2016/02/11 by Robert A. Murphy, Murphy, Robert A.
Computer Science · #60D05 #62C99 #FOS: Computer and information sciences #Machine Learning (cs.LG) #cs.LG #msc:60D05 #msc:62C99
paper · pdf · doi:10.48550/arxiv.1602.03822
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(arXiv:1412.4178) and "Estimating the Mean Number of K-Means Clusters to Form" (arXiv:1503.03488), which have all been withdrawn
arxiv created 2021/09/05 · arxiv updated 2021/09/07
Motivated by a 2-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, 2-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".