基于β分布信息几何的医学数据直方图分类
Classifying histograms of medical data using information geometry of beta distributions
摘要：
在本文中，我们使用信息几何的工具，比较，平均和分类直方图。将β分布拟合到直方图，并使用相应的费舍尔信息几何结构进行比较。我们表明，这种几何形状是负弯曲的，这保证了唯一的平均值的概念，并使其适合通过流行的K-均值算法对直方图进行分类。我们说明了使用这些几何工具的监督和无监督的分类程序的两个医疗数据集，心脏形状变形检测肺动脉高压和脑皮质厚度诊断阿尔茨海默氏病。
英文摘要：
In this paper, we use tools of information geometry to compare, average and classify histograms. Beta distributions are fitted to the histograms and the corresponding Fisher information geometry is used for comparison. We show that this geometry is negatively curved, which guarantees uniqueness of the notion of mean, and makes it suitable to classify histograms through the popular K-means algorithm. We illustrate the use of these geometric tools in supervised and unsupervised classification procedures of two medical data-sets, cardiac shape deformations for the detection of pulmonary hypertension and brain cortical thickness for the diagnosis of Alzheimer's disease.
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