BSS) to represent a D-dimensional observation vector as an unknown multivariate nonlinear mapping of C latent variables. Assuming the mapping is differentiable up to an unknown order K, we approximate NMM by a K-th order Taylor expansion, yielding a model equivalent to the linear UoS framework underlying SC. This establishes that: (i) the smoothness order K corresponds to the unknown subspace dimension d; (ii) KC equals the number of anchors; and (iii) the sparsity of the representation vector equals K (i.e., d). These relationships enable estimation of bounds on subspace dimension, and that is validated on six benchmark datasets using five established SC algorithms. Established theoretical results are important for post-processing of self-representation matrices estimated by SC algorithms.