



@article {2765,
	title = {Theoretical bounds on data requirements for the ray-based classification},
	journal = {SN Comput. Sci.},
	volume = {3},
	year = {2022},
	month = {02/26/2022},
	abstract = {<p>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 [1] and, more recently, has also been validated experimentally [2]. 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\&$\#$39;s length, diameter, and exterior angles. For convex polytopes in R^N, 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.</p>},
	doi = {https://doi.org/10.1007/s42979-021-00921-0},
	url = {https://arxiv.org/abs/2103.09577},
	author = {Brian J. Weber and Sandesh S. Kalantre and Thomas McJunkin and J. M. Taylor and Justyna P. Zwolak}
}
@article {2685,
	title = {Ray-based classification framework for high-dimensional data},
	journal = {Proceedings of the Machine Learning and the Physical Sciences Workshop at NeurIPS 2020, Vancouver, Canada},
	year = {2020},
	month = {10/1/2020},
	abstract = {<p>While classification of arbitrary structures in high dimensions may require complete quantitative information, for simple geometrical structures, low-dimensional qualitative information about the boundaries defining the structures can suffice. Rather than using dense, multi-dimensional data, we propose a deep neural network (DNN) classification framework that utilizes a minimal collection of one-dimensional representations, called \emph{rays}, to construct the \&quot;fingerprint\&quot; of the structure(s) based on substantially reduced information. We empirically study this framework using a synthetic dataset of double and triple quantum dot devices and apply it to the classification problem of identifying the device state. We show that the performance of the ray-based classifier is already on par with traditional 2D images for low dimensional systems, while significantly cutting down the data acquisition cost.</p>},
	url = {https://arxiv.org/abs/2010.00500},
	author = {Justyna P. Zwolak and Sandesh S. Kalantre and Thomas McJunkin and Brian J. Weber and J. M. Taylor}
}
