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cloud.google.com·6h ago
AI Research
arXiv CS.AI·Aug 31·5 min read
Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification
TL;DR
Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification (CARSANN) enhances $k$-NN by adapting neighborhood sizes based on local geometric complexity, leading to improved classification accuracy.
✦ Why It Matters
Implement CARSANN to improve classification accuracy in datasets with varying local geometries.
Key Takeaways
- Use CARSANN for datasets with complex local geometries.
- Estimate local mean curvature to adjust neighborhood sizes.
- Leverage intrinsic dimensionality for better data representation.
- Achieve statistically significant improvements over standard $k$-NN.
How It Works
CARSANN first estimates the intrinsic dimensionality of the data using a method called TwoNN, which helps in understanding the data's structure. It then applies principal component analysis to create an intrinsic representation of the data.
The local mean curvature is calculated using a shape-operator-based approach, which informs how much to shrink the neighborhood radius. In regions with high curvature, the radius is reduced significantly, while flatter areas maintain a larger neighborhood size, allowing for more effective classification.