Abstract
Brain imaging genetics attracts more and more attention since it can reveal associations between genetic factors and the structures or functions of human brain. Sparse canonical correlation analysis (SCCA) is a powerful bi-multivariate association identification technique in imaging genetics. There have been many SCCA methods which could capture different types of structured imaging genetic relationships. These methods either use the group lasso to recover the group structure, or employ the graph/network guided fused lasso to find out the network structure. However, the group lasso methods have limitation in generalization because of the incomplete or unavailable prior knowledge in real world. The graph/network guided methods are sensitive to the sign of the sample correlation which may be incorrectly estimated. We introduce a new SCCA model using a novel graph guided pairwise group lasso penalty, and propose an efficient optimization algorithm. The proposed method has a strong upper bound for the grouping effect for both positively and negatively correlated variables. We show that our method performs better than or equally to two state-of-the-art SCCA methods on both synthetic and real neuroimaging genetics data. In particular, our method identifies stronger canonical correlations and captures better canonical loading profiles, showing its promise for revealing biologically meaningful imaging genetic associations.
L. Shen—This work was supported by NSFC under Grant 61602384, and the Fundamental Research Funds for the Central Universities under Grant 3102016OQD0065. This work was also supported by NIH R01 EB022574, R01 LM011360, U01 AG024904, P30 AG10133, R01 AG19771, UL1 TR001108, R01 AG 042437, R01 AG046171, and R01 AG040770, by DoD W81XWH-14-2-0151, W81XWH-13-1-0259, W81XWH-12-2-0012, and NCAA 14132004.
Data used in preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf.
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Notes
- 1.
Each \(u_i\) can be solved with \(u_j\)’s (\(j \ne i\)) fixed (i.e., we use \(u_j^t\) to approximate \(u_j^{t+1}\) in C), thus \(u_j\)’s do not contribute to the optimization of \(u_i\) [9].
- 2.
Note that an element of diagonal matrix \(\mathbf {D}_1\) will nonexist if \(\sqrt{u_i^2+u_{k_1}^2}=0\). We handle this issue by regularizing it as \(\sqrt{u_i^2+u_{k_1}^2+\zeta }\) with \(\zeta \) being a tiny positive number. Then the objective function regarding \(\mathbf {u}\) becomes \(\mathbf {\tilde{\mathcal {L}}(u)} = \sum _{i=1}^p (-u_i \mathbf {x}_{i}^T \mathbf {Y} \mathbf {v} + \lambda _1\sum _{k_1}\sqrt{u_i^2+u_{k_1}^2+\zeta } +\frac{\gamma _1}{2}||\mathbf {x}_{i}u_i||_{2}^{2})\). We can prove that \(\tilde{\mathcal {L}}(\mathbf {u})\) will reduce to the original problem (3) when \(\zeta \) approaching zero. Likewise, \(\sqrt{v_j^2+v_{k_2}^2}=0\) can be regularized by the same method.
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Du, L. et al. (2017). Identifying Associations Between Brain Imaging Phenotypes and Genetic Factors via a Novel Structured SCCA Approach. In: Niethammer, M., et al. Information Processing in Medical Imaging. IPMI 2017. Lecture Notes in Computer Science(), vol 10265. Springer, Cham. https://doi.org/10.1007/978-3-319-59050-9_43
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