Viewers and readers my wonder why an academic paper on optimizing lossy compression of data is on a site about history and Islam. In this paper, Dr. Peter Harremoës uses Gibson’s Mosque Database to demonstrate how mathematics can be used to pinpoint the spot that was aimed at, even though the target locations are all scattered. Some of you will find Dr. Harremoës’s historical application of Rate distortion theory interesting.
To read the paper, click on this link: Rate_Distortion_Theory_for_Descriptive_Statistics.pdf
Dr. Harremoes demonstrated how mosques face close to Petra.
Abstract:
Rate distortion theory was developed for optimizing lossy compression of data, but it also has applications in statistics. In this paper, we illustrate how rate distortion theory can be used to analyze various datasets. The analysis involves testing, identification of outliers, choice of compression rate, calculation of optimal reconstruction points, and assigning “descriptive confidence regions” to the reconstruction points. We study four models or datasets of increasing complexity: clustering, Gaussian models, linear regression, and a dataset describing orientations of early Islamic mosques. These examples illustrate how rate distortion analysis may serve as a common framework for handling different statistical problems.
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