Linear Convergence of the Subspace Constrained Mean Shift Algorithm: From Euclidean to Directional Data
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909606109773824 |
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| author | Zhang, Yikun Chen, Yen-Chi |
| author_facet | Zhang, Yikun Chen, Yen-Chi |
| contents | This paper studies the linear convergence of the subspace constrained mean shift (SCMS) algorithm, a well-known algorithm for identifying a density ridge defined by a kernel density estimator. By arguing that the SCMS algorithm is a special variant of a subspace constrained gradient ascent (SCGA) algorithm with an adaptive step size, we derive the linear convergence of such SCGA algorithm. While the existing research focuses mainly on density ridges in the Euclidean space, we generalize density ridges and the SCMS algorithm to directional data. In particular, we establish the stability theorem of density ridges with directional data and prove the linear convergence of our proposed directional SCMS algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_14977 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Linear Convergence of the Subspace Constrained Mean Shift Algorithm: From Euclidean to Directional Data Zhang, Yikun Chen, Yen-Chi Machine Learning Optimization and Control Statistics Theory Methodology 62G05, 49Q12, 62H11 This paper studies the linear convergence of the subspace constrained mean shift (SCMS) algorithm, a well-known algorithm for identifying a density ridge defined by a kernel density estimator. By arguing that the SCMS algorithm is a special variant of a subspace constrained gradient ascent (SCGA) algorithm with an adaptive step size, we derive the linear convergence of such SCGA algorithm. While the existing research focuses mainly on density ridges in the Euclidean space, we generalize density ridges and the SCMS algorithm to directional data. In particular, we establish the stability theorem of density ridges with directional data and prove the linear convergence of our proposed directional SCMS algorithm. |
| title | Linear Convergence of the Subspace Constrained Mean Shift Algorithm: From Euclidean to Directional Data |
| topic | Machine Learning Optimization and Control Statistics Theory Methodology 62G05, 49Q12, 62H11 |
| url | https://arxiv.org/abs/2104.14977 |