 Methodology
 Open access
 Published:
Identification of multimodal brain imaging association via a parameter decomposition based sparse multiview canonical correlation analysis method
BMC Bioinformatics volumeÂ 23, ArticleÂ number:Â 128 (2022)
Abstract
Background
With the development of noninvasive imaging technology, collecting different imaging measurements of the same brain has become more and more easy. These multimodal imaging data carry complementary information of the same brain, with both specific and shared information being intertwined. Within these multimodal data, it is essential to discriminate the specific information from the shared information since it is of benefit to comprehensively characterize brain diseases. While most existing methods are unqualified, in this paper, we propose a parameter decomposition based sparse multiview canonical correlation analysis (PDSMCCA) method. PDSMCCA could identify both modalityshared and specific information of multimodal data, leading to an indepth understanding of complex pathology of brain disease.
Results
Compared with the SMCCA method, our method obtains higher correlation coefficients and better canonical weights on both synthetic data and real neuroimaging data. This indicates that, coupled with modalityshared and specific feature selection, PDSMCCA improves the multiview association identification and shows meaningful feature selection capability with desirable interpretation.
Conclusions
The novel PDSMCCA confirms that the parameter decomposition is a suitable strategy to identify both modalityshared and specific imaging features. The multimodal association and the diverse information of multimodal imaging data enable us to better understand the brain disease such as Alzheimerâ€™s disease.
Background
Alzheimerâ€™s Disease (AD) [1,2,3,4,5], the most common type of dementia, is a terrible neurodegenerative but its pathology is still unclear. And with the advance of imaging technologies, we can obtain multimodal imaging data of brain structure and function easily [6]. For example, the structural changes of the brain can be measured by structural magnetic resonance imaging (sMRI) scans, and the positron emission tomography (PET) scans can capture the brain activities such as the metabolic rate of glucose (FDGPET) and amyloid depositions (AV45PET) [7,8,9,10]. These different types of imaging data, including both modalityshared and specific information, are collected simultaneously. As a result, it is essential to discriminate the modalityspecific information from the modalityshared information, which could enable a better understanding of multimodal data and prompt reasonable multimodal brain imaging data integration [11,12,13,14,15,16,17].
The statistical pairwise correlation analysis has been widely used for medical image analysis. For example, researchers use both PET and functional magnetic resonance imaging(fMRI) data to study the relationship between brain and genes metabolism indicators [18]. With the deepening of research, researchers begin to use machine learning instead to focus on prediction tasks. However, they ignore the complex relationships in multimodal data. In contrast, exploring the correlation between multimodal brain imaging helps to reveal the pathogenesis of AD, thereby promotes the advancement of early diagnosis technology of the disease and the development of pharmaceutical research.
The existing correlation methods are mostly designed for two views [19, 20]. For instance, sparse canonical correlation analysis (SCCA) [21,22,23,24,25,26,27] has been widely used in brain imaging analysis. However, they cannot analyze multimodal imaging in a unified model. Although the multistep strategy can be used to analyze the pairwise association between multiple modalities [2], it will inevitably cause the loss of potentially effective information. Thus these methods are suboptimal. In order to analyze more than two modalities, SCCA can be directly and simply extended to multiview paradigm [28] which has gained a lot of attentions. For example, based on sparse multiple/multiview/multiset canonical correlation analysis (SMCCA) [28, 29], researchers explored the association between