# Theoretical bounds on data requirements for the ray-based classification

arXiv: https://arxiv.org/abs/2103.09577 · HTML: https://mlsanity.com/paper/2103.09577/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 17 Mar 2021.

## Builds on (most cited first, 10 of 10)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PatchNets: Patch-Based Generalizable Deep Implicit 3D Shape Representations](https://mlsanity.com/paper/2008.01639/) (2020)
- [Learning to Segment 3D Point Clouds in 2D Image Space](https://mlsanity.com/paper/2003.05593/) (2020)
- [Machine learning enables completely automatic tuning of a quantum device faster than human experts](https://mlsanity.com/paper/2001.02589/) (2020)
- [Ray-based framework for state identification in quantum dot devices](https://mlsanity.com/paper/2102.11784/) (2021)
- [Quantum device fine-tuning using unsupervised embedding learning](https://mlsanity.com/paper/2001.04409/) (2020)
- [Ray-based classification framework for high-dimensional data](https://mlsanity.com/paper/2010.00500/) (2020)
- [3D Object Classification via Spherical Projections](https://mlsanity.com/paper/1712.04426/) (2017)
- [Efficiently measuring a quantum device using machine learning](https://mlsanity.com/paper/1810.10042/) (2018)
- [RGB-D image-based Object Detection: from Traditional Methods to Deep Learning Techniques](https://mlsanity.com/paper/1907.09236/) (2019)

## Built on by (most cited first, 4 of 4)

- [Colloquium: Advances in automation of quantum dot devices control](https://mlsanity.com/paper/2112.09362/) (2021)
- [Estimation of Convex Polytopes for Automatic Discovery of Charge State Transitions in Quantum Dot Arrays](https://mlsanity.com/paper/2108.09133/) (2021)
- [Learning Coulomb Diamonds in Large Quantum Dot Arrays](https://mlsanity.com/paper/2205.01443/) (2022)
- [QDA2: A principled approach to automatically annotating charge stability diagrams](https://mlsanity.com/paper/2312.11206/) (2023)

## Abstract (arXiv)

The problem of classifying high-dimensional shapes in real-world data grows in complexity as the dimension of the space increases. For the case of identifying convex shapes of different geometries, a new classification framework has recently been proposed in which the intersections of a set of one-dimensional representations, called rays, with the boundaries of the shape are used to identify the specific geometry. This ray-based classification (RBC) has been empirically verified using a synthetic dataset of two- and three-dimensional shapes (Zwolak et al. in Proceedings of Third Workshop on Machine Learning and the Physical Sciences (NeurIPS 2020), Vancouver, Canada [December 11, 2020], arXiv:2010.00500, 2020) and, more recently, has also been validated experimentally (Zwolak et al., PRX Quantum 2:020335, 2021). Here, we establish a bound on the number of rays necessary for shape classification, defined by key angular metrics, for arbitrary convex shapes. For two dimensions, we derive a lower bound on the number of rays in terms of the shape's length, diameter, and exterior angles. For convex polytopes in ℝN, we generalize this result to a similar bound given as a function of the dihedral angle and the geometrical parameters of polygonal faces. This result enables a different approach for estimating high-dimensional shapes using substantially fewer data elements than volumetric or surface-based approaches.