用沃罗诺伊单元实现高维散点回归，精度超98%。
Cellular Learning: Scattered Data Regression in High Dimensions via Voronoi Cells
- 基于沃罗诺伊单元组合线性函数，构建连续分段光滑回归模型。
- 在无数据增强的MNIST上达98.2%准确率，72万自由度仍高效。
- 适合高维散点拟合，尤其适用于无几何先验的复杂数据。
本文提出一种回归算法，可对散点数据生成连续、分段光滑的函数近似。该方法基于在沃罗诺伊单元上组合与混合线性函数，且能扩展至高维空间。算法通过种子顶点推断沃罗诺伊单元，并为每个单元及其邻域内的输入数据构建线性函数。由于无需显式计算沃罗诺伊图，避免了维度灾难。在未使用数据增强、卷积或其它几何算子的情况下，于MNIST数据集上达到约98.2%的准确率，具备722,200个自由度，证明了该算法的适用性与可扩展性。
原文摘要 · Abstract (English)
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.
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