Nonlinear mixture model motivated subspace clustering
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Computer Science > Machine Learning
Title:Nonlinear mixture model motivated subspace clustering
Abstract: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.
| Comments: | 5 pages, 1 table, conference |
| Subjects: | Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV) |
| MSC classes: | 68T10 |
| ACM classes: | I.5 |
| Cite as: | arXiv:2606.29261 [cs.LG] |
| (or arXiv:2606.29261v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.29261
arXiv-issued DOI via DataCite (pending registration)
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