arXiv Machine Learning By Yiqun Zhang, Hou-biao Li

Anisotropic View Distance Metric for High-Dimensional Data: Theory, Geometry, and Fast Computation

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The paper introduces View distance, a novel metric that projects high‑dimensional data onto all pairwise two‑dimensional planes and sums the Euclidean distances across these projections. It satisfies metric axioms, couples features, suppresses redundancy, and captures anisotropic geometry. To make it scalable, the authors propose a plane‑selection strategy using iterative Maximum Weight Matching, reducing complexity from ω(n²) to ω(k) and demonstrating competitive performance on twelve datasets.

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arXiv Machine Learning
Aug 31

Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification

Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification (CARSANN) is a geometry-driven framework that adapts the spatial support of each neighborhood based on local geometric complexity. It estimates intrinsic dimensionality with TwoNN, builds an intrinsic representation via PCA, and uses a shape-operator-based estimate of local mean curvature to shrink the radius in highly curved regions while keeping a broader support in flatter areas. Experiments on over 70 OpenML datasets show that CARSANN consistently outperforms standard k‑NN and rivals other adaptive nearest‑neighbor methods, achieving a mean balanced accuracy increase from 0.6506 to 0.7528 and statistically significant improvements on most datasets.

By Alexandre L. M. Levada