Spherical Rotation Dimension Reduction with Geometric Loss Functions

• URL: http://arxiv.org/abs/2204.10975v2
• Date: Thu, 27 Apr 2023 15:47:22 GMT
• Title: Spherical Rotation Dimension Reduction with Geometric Loss Functions
• Authors: Hengrui Luo, Jeremy E. Purvis, Didong Li
• Abstract summary: A prime example of such a dataset is a collection of cell cycle measurements, where the inherently cyclical nature of the process can be represented as a circle or sphere. We propose a nonlinear dimension reduction method, Spherical Rotation Component Analysis (SRCA), that incorporates geometric information to better approximate low-dimensional manifold.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modern datasets often exhibit high dimensionality, yet the data reside in low-dimensional manifolds that can reveal underlying geometric structures critical for data analysis. A prime example of such a dataset is a collection of cell cycle measurements, where the inherently cyclical nature of the process can be represented as a circle or sphere. Motivated by the need to analyze these types of datasets, we propose a nonlinear dimension reduction method, Spherical Rotation Component Analysis (SRCA), that incorporates geometric information to better approximate low-dimensional manifolds. SRCA is a versatile method designed to work in both high-dimensional and small sample size settings. By employing spheres or ellipsoids, SRCA provides a low-rank spherical representation of the data with general theoretic guarantees, effectively retaining the geometric structure of the dataset during dimensionality reduction. A comprehensive simulation study, along with a successful application to human cell cycle data, further highlights the advantages of SRCA compared to state-of-the-art alternatives, demonstrating its superior performance in approximating the manifold while preserving inherent geometric structures.

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