, Volume 16, Issue 3–4, pp 351–361 | Cite as

A Robust Reduced Rank Graph Regression Method for Neuroimaging Genetic Analysis

  • Xiaofeng Zhu
  • Weihong Zhang
  • Yong Fan
  • Alzheimer’s Disease Neuroimaging Initiative
Original Article


To characterize associations between genetic and neuroimaging data, a variety of analytic methods have been proposed in neuroimaging genetic studies. These methods have achieved promising performance by taking into account inherent correlation in either the neuroimaging data or the genetic data alone. In this study, we propose a novel robust reduced rank graph regression based method in a linear regression framework by considering correlations inherent in neuroimaging data and genetic data jointly. Particularly, we model the association analysis problem in a reduced rank regression framework with the genetic data as a feature matrix and the neuroimaging data as a response matrix by jointly considering correlations among the neuroimaging data as well as correlations between the genetic data and the neuroimaging data. A new graph representation of genetic data is adopted to exploit their inherent correlations, in addition to robust loss functions for both the regression and the data representation tasks, and a square-root-operator applied to the robust loss functions for achieving adaptive sample weighting. The resulting optimization problem is solved using an iterative optimization method whose convergence has been theoretically proved. Experimental results on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset have demonstrated that our method could achieve competitive performance in terms of regression performance between brain structural measures and the Single Nucleotide Polymorphisms (SNPs), compared with state-of-the-art alternative methods.


Image-genetic analysis Variable selection Sparse learning Graph representation 



This work was supported in part by National Institutes of Health grants [EB022573, CA223358, DK114786, DA039215, and DA039002].


