Cellular Learning: Scattered Data Regression in High Dimensions via Voronoi Cells
This addresses the challenge of scalable regression for high-dimensional data, though it appears incremental as it builds on Voronoi-based methods without major paradigm shifts.
The paper tackles the problem of regression on scattered data in high dimensions by proposing an algorithm that composes and blends linear functions over Voronoi cells, achieving 98.2% accuracy on MNIST with 722,200 degrees of freedom.
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.