Classifying Histograms of Medical Data Using Information Geometry of Beta Distributions

In this paper, we use tools of information geometry to compare, average andclassify histograms. Beta distributions are fitted to the histograms and thecorresponding Fisher information geometry is used for comparison. We show thatthis geometry is negatively curved, which guarantees uniqueness of the notionof mean, and makes it suitable to classify histograms through the popularK-means algorithm. We illustrate the use of these geometric tools in supervisedand unsupervised classification procedures of two medical data-sets, cardiacshape deformations for the detection of pulmonary hypertension and braincortical thickness for the diagnosis of Alzheimer's disease.