# Study of Manifold Geometry using Multiscale Non-Negative Kernel Graphs

arXiv: https://arxiv.org/abs/2210.17475 · HTML: https://mlsanity.com/paper/2210.17475/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 37 references that are in the map.
- First posted on arXiv 31 Oct 2022.

## Builds on (most cited first, 9 of 9)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Deep geometric knowledge distillation with graphs](https://mlsanity.com/paper/1911.03080/) (2019)
- [Channel-Wise Early Stopping without a Validation Set via NNK Polytope Interpolation](https://mlsanity.com/paper/2107.12972/) (2021)
- [Laplacian Networks: Bounding Indicator Function Smoothness for Neural Network Robustness](https://mlsanity.com/paper/1805.10133/) (2018)
- [Representing Deep Neural Networks Latent Space Geometries with Graphs](https://mlsanity.com/paper/2011.07343/) (2020)
- [The Geometry of Self-supervised Learning Models and its Impact on Transfer Learning](https://mlsanity.com/paper/2209.08622/) (2022)
- [Channel redundancy and overlap in convolutional neural networks with channel-wise NNK graphs](https://mlsanity.com/paper/2110.11400/) (2021)
- [Efficient graph construction for image representation](https://mlsanity.com/paper/2002.06662/) (2020)

## Built on by (most cited first, 1 of 1)

- [Geometry-Aware Graph Construction via Adaptive Spectral Bandwidth Control](https://mlsanity.com/paper/2609.03306/) (2026)

## Abstract (arXiv)

Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the geometric structure of the data. We make use of our recently introduced non-negative kernel (NNK) regression graphs to estimate the point density, intrinsic dimension, and the linearity of the data manifold (curvature). We further generalize the graph construction and geometric estimation to multiple scale by iteratively merging neighborhoods in the input data. Our experiments demonstrate the effectiveness of our proposed approach over other baselines in estimating the local geometry of the data manifolds on synthetic and real datasets.