  1. Argyriou, A., Evgeniou, T., & Pontil, M. (2007). Multi-task feature learning. In B. Schölkopf, J. Platt, & T. Hoffman (Eds.), Advances in neural information processing systems (Vol. 19, pp. 41–48). Cambridge: MIT Press.Google Scholar
  2. Bertram, L., McQueen, M. B., Mullin, K., Blacker, D., & Tanzi, R. E. (2007). Systematic meta-analyses of Alzheimer disease genetic association studies: The AlzGene database. Nature Genetics, 39(1), 17–23.CrossRefPubMedGoogle Scholar
  3. Bettens, K., Sleegers, K., & Van Broeckhoven, C. (2013). Genetic insights in Alzheimer's disease. Lancet Neurology, 12(1), 92–104.CrossRefPubMedGoogle Scholar
  4. Chen, L. H., Kao, P. Y. P., Fan, Y. H., Ho, D. T. Y., Chan, C. S. Y., Yik, P. Y., Ha, J. C. T., Chu, L. W., & Song, Y.-Q. (2012). Polymorphisms of CR1, CLU and PICALM confer susceptibility of Alzheimer's disease in a southern Chinese population. Neurobiol Aging, 33(1), 210 e211–210. e217., 210.e1, 210.e7.CrossRefPubMedGoogle Scholar
  5. Chen, L., Pourahmadi, M., & Maadooliat, M. (2014). Regularized multivariate regression models with skew-t error distributions. Journal of Statistical Planning and Inference, 149, 125–139.CrossRefGoogle Scholar
  6. Corder, E., Saunders, A., Strittmatter, W., Schmechel, D., Gaskell, P., Small, G. a., Roses, A., Haines, J., & Pericak-Vance, M. A. (1993). Gene dose of apolipoprotein E type 4 allele and the risk of Alzheimer’s disease in late onset families. Science, 261(5123), 921–923.CrossRefPubMedGoogle Scholar
  7. Du, L., Liu, K., Zhang, T., Yao, X., Yan, J., Risacher, S. L., Han, J., Guo, L., Saykin, A. J., & Shen, L. (2017). A novel SCCA approach via truncated ℓ1-norm and truncated group lasso for brain imaging genetics. Bioinformatics.
  8. Fallin, D., Cohen, A., Essioux, L., Chumakov, I., Blumenfeld, M., Cohen, D., & Schork, N. J. (2001). Genetic analysis of case/control data using estimated haplotype frequencies: Application to APOE locus variation and Alzheimer's disease. Genome Res, 11(1), 143–151.CrossRefPubMedPubMedCentralGoogle Scholar
  9. Fan, Y., Shen, D., & Davatzikos, C. (2005). Classification of structural images via high-dimensional image warping, robust feature extraction and SVM. Med Image Comput Comput Assist Interv, 8(Pt 1), 1–8.PubMedGoogle Scholar
  10. Fan, Y., Shen, D., Gur, R. C., Gur, R. E., & Davatzikos, C. (2007). COMPARE: Classification of morphological patterns using adaptive regional elements. IEEE Trans Med Imaging, 26(1), 93–105.CrossRefPubMedGoogle Scholar
  11. Fan, Y., Shi, F., Smith, J. K., Lin, W., Gilmore, J. H., & Shen, D. (2011). Brain anatomical networks in early human brain development. Neuroimage, 54(3), 1862–1871.CrossRefPubMedGoogle Scholar
  12. Fu, L., Liu, L., Zhang, J., Xu, B., Fan, Y., & Tian, J. (2014). Comparison of dual-biomarker PIB-PET and dual-tracer PET in AD diagnosis. Eur Radiol, 24(11), 2800–2809.CrossRefPubMedGoogle Scholar
  13. Fu, L., Liu, L., Zhang, J., Xu, B., Fan, Y., & Tian, J. (2018). Brain network alterations in Alzheimer’s disease identified by early-phase PIB-PET. Contrast Media & Molecular Imaging, 2018, 10.CrossRefGoogle Scholar
  14. Ge, T., Schumann, G., & Feng, J. (2013). Imaging genetics — Towards discovery neuroscience. Quantitative Biology, 1(4), 227–245.CrossRefGoogle Scholar
  15. Greenlaw, K., Szefer, E., Graham, J., Lesperance, M., Nathoo, F. S., & Initi, A. s. D. N. (2017). A Bayesian group sparse multi-task regression model for imaging genetics. Bioinformatics, 33(16), 2513–2522.CrossRefPubMedPubMedCentralGoogle Scholar
  16. Hao, X. K., Yao, X. H., Yan, J. W., Risacher, S. L., Saykin, A. J., Zhang, D. Q., Shen, L., & Neuroimaging, A. s. D. (2016). Identifying multimodal intermediate phenotypes between genetic risk factors and disease status in Alzheimer's disease. Neuroinformatics, 14(4), 439–452.CrossRefPubMedPubMedCentralGoogle Scholar
  17. Harold, D., Abraham, R., Hollingworth, P., Sims, R., Gerrish, A., Hamshere, M. L., Pahwa, J. S., Moskvina, V., Dowzell, K., & Williams, A. (2009). Genome-wide association study identifies variants at CLU and PICALM associated with Alzheimer's disease. Nature Genetics, 41(10), 1088–1093.CrossRefPubMedPubMedCentralGoogle Scholar
