# 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
##### References:
 [1] , Alzheimer's Association: Alzheimer's disease facts and figures., Alzheimer's & Dementia, 9 (2013), 208. Google Scholar [2] N. Ahmed, T. Natarajan and K. R. Rao, Discrete cosine transform,, IEEE Transactions on Computers, 23 (1974), 90. doi: 10.1109/T-C.1974.223784. Google Scholar [3] R. R. Coifman and S. Lafon, Diffusion maps,, Appl. Comp. Harm. Anal., 21 (2006), 5. doi: 10.1016/j.acha.2006.04.006. Google Scholar [4] D. Duncan, R. Talmon, H. P. Zaveri and R. R. Coifman, Identifying preseizure state in intracranial EEG data using diffusion kernels,, Math Biosci Eng, 10 (2013), 579. doi: 10.3934/mbe.2013.10.579. Google Scholar [5] C. Habeck and Y. Stern, Alzheimer's disease neuroimaging initiative, Multivariate data analysis for neuroimaging data: Overview and application to Alzheimer's disease,, Cell Biochem Biophys., 58 (2010), 53. Google Scholar [6] P. Hagmann, M. Kurant, X. Gigandet, P. Thiran, V. J. Wedeen, R. Meuli and J.-P. Thiran, Mapping human whole-brain structural networks with diffusion MRI,, PLoS ONE, 2 (2007). doi: 10.1371/journal.pone.0000597. Google Scholar [7] P. Hagmann, L. Cammoun, X. Gigandet, R. Meuli, C. J. Honey, V. J. Wedeen and O. Sporns, Mapping the structural core of human cerebral cortex,, PLoS Biol, 6 (2008). doi: 10.1371/journal.pbio.0060159. Google Scholar [8] S. Norton, F. E. Matthews, D. Barnes, K. Yaffe and C. Brayne, Potential for primary prevention of Alzheimer's disease: an analysis of population-based data,, Lancet Neurology, 13 (2014), 788. doi: 10.1016/S1474-4422(14)70136-X. Google Scholar [9] C. Syms, Principal components analysis,, Reference Module in Earth Systems and Environmental Sciences Encyclopedia of Ecology, (2008), 2940. doi: 10.1016/B978-008045405-4.00538-3. Google Scholar [10] R. C. Petersen, Mild cognitive impairment clinical trials,, Nature Reviews Drug Discovery, 2 (2003), 646. doi: 10.1038/nrd1155. Google Scholar [11] Y. Rubner, C. Tomasi and L. J. Guibas, A metric for distributions with applications to image databases,, IEEE 6th International Conference on Computer Vision, (1998), 59. doi: 10.1109/ICCV.1998.710701. Google Scholar [12] R. Talmon and R. R. Coifman, Differential stochastic sensing: intrinsic modeling of random time series with applications to nonlinear tracking,, PNAS, (2012), 1. Google Scholar [13] R. Talmon, D. Kushnir, R. R. Coifman, I. Cohen and S. Gannot, Parametrization of linear systems using diffusion kernels,, IEEE Transactions on Signal Processing, 60 (2012), 1159. doi: 10.1109/TSP.2011.2177973. Google Scholar [14] W. Yang, R. L. Lui, J. H. Gao, T. F. Chan, S. T. Yau, R. A. Sperling and X. Huang, Independent component analysis-based classification of Alzheimer's disease MRI data,, J. Alzheimers Dis, 24 (2011), 775. Google Scholar [15] J. Ye, M. Farnum, E. Yang, R. Verbeeck, V. Lobanov, N. Raghavan, G. Novak, A. DiBernardo and V. A. Narayan, Sparse learning and stability selection for predicting MCI to AD conversion using baseline ADNI data,, BMC Neurology, 12 (2012), 1. Google Scholar

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##### References:
 [1] , Alzheimer's Association: Alzheimer's disease facts and figures., Alzheimer's & Dementia, 9 (2013), 208. Google Scholar [2] N. Ahmed, T. Natarajan and K. R. Rao, Discrete cosine transform,, IEEE Transactions on Computers, 23 (1974), 90. doi: 10.1109/T-C.1974.223784. Google Scholar [3] R. R. Coifman and S. Lafon, Diffusion maps,, Appl. Comp. Harm. Anal., 21 (2006), 5. doi: 10.1016/j.acha.2006.04.006. Google Scholar [4] D. Duncan, R. Talmon, H. P. Zaveri and R. R. Coifman, Identifying preseizure state in intracranial EEG data using diffusion kernels,, Math Biosci Eng, 10 (2013), 579. doi: 10.3934/mbe.2013.10.579. Google Scholar [5] C. Habeck and Y. Stern, Alzheimer's disease neuroimaging initiative, Multivariate data analysis for neuroimaging data: Overview and application to Alzheimer's disease,, Cell Biochem Biophys., 58 (2010), 53. Google Scholar [6] P. Hagmann, M. Kurant, X. Gigandet, P. Thiran, V. J. Wedeen, R. Meuli and J.-P. Thiran, Mapping human whole-brain structural networks with diffusion MRI,, PLoS ONE, 2 (2007). doi: 10.1371/journal.pone.0000597. Google Scholar [7] P. Hagmann, L. Cammoun, X. Gigandet, R. Meuli, C. J. Honey, V. J. Wedeen and O. Sporns, Mapping the structural core of human cerebral cortex,, PLoS Biol, 6 (2008). doi: 10.1371/journal.pbio.0060159. Google Scholar [8] S. Norton, F. E. Matthews, D. Barnes, K. Yaffe and C. Brayne, Potential for primary prevention of Alzheimer's disease: an analysis of population-based data,, Lancet Neurology, 13 (2014), 788. doi: 10.1016/S1474-4422(14)70136-X. Google Scholar [9] C. Syms, Principal components analysis,, Reference Module in Earth Systems and Environmental Sciences Encyclopedia of Ecology, (2008), 2940. doi: 10.1016/B978-008045405-4.00538-3. Google Scholar [10] R. C. Petersen, Mild cognitive impairment clinical trials,, Nature Reviews Drug Discovery, 2 (2003), 646. doi: 10.1038/nrd1155. Google Scholar [11] Y. Rubner, C. Tomasi and L. J. Guibas, A metric for distributions with applications to image databases,, IEEE 6th International Conference on Computer Vision, (1998), 59. doi: 10.1109/ICCV.1998.710701. Google Scholar [12] R. Talmon and R. R. Coifman, Differential stochastic sensing: intrinsic modeling of random time series with applications to nonlinear tracking,, PNAS, (2012), 1. Google Scholar [13] R. Talmon, D. Kushnir, R. R. Coifman, I. Cohen and S. Gannot, Parametrization of linear systems using diffusion kernels,, IEEE Transactions on Signal Processing, 60 (2012), 1159. doi: 10.1109/TSP.2011.2177973. Google Scholar [14] W. Yang, R. L. Lui, J. H. Gao, T. F. Chan, S. T. Yau, R. A. Sperling and X. Huang, Independent component analysis-based classification of Alzheimer's disease MRI data,, J. Alzheimers Dis, 24 (2011), 775. Google Scholar [15] J. Ye, M. Farnum, E. Yang, R. Verbeeck, V. Lobanov, N. Raghavan, G. Novak, A. DiBernardo and V. A. Narayan, Sparse learning and stability selection for predicting MCI to AD conversion using baseline ADNI data,, BMC Neurology, 12 (2012), 1. Google Scholar
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