A Critical Connectivity Radius for Segmenting Randomly-Generated, High Dimensional Data Points
Abstract
Motivated by a -dimensional (unsupervised) image segmentation task whereby local regions of pixels are clustered via edge detection methods, a more general probabilistic mathematical framework is devised. Critical thresholds are calculated that indicate strong correlation between randomly-generated, high dimensional data points that have been projected into structures in a partition of a bounded, -dimensional area, of which, an image is a special case. A neighbor concept for structures in the partition is defined and a critical radius is uncovered. Measured from a central structure in localized regions of the partition, the radius indicates strong, long and short range correlation in the count of occupied structures. The size of a short interval of radii is estimated upon which the transition from short-to-long range correlation is virtually assured, which defines a demarcation of when an image ceases to be "interesting".
Cite
@article{arxiv.1602.03822,
title = {A Critical Connectivity Radius for Segmenting Randomly-Generated, High Dimensional Data Points},
author = {Robert A. Murphy},
journal= {arXiv preprint arXiv:1602.03822},
year = {2021}
}
Comments
This paper is a combined replacement for the papers "A Neural Network Anomaly Detector using the Random Cluster Model" (arXiv:1501.07227), "On the Sharp Threshold Interval Length of Partially Connected Random Geometric Graphs During K-Means Classification" (arXiv:1412.4178) and "Estimating the Mean Number of K-Means Clusters to Form" (arXiv:1503.03488), which have all been withdrawn