multiview data sets such as brain imaging data, genetic data and cognitive scores [30, 31]. However, SMCCA suffers from serious shortcomings which limit its application. First and foremost, SMCCA employs the \(\ell _{1}\)norm, and thus cannot clearly report the modalityshared and specific imaging features due to its overlook of the shared features of multiple modalities. In addition, the independent assumption of the inset covariance of SMCCA makes the Pearson correlation coefficient break the range of \([1,1]\), and there is no measure to avoid the additional risk caused by this assumption. According to [27], this independent assumption may not guarantee the convergence and consistency. Therefore, SMCCA is insufficient and inadequate in multimodal brain imaging analysis problem.
With above observations, to better identify the complex multiway correlations among multimodal imaging data, we propose a novel sparse multiview canonical correlation analysis (PDSMCCA) method based on the parameter decomposition. On the one hand, to improve interpretability, PDSMCCA contains two types of regularization(\(\ell _{1}\)norm and \(\ell _{2,1}\)norm). The \(\ell _{1}\)norm penalizes each imaging feature of each modality separately [32], and \(\ell _{2,1}\)norm penalizes imaging features of multiple modalities jointly to obtain the modalityshared features [33, 34]. Using \(\ell _{1}\)norm and \(\ell _{2,1}\)norm together could offer a diverse feature selection. On the other hand, PDSMCCA decomposes the canonical weight into viewshared and private components, which correspond to the modalityshared and specific imaging features respectively. Owing to the decomposition strategy, PDSMCCA is able to obtain flexible imaging features. In addition, we relax the independent assumption of traditional SMCCA which treats the inset covariance \({\mathbf {X}}^\top {\mathbf {X}}\) to be an identify [23]. Moreover, we introduce an efficient algorithm to solve the PDSMCCA model which converges to a local optimum. The results on synthetic data and real neuroimaging data show that, compared with the SMCCA method, our method obtains better or comparable canonical correlation coefficients (CCCs) and canonical weights. This indicates that our method is a powerful tool for multimodal brain imaging data association identification with diverse and desirable feature selection.
The contents of this article are arranged as follows. First, the SMCCA method is briefly introduced. Then, we describe the PDSMCCA in detail. Furthermore, we present the iterative optimization algorithm and prove its convergence, which is followed by experiments and results. Finally, the discussion and conclusion are provided.
Experimental results
We use synthetic data and real data to evaluate the performance of our method and employ the stateoftheart method (SMCCA) as the benchmark method. The experiment adopts the nested fivefold crossvalidation and the grid search strategy to tune suitable \(\lambda _B\) and \(\lambda _S\), and the candidate parameter set is [0.01,Â 0.1,Â 1,Â 10,Â 100] which makes an appropriate feature selection since too large parameters and too small ones could incur undesirable features of interest. Besides, all methods are terminated when \(\max ({\mathbf {b}}_k+{\mathbf {s}}_k)^{t+1}({\mathbf {b}}_k+{\mathbf {s}}_k)^t \le 10^{5}\) is met. The canonical correlation coefficient (CCC) and the feature selection (heatmap) are utilized as the evaluation criteria. The CCC is defined as
where \({\mathbf {X}}\) assumed to have been centered (zero mean), and \({\mathbf {v}}\) = \({\mathbf {b}} + {\mathbf {s}}\). For CCC, a larger score indicates a better performance of identifying the biassociations among multiple modalities.
Results on synthetic data
In this simulation study, we use two synthetic data sets which contain different ground truth and noise intensity. We first generate three canonical weight vectors \({\mathbf {v}}_j \in {\mathbb {R}}^{200 \times 1}\) and a latent vector \(\mu\) with unit norm. The data matrix \({\mathbf {X}}_k\) is generated by \(({\mathbf {x}}_{i,j})_k \sim N(\mu _i{\mathbf {v}}_{j,k}, e \cdot {\mathbf {I}}_{200 \times 200})\), where e denotes the noise level.

