ISOMAP induced manifold embedding and its application to Alzheimer's disease and mild cognitive impairment.

Neuroimaging data are high dimensional and thus cumbersome to analyze. Manifold learning is a technique to find a low dimensional representation for high dimensional data. With manifold learning, data analysis becomes more tractable in the low dimensional space. We propose a novel shape quantification method based on a manifold learning method, ISOMAP, for brain MRI. Existing work applied another manifold learning method, multidimensional scaling (MDS), to quantify shape information for distinguishing Alzheimer's disease (AD) from normal. We enhance the existing methodology by (1) applying it to distinguish mild cognitive impairment (MCI) from normal, (2) adopting a more advanced manifold learning technique, ISOMAP, and (3) showing the effectiveness of the induced low dimensional embedding space to predict key clinical variables such as mini mental state exam scores and clinical diagnosis using the standard multiple linear regression. Our methodology was tested using 25 normal, 25 AD, and 25 MCI patients.