Classification of Alzheimer's disease using unsupervised diffusion component analysis

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Mathematical methods in systems biology

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

Classification of Alzheimer's disease using unsupervised diffusion component analysis

Dominique Duncan ^1, and Thomas Strohmer ^2,

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

Abstract
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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.

Keywords: manifold learning, kernel methods., diffusion maps, MRI, Alzheimer's disease.

Mathematics Subject Classification: 68T10, 65F15, 92B99, 92C20, 00A6.

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.
[2]	N. Ahmed, T. Natarajan and K. R. Rao, Discrete cosine transform, IEEE Transactions on Computers, 23 (1974), 90-93. doi: 10.1109/T-C.1974.223784.
[3]	R. R. Coifman and S. Lafon, Diffusion maps, Appl. Comp. Harm. Anal., 21 (2006), 5-30. doi: 10.1016/j.acha.2006.04.006.
[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), 579-590. doi: 10.3934/mbe.2013.10.579.
[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), 53-67.
[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), e597. doi: 10.1371/journal.pone.0000597.
[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), e159. doi: 10.1371/journal.pbio.0060159.
[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), 788-794. doi: 10.1016/S1474-4422(14)70136-X.
[9]	C. Syms, Principal components analysis, Reference Module in Earth Systems and Environmental Sciences Encyclopedia of Ecology, (2008), 2940-2949. doi: 10.1016/B978-008045405-4.00538-3.
[10]	R. C. Petersen, Mild cognitive impairment clinical trials, Nature Reviews Drug Discovery, 2 (2003), 646-653. doi: 10.1038/nrd1155.
[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), 59-66. doi: 10.1109/ICCV.1998.710701.
[12]	R. Talmon and R. R. Coifman, Differential stochastic sensing: intrinsic modeling of random time series with applications to nonlinear tracking, PNAS, (2012), 1-14.
[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), 1159-1173. doi: 10.1109/TSP.2011.2177973.
[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), 775-783.
[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), 1-12.

show all references

References:

[1]	, Alzheimer's Association: Alzheimer's disease facts and figures., Alzheimer's & Dementia, 9 (2013), 208.
[2]	N. Ahmed, T. Natarajan and K. R. Rao, Discrete cosine transform, IEEE Transactions on Computers, 23 (1974), 90-93. doi: 10.1109/T-C.1974.223784.
[3]	R. R. Coifman and S. Lafon, Diffusion maps, Appl. Comp. Harm. Anal., 21 (2006), 5-30. doi: 10.1016/j.acha.2006.04.006.
[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), 579-590. doi: 10.3934/mbe.2013.10.579.
[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), 53-67.
[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), e597. doi: 10.1371/journal.pone.0000597.
[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), e159. doi: 10.1371/journal.pbio.0060159.
[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), 788-794. doi: 10.1016/S1474-4422(14)70136-X.
[9]	C. Syms, Principal components analysis, Reference Module in Earth Systems and Environmental Sciences Encyclopedia of Ecology, (2008), 2940-2949. doi: 10.1016/B978-008045405-4.00538-3.
[10]	R. C. Petersen, Mild cognitive impairment clinical trials, Nature Reviews Drug Discovery, 2 (2003), 646-653. doi: 10.1038/nrd1155.
[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), 59-66. doi: 10.1109/ICCV.1998.710701.
[12]	R. Talmon and R. R. Coifman, Differential stochastic sensing: intrinsic modeling of random time series with applications to nonlinear tracking, PNAS, (2012), 1-14.
[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), 1159-1173. doi: 10.1109/TSP.2011.2177973.
[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), 775-783.
[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), 1-12.

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