Data 1: \(n = 120\), \({\mathbf {v}}_1=(\underbrace{0,...,0}_{80}, \underbrace{1,...,1}_{40}, \underbrace{0,...,0}_{80})^\top\), \({\mathbf {v}}_2=(\underbrace{0,...,0}_{80}, \underbrace{2,...,2}_{40}, \underbrace{0,...,0}_{80})^\top\), \({\mathbf {v}}_3=(\underbrace{0,...,0}_{80}, \underbrace{1,...,1}_{40}, \underbrace{0,...,0}_{80})^\top\).

Data 2: \(n = 120\), \({\mathbf {v}}_1=(\underbrace{0,...,0}_{75}, \underbrace{1,...,1}_{60}, \underbrace{0,...,0}_{65})^\top\), \({\mathbf {v}}_2=(\underbrace{0,...,0}_{40}, \underbrace{2,...,2}_{60}, \underbrace{0,...,0}_{40}, \underbrace{2,...,2}_{30}, \underbrace{0,...,0}_{30})^\top\), \({\mathbf {v}}_3=(\underbrace{0,...,0}_{70}, \underbrace{2,...,2}_{50}, \underbrace{0,...,0}_{80})^\top\).
In summary, we construct simulation data under different conditions to compare the proposed algorithm with the benchmark method.
FigureÂ 1 shows the feature selection of the two methods on both synthetic data. It is worth noting that the intensity of the color reflects the relative importance of features. On the first data which only contains modalityshared features, both PDSMCCA and SMCCA can successfully identify these shared features. On the second data where both modalityshared and specific features exist, SMCCA mixes these two types of features which is undesirable. On the contrary, PDSMCCA yields two types of features, including the modalityshared and specific ones, which is more meaningful and practical. TableÂ 1 presents the estimated canonical correlation coefficients between every two modalities. PDSMCCA obtains higher CCCs than SMCCA on both training and testing sets for two data sets. Therefore, PDSMCCA outperforms SMCCA in this simulation study.
Results on real data
The brain imaging data were obtained from the Alzheimerâ€™s Disease Neuroimaging Initiative (ADNI) database (https://adni.loni.usc.edu). and the primary goal of ADNI is to test whether serial magnetic resonance imaging (MRI), positron emission tomography (PET), other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of mild cognitive impairment (MCI) and early AD. For uptodate information, see www.adniinfo.org.
There were 755 samples including 281 ADs, 292 MCIs and 182 normal controls (NCs) nonHispanic Caucasian participants. Three modalities of brain imaging data, including sMRI, FDGPET and AV45PET were used in this paper. FDGPET and AV45PET scans were coregistered to the standard MNI space. sMRI scans were processed with voxelbased morphometry (VBM) [35, 36] by the SPM software, and aligned to a T1weighted template, then segmented to white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF) maps, finally normalized to the same MNI space, and smoothed with an 8 \({\hbox {mm}}^3\) FWHM kernel. According to the automated anatomical labeling (AAL) atlas, we obtained 116 regions of interest (ROI) measurements. In order to eliminate the influence of baseline age, gender, habit, and education level, we used regression weights obtained from NC subjects to preadjust these imaging QTs. We aim to improve the interpretability of multimodal data for complex pathogenesis mechanisms, as well as select imaging QTs of interest.
FigureÂ 2 shows the feature selection results on real neuroimaging data. According to the intensity of the color, we can determine the relative importance of features. It is clear that PDSMCCA identifies more diverse imaging QTs than SMCCA. For the modalityshared features conveyed by \({\mathbf {S}}\), PDSMCCA identifies the left and right hippocampus [4, 37], the left and right middle temporal [38], the left and right precuneus as the most relevant shared ROIs. Besides, PDSMCCA also identifies the modalityspecific features which is shown in weight \({\mathbf {B}}\). It is clear that the left and right medial orbitofrontal [9] are relevant only in AV45 scans [20, 39]. Meanwhile, the left post cingulum is relevant in FDG scans, and both the left and right hippocampus are relevant in sMRI scans. In contrast, SMCCA misses the brain regions shared by multiple modalities, since it cannot obtain the diverse feature selection results. It mixes both modalityshared features and modalityspecific ones which is insufficient in real applications. We also present the CCCs of both methods in TableÂ 2. Our method obtains better CCCs than SMCCA, which indicates that our method can identify stronger bimultivariate associations. In summary, PDSMCCA holds the capability to identify the multiway correlations between multiple modalities of data, and can identify more meaningful features.
