Abstract
The Fisher information metric provides a smooth family of probability measures with a Riemannian manifold structure, which is an object in information geometry. The information geometry of the gamma manifold associated with the family of gamma distributions has been well studied. However, only a few results are known for the generalized gamma family that adds an extra shape parameter. The present article gives some new results about the generalized gamma manifold. This paper also introduces an application in medical imaging that is the classification of Alzheimer’s disease population. In the medical field, over the past two decades, a growing number of quantitative image analysis techniques have been developed, including histogram analysis, which is widely used to quantify the diffuse pathological changes of some neurological diseases. This method presents several drawbacks. Indeed, all the information included in the histogram is not used and the histogram is an overly simplistic estimate of a probability distribution. Thus, in this study, we present how using information geometry and the generalized gamma manifold improved the performance of the classification of Alzheimer’s disease population.
Highlights
In the medical field, the use of medical imaging techniques, such as Magnetic Resonance Imaging (MRI), is important for measuring brain activity in different parts of the anatomy of the central nervous system
The Fisher information metric provides a smooth family of probability measures with a Riemannian manifold structure, which is an object in information geometry
This paper introduces an application in medical imaging that is the classification of Alzheimer’s disease population
Summary
The use of medical imaging techniques, such as Magnetic Resonance Imaging (MRI), is important for measuring brain activity in different parts of the anatomy of the central nervous system. This technique is of major interest in the context of neurodegenerative diseases such as Alzheimer’s disease [1,2,3]. Previous works have already studied measures of central tendency of biomarkers of the brain activity These are implemented in a statistical data analysis, such as classification algorithms for detecting changes in the pathological disease. A clustering technique has been successfully extended by using a geodesic distance of which an approximation is computed in two steps for numerical considerations
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