2025/10/04 by Shankar P. Sastry, Sastry, Shankar Prasad
Biochemistry, Genetics and Molecular Biology · Computer Science · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Single-cell and spatial transcriptomics #Stochastic Gradient Optimization Techniques #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2510.03810
openalex publication_date 2025/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I present a regression algorithm that provides a continuous, piecewise-smooth function approximating scattered data. It is based on composing and blending linear functions over Voronoi cells, and it scales to high dimensions. The algorithm infers Voronoi cells from seed vertices and constructs a linear function for the input data in and around each cell. As the algorithm does not explicitly compute the Voronoi diagram, it avoids the curse of dimensionality. An accuracy of around 98.2% on the MNIST dataset with 722,200 degrees of freedom (without data augmentation, convolution, or other geometric operators) demonstrates the applicability and scalability of the algorithm.