To further show the meaning of these selected imaging QTs, the ANOVA and population stratification analysis were conducted. The oneway ANOVA results showed that the top selected imaging QTs reached the level of significance (pÂ <Â 0.01). This indicated imaging QTs were significantly related to the diagnosis. Moreover, in order to verify the biological effects of the selected imaging QTs. We further analyzed the prominent imaging QT of each modality, which were FrontalMedOrbLeft in AV45 [40], CingulumPostLeft [41] in FDG and HippocampusRight [37] in VBM. Since there were three diagnostic groups, we decided to investigate whether they were significantly different among different groups. FigureÂ 3 showed that FrontalMedOrbLeft and CingulumPostLeft exhibited significant changes in FDG and AV45 which was consistent with the decline of metabolic rates of cerebral glucose and the variety of extracellular amyloid deposition. Besides, the HippocampusRight showed consistent patterns that decreased measurement were observed in all modalities. This may be attributed to its high correlation to AD. In summary, benefiting from the parameter decomposition strategy, our proposed method can obtain interesting and meaningful biomarkers in multimodal brain imaging analysis.
Discussion
Generally, different techniques yield different measurements of the same brain, and could carry shared and specific information simultaneously. In this paper, PDSMCCA is proposed to explore the multiway relationship among multiple brain imaging modalities, and it can identify both modalityshared and specific imaging features through the parameter decomposition technology. Importantly, this decomposition technology is flexible via balancing between two contradictory constraints (\(\ell _{1}\)norm and \(\ell _{2,1}\)norm), and thus assures a better performance [42]. This improves the interpretability of traditional SMCCA method. Of note, similar to SMCCA, PDSMCCA is also unsupervised which could be a limitation. The future work is to incorporate the diagnostic labels into the PDSMCCA model, and build a supervised method to better mine the brain imaging association with selecting relevant imaging features.
Conclusion
To improve the interpretability of multimodal data for complex pathogenesis mechanisms, we proposed a novel sparse multiview canonical correlation analysis method (PDSMCCA) based on parameter decomposition. In our model, the canonical weights were decomposed into modalityshared and modalityspecific components, resulting in a flexible and meaningful interpretability. We also introduced an efficient optimization algorithm to solve PDSMCCA, and proved the convergence. The results on both synthetic and real neuroimaging data showed that compared with SMCCA, PDSMCCA accurately selected the modalityshared and specific features, and obtained higher or comparable correlation coefficients. The diverse feature selection might provide a new insight for revealing AD pathology.
Method
In this paper, italic letters indicate scalars, boldface lowercase letters and boldface capitals represents column vectors and matrices respectively. Specifically, the ith row and jth column of \({\mathbf {V}}\) is denoted as \({\mathbf {v}}^i\) and \({\mathbf {v}}_j\).Â \(\Vert {{\mathbf {V}}}\Vert _{2,1} = \sum _i \Vert {{\mathbf {v}}^{i}}\Vert _2\) is the \(\ell _{2,1}\)norm. In addition,Â \(\Vert {{\mathbf {V}}}\Vert _{1,1}\) denotes the elementwise \(\ell _1\)norm of \({\mathbf {V}}\), i.e., \(\Vert {{\mathbf {V}}}\Vert _{1,1}=\sum _j \Vert {{\mathbf {v}}_{j}}\Vert _1=\sum _i \Vert {{\mathbf {v}}^{i}}\Vert _1=\sum _i\sum _j {v_{ij}}\).
SMCCA
SMCCA extends the conventional twoview SCCA model to multiview oriented, which can handle the association identification among multiple data sets. Generally, the definition of SMCCA is as follows:
According to [43, 44], (2) can be rewritten as a multivariate multiple regression model.
where \({\mathbf {X}}_k \in {\mathbb {R}}^{n \times p}(k =1,\ldots , K)\) represents the kth modality of imaging data with n samples and p imaging quantitative traits (QTs) and K is the number of imaging modalities. \({\mathbf {v}}_k \in {\mathbb {R}}^{p \times 1}\) represents the canonical weight corresponding to the kth modality, and \({\mathbf {V}}=[{\mathbf {v}}_{1},\ldots ,{\mathbf {v}}_{K}]\). These weights yielded by SMCCA show the importance of each imaging feature in associating multiple brain imaging modalities. However, SMCCA supposes \({\mathbf {X}}_k^\top {\mathbf {X}}_k = {\mathbf {I}}\) which weakens the performance of the model [23]. Whatâ€™s worse, the modalityshared imaging features mix up with those modalityspecific ones, resulting in poor interpretability.
PDSMCCA
In order to better identify the relationship between multimodal brain imaging data and overcome the drawbacks of SMCCA, we propose a novel SMCCA (PDSMCCA) model. PDSMCCA is defined as follows:
where \(\lambda _B\) and \(\lambda _S\) are two nonnegative tuning parameters, and \({\mathbf {V=B+S}}\). The decomposition of \({\mathbf {V}}\) is interesting and meaningful.
Specifically, by using different regularization functions for \({\mathbf {B}}\) and \({\mathbf {S}}\), we can enable them to select different types of features, e.g. the modalityshared and specific features. In this paper, we impose the \(\ell _{2,1}\)norm [33] on \({\mathbf {S}}\) to select the shared features across multiple modalities, and this penalty is defined as \(\Vert {{\mathbf {S}}}\Vert _{2,1} = \sum _i \Vert {{\mathbf {s}}^{i}}\Vert _2\). In addition, we use the \(\ell _{1}\)norm for an imaging QT across all imaging modalities. This might identify features that can only be recognized under certain technologies. And the penalty is defined as \(\Vert {{\mathbf {B}}}\Vert _{1,1}=\sum _j \Vert {{\mathbf {b}}_{j}}\Vert _1=\sum _i \Vert {{\mathbf {b}}^{i}}\Vert _1=\sum _i\sum _j {b_{ij}}\).
The merits of PDSMCCA are as follows. First of all, our model directly calculates the multiway association among multiple data modalities, which holds a powerful modeling capability. Besides, we use \(\ell _{1}\)norm to identify related QTs that may only change in a single imaging modality, and use \(\ell _{2,1}\)norm to identify related imaging QTs that change together due to the covarying effects of AD, which demonstrates a diverse and desirable feature selection capability. Most importantly, attributing to the parameter decomposition and diverse regularization, the modalityshared features and modalityspecific features can be obtained in a unified model, which could provide a better interpretation for biomedical studies.
The optimization algorithm
According to Lemma 2.2 in [45], the optimum \({\mathbf {b}}_k\) and \({\mathbf {s}}_k\) can be obtained by \({\mathbf {b}}_k^* = \frac{\hat{{\mathbf {b}}_k}}{\Vert {{{{{\mathbf {X}}_k}({\mathbf {b}}_k+{\mathbf {s}}_k)}}}\Vert _2}\) and \({\mathbf {s}}_k^* = \frac{\hat{{\mathbf {s}}_k}}{\Vert {{{{{\mathbf {X}}_k}({\mathbf {b}}_k+{\mathbf {s}}_k)}}}\Vert _2}\) respectively. Further, \(\hat{{\mathbf {b}}_k}\) and \(\hat{{\mathbf {s}}_k}\) are solutions to the following objective,
Equation (5) is a typical biconvex function, and we can use the alternating convex search (ACS) method [46] to solve this objective. That is, we update one variable and fix all the remaining ones at each step. Since \({{{\mathbf {X}}_k}({\mathbf {b}}_k+{\mathbf {s}}_k)_2^2}=1\), (5) is processed as follows:
according to inequality \({{\frac{1}{4}\Vert {{\mathbf {X}}_k({\mathbf {b}}_k+{\mathbf {s}}_k)}\Vert _2^2}}\le {\frac{1}{2}{\Vert {{\mathbf {X}}_k{\mathbf {b}}_k}\Vert _2^2}}+{\frac{1}{2}{\Vert {{\mathbf {X}}_k{\mathbf {s}}_k}\Vert _2^2}}\), we equivalently have the following objective with respect to \({\mathbf {b}}_k\) and \({\mathbf {s}}_k\),
Equation (7) is convex in \({\mathbf {b}}_k\) when fixing \({\mathbf {s}}_k\) as constants.
Then based on the ACS strategy, we take the derivative with respect to each \({\mathbf {b}}_k\), and letting it be zero, we obtain
where \({\mathbf {D}}_b\) is a diagonal matrix with the ith diagonal element being \(\frac{1}{{{\mathbf {b}}_{ik}}}\).
Similarly, the optimal \({\mathbf {s}}_k\) can be obtained by solving (10)
then we have the closedfrom updating rule for each \({\mathbf {s}}_k\),
where \({\mathbf {D}}_s\) is a diagonal matrix, and its ith diagonal element is \(\frac{1}{\Vert {{\mathbf {s}}^{i}}\Vert _{2}}\) (\(i=1,\ldots ,p\)).
Once every \({\mathbf {b}}_k\) and \({\mathbf {s}}_k\) is attained, \({\mathbf {B}}\) and \({\mathbf {S}}\) can be attained as well. Finally, we present the pseudocode in Algorithm 1. The input of PDSMCCA is the neuroimaging quantitative trait data from multiple modalities, and the output is the canonical weight (absolute value) showing the relative importance of each imaging feature. Step 1 initializes \({\mathbf {B}}\) and \({\mathbf {S}}\). Step 3 to 6 are iteration procedure to seek the final solutions.
Convergence analysis
Theorem 1 will prove that Algorithm 1 converge to a local optimum.
Theorem 1
The value of (4) keeps decreasing througout the iteration of Algorithm 1.
We use \(\left\{ {\mathbf {b}}_k^{(t)}, {\mathbf {s}}_k^{(t)}\right\}\) to represent the estimate of \(\left\{ {\mathbf {b}}_k, {\mathbf {s}}_k\right\}\) in the tth iteration. Next, we will prove that the value of (8) is continuously decreasing when solving \({\mathbf {b}}_k\). To facilitate understanding, we denote the objective of (8) as \(F\left( {\mathbf {b}}_k\right)\):
Then we define
where \({\mathbf {D}}_b\) is defined in (9), and (14) can be easily proved. It is obvious that \(G\left( {\mathbf {b}}_k\right)\) is a convex quadratic function that satisfies
Since the estimate of \({\mathbf {b}}_k\) at the next iteration \(t+\)1, expressed in (8) and denoted as \({\mathbf {b}}_k^{(t+1)}\), is the minimizer of \(G\left( {\mathbf {b}}_k\right)\), we have
Putting (13)â€“(15) together, we have
This formula shows that the objective decreases by fixing \({\mathbf {s}}_k\), which guarantees the convergence. And after the rescaling, the conclusion is still valid. Thus, for \({\mathbf {s}}_k\), we can get the same conclusion in the same way. By denoting the objective as \({\mathcal {L}}({\mathbf {b}}_k,{\mathbf {s}}_k)\), then according to the conclusions above, we have
We further know \({\mathcal {L}}({\mathbf {b}}_k,{\mathbf {s}}_k )\) is lower bounded by zero. Therefore, we combine (16)â€“(17), AlgorithmÂ 1 will converge to the optimum.
Availability of data and materials
Data used in this study are publicly available at the ADNI database (www.adniinfo.org). They are from the ADNI1, ADNI GO and ADNI2 standard data sets that are considered in experiments with the MRI and PET data sets.
Abbreviations
 CCC:

Canonical correlation coefficient
 PDSMCCA:

Parameter decomposition based sparse multiview canonical correlation analysis
 AD:

Alzheimerâ€™s Disease
 ADNI:

Alzheimerâ€™s Disease Neuroimaging Initiative
 ACS:

Alternating convex search
 MRI:

Magnetic resonance imaging
 MCI:

Mild cognitive impairment
 sMRI:

Structural magnetic resonance imaging
 FDG:

Fluorodeoxyglucose
 QTs:

Quantitative traits
 ROI:

Regions of interest
 AAL:

Automated anatomical labeling
 CSF:

Cerebrospinal fluid
 GM:

Gray matter
 WM:

White matter
 SCCA:

Sparse canonical correlation analysis
 