  18. He, X., Cai, D., & Niyogi, P. (2006). Laplacian score for feature selection. Advances in Neural Information Processing Systems, 18, 507–514.Google Scholar
  19. Hibar, D. P., Stein, J. L., Renteria, M. E., et al. (2015). Common genetic variants influence human subcortical brain structures. Nature, 520(7546), 224–U216.CrossRefPubMedPubMedCentralGoogle Scholar
  20. Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55–67.CrossRefGoogle Scholar
  21. Holland, P. W., & Welsch, R. E. (1977). Robust regression using iteratively reweighted least-squares. Communications in Statistics-theory and Methods, 6(9), 813–827.CrossRefGoogle Scholar
  22. Hu, R., Zhu, X., Cheng, D., He, W., Yan, Y., Song, J., & Zhang, S. (2017). Graph self-representation method for unsupervised feature selection. Neurocomputing, 220, 130–137.CrossRefGoogle Scholar
  23. Huang, C., Thompson, P., Wang, Y., Yu, Y., Zhang, J., Kong, D., Colen, R. R., Knickmeyer, R. C., & Zhu, H. (2017). FGWAS: Functional genome wide association analysis. NeuroImage, 159(Supplement C), 107–121.CrossRefPubMedPubMedCentralGoogle Scholar
  24. Jack, C. R., Bernstein, M. A., Fox, N. C., Thompson, P., Alexander, G., Harvey, D., Borowski, B., Britson, P. J., Whitwell, J. L., & Ward, C. (2008). The Alzheimer's disease neuroimaging initiative (ADNI): MRI methods. Journal of Magnetic Resonance Imaging, 27(4), 685–691.CrossRefPubMedGoogle Scholar
  25. Kong, D., Giovanello, K. S., Wang, Y., Lin, W., Lee, E., Fan, Y., Doraiswamy, P. M., & Zhu, H. (2015). Predicting Alzheimer's disease using combined imaging-whole genome SNP data. Journal of Alzheimer's Disease, 46, 695–702.CrossRefPubMedGoogle Scholar
  26. Liu, L., J. J. Wang and Y. Fan (2014). Morphological and functional changes in the developing brain during childhood and Adolescence OHBM Annual Meeting. Hamburg, Germany.Google Scholar
  27. Liu, L., Fu, L., Zhang, X., Zhang, J., Zhang, X., Xu, B., Tian, J., & Fan, Y. (2015). Combination of dynamic (11)C-PIB PET and structural MRI improves diagnosis of Alzheimer's disease. Psychiatry Research, 233(2), 131–140.CrossRefPubMedGoogle Scholar
  28. Lu, Z. H., Khondker, Z., Ibrahim, J. G., Wang, Y., Zhu, H. T., & Initi, A. s. D. N. (2017). Bayesian longitudinal low-rank regression models for imaging genetic data from longitudinal studies. Neuroimage, 149, 305–322.CrossRefPubMedPubMedCentralGoogle Scholar
  29. Medland, S. E., Jahanshad, N., Neale, B. M., & Thompson, P. M. (2014). Whole-genome analyses of whole-brain data: Working within an expanded search space. Nature Neuroscience, 17(6), 791–800.CrossRefPubMedPubMedCentralGoogle Scholar
  30. Peng, H., & Fan, Y. (2016). Direct sparsity optimization based feature selection for multi-class classification. Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, pp. 1918–1924. New York: AAAI Press.Google Scholar
  31. Peng, H., & Fan, Y. (2017a). Feature selection by optimizing a lower bound of conditional mutual information. Information Sciences, 418, 652–667.CrossRefPubMedGoogle Scholar
  32. Peng, H. and Y. Fan (2017b). A general framework for sparsity regularized feature selection via iteratively reweighted Least Square minimization. AAAI.Google Scholar
  33. Reitz, C. (2012). Alzheimer’s disease and the amyloid cascade hypothesis: a critical review. International Journal of Alzheimer’s Disease, 2012.
  34. Reitz, C., Brayne, C., & Mayeux, R. (2011a). Epidemiology of Alzheimer disease. Nature Reviews Neurology, 7(3), 137–152.CrossRefPubMedPubMedCentralGoogle Scholar
  35. Reitz, C., Tokuhiro, S., Clark, L. N., Conrad, C., Vonsattel, J. P., Hazrati, L. N., Palotás, A., Lantigua, R., Medrano, M., & Jiménez-Velázquez, I. Z. (2011b). SORCS1 alters amyloid precursor protein processing and variants may increase Alzheimer's disease risk. Annals of Neurology, 69(1), 47–64.CrossRefPubMedPubMedCentralGoogle Scholar
  36. Rogaeva, E., Meng, Y., Lee, J. H., Gu, Y., Kawarai, T., Zou, F., Katayama, T., Baldwin, C. T., Cheng, R., & Hasegawa, H. (2007). The neuronal sortilin-related receptor SORL1 is genetically associated with Alzheimer’s disease. Nature Genetics, 39(2), 168–177.CrossRefPubMedPubMedCentralGoogle Scholar
  37. Schuff, N., N. Woerner, L. Boreta, T. Kornfield, L. Shaw, J. Trojanowski, P. Thompson, C. Jack Jr, M. Weiner, Alzheimer's and D. N. Initiative (2009). "MRI of hippocampal volume loss in early Alzheimer's disease in relation to ApoE genotype and biomarkers." Brain 132(4): 1067–1077.Google Scholar
  38. Thompson, P. M., Ge, T., Glahn, D. C., Jahanshad, N., & Nichols, T. E. (2013). Genetics of the connectome. Neuroimage, 80, 475–488.CrossRefPubMedPubMedCentralGoogle Scholar
  39. Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., & Joliot, M. (2002). Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage, 15(1), 273–289.CrossRefPubMedPubMedCentralGoogle Scholar
  40. Vounou, M., Nichols, T. E., Montana, G., & Initia, A. D. N. (2010). Discovering genetic associations with high-dimensional neuroimaging phenotypes: A sparse reduced-rank regression approach. Neuroimage, 53(3), 1147–1159.CrossRefPubMedPubMedCentralGoogle Scholar
  41. Vounou, M., Janousova, E., Wolz, R., Stein, J. L., Thompson, P. M., Rueckert, D., Montana, G., & Initia, A. D. N. (2012). Sparse reduced-rank regression detects genetic associations with voxel-wise longitudinal phenotypes in Alzheimer's disease. Neuroimage, 60(1), 700–716.CrossRefPubMedGoogle Scholar
  42. Wang, H., Nie, F., Huang, H., Risacher, S. L., Saykin, A. J., Shen, L., & Alzheimer's Dis Neuroimaging, I. (2012a). Identifying disease sensitive and quantitative trait-relevant biomarkers from multidimensional heterogeneous imaging genetics data via sparse multimodal multitask learning. Bioinformatics, 28(12), I127–I136.CrossRefPubMedPubMedCentralGoogle Scholar
  43. Wang, H., Nie, F. P., Huang, H., Yan, J. W., Kim, S., Nho, K., Risacher, S. L., Saykin, A. J., Shen, L., & Initi, A. s. D. N. (2012b). From phenotype to genotype: An association study of longitudinal phenotypic markers to Alzheimer's disease relevant SNPs. Bioinformatics, 28(18), I619–I625.CrossRefPubMedPubMedCentralGoogle Scholar
  44. Wen, Z., & Yin, W. (2013). A feasible method for optimization with orthogonality constraints. Math Program, 142(1–2), 397–434.CrossRefGoogle Scholar
  45. Zhang, D. Q., Wang, Y. P., Zhou, L. P., Yuan, H., Shen, D. G., & Initia, A. D. N. (2011). Multimodal classification of Alzheimer's disease and mild cognitive impairment. Neuroimage, 55(3), 856–867.CrossRefPubMedPubMedCentralGoogle Scholar
  46. Zhang, D. Q., Shen, D. G., & Neuroimaging, A. s. D. (2012). Multi-modal multi-task learning for joint prediction of multiple regression and classification variables in Alzheimer's disease. Neuroimage, 59(2), 895–907.CrossRefPubMedGoogle Scholar
  47. Zhang, Y., Caspers, S., Fan, L. Z., Fan, Y., Song, M., Liu, C. R., Mo, Y., Roski, C., Eickhoff, S., Amunts, K., & Jiang, T. Z. (2015). Robust brain parcellation using sparse representation on resting-state fMRI. Brain Structure and Function, 220(6), 3565–3579.CrossRefPubMedGoogle Scholar
  48. Zheng, W., Zhu, X., Zhu, Y., Hu, R., & Lei, C. (2017). Dynamic graph learning for spectral feature selection. Multimedia Tools and Applications, 1–17.Google Scholar
  49. Zhu, X., Li, X., Zhang, S., Ju, C., & Wu, X. (2017a). Robust joint graph sparse coding for unsupervised spectral feature selection. IEEE transactions on neural networks and learning systems, 28(6), 1263–1275.CrossRefPubMedGoogle Scholar
  50. Zhu, X., Suk, H. I., Huang, H., & Shen, D. (2017b). Low-rank graph-regularized structured sparse regression for identifying genetic biomarkers. IEEE Transactions on Big Data PP(99), 1–1.Google Scholar
  51. Zhu, X., Zhang, S., Hu, R., & Zhu, Y. (2018). Local and global structure preservation for robust unsupervised spectral feature selection. IEEE Transactions on Knowledge and Data Engineering, 30(3), 517–529.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Radiology, Perelman School of MedicineUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Peking Union Medical College HospitalBeijingChina

Personalised recommendations