Spherical Rotation Dimension Reduction with Geometric Loss Functions
This provides a method for analyzing high-dimensional datasets with geometric structures, like cell cycle measurements, but it appears incremental as it builds on existing dimension reduction techniques.
The paper tackled the problem of dimensionality reduction for datasets with underlying geometric structures, such as cyclical cell cycle data, by proposing Spherical Rotation Component Analysis (SRCA), which demonstrated superior performance in approximating low-dimensional manifolds compared to state-of-the-art methods.
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.