# American Institute of Mathematical Sciences

2016, 13(6): 1119-1130. doi: 10.3934/mbe.2016033

## Classification of Alzheimer's disease using unsupervised diffusion component analysis

 1 Laboratory of Neuro Imaging, USC Stevens Neuroimaging and Informatics Institute, Keck School of Medicine of USC, University of Southern California, United States 2 Department of Mathematics, University of California, Davis, United States

Received  October 2015 Revised  April 2016 Published  August 2016

The goal of this study is automated discrimination between early stage Alzheimer$'$s disease (AD) magnetic resonance imaging (MRI) and healthy MRI data. Unsupervised Diffusion Component Analysis, a novel approach based on the diffusion mapping framework, reduces data dimensionality and provides pattern recognition that can be used to distinguish AD brains from healthy brains. The new algorithm constructs coordinates as an extension of diffusion maps and generates efficient geometric representations of the complex structure of the MRI data. The key difference between our method and others used to classify and detect AD early in its course is our nonlinear and local network approach, which overcomes calibration differences among different scanners and centers collecting MRI data and solves the problem of individual variation in brain size and shape. In addition, our algorithm is completely automatic and unsupervised, which could potentially be a useful and practical tool for doctors to help identify AD patients.
Citation: Dominique Duncan, Thomas Strohmer. Classification of Alzheimer's disease using unsupervised diffusion component analysis. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1119-1130. doi: 10.3934/mbe.2016033
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