no code implementations • 9 Apr 2021 • Robert A. Murphy
Random field and random cluster theory are used to describe certain mathematical results concerning the probability distribution of image pixel intensities characterized as generic $2D$ integer arrays.
no code implementations • 14 Nov 2019 • Robert A. Murphy
We started with a knowledge graph of connected entities and descriptive properties of those entities, from which, a hierarchical representation of the knowledge graph is derived.
no code implementations • 1 Apr 2017 • Robert A. Murphy
As the title suggests, we will describe (and justify through the presentation of some of the relevant mathematics) prediction methodologies for sensor measurements.
no code implementations • 11 Feb 2016 • Robert A. Murphy
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.
no code implementations • 8 Jan 2016 • Robert A. Murphy
Given a data set of numerical values which are sampled from some unknown probability distribution, we will show how to check if the data set exhibits the Markov property and we will show how to use the Markov property to predict future values from the same distribution, with probability 1.
no code implementations • 7 Mar 2015 • Robert A. Murphy
Utilizing the sample size of a dataset, the random cluster model is employed in order to derive an estimate of the mean number of K-Means clusters to form during classification of a dataset.
no code implementations • 28 Jan 2015 • Robert A. Murphy
The random cluster model is used to define an upper bound on a distance measure as a function of the number of data points to be classified and the expected value of the number of classes to form in a hybrid K-means and regression classification methodology, with the intent of detecting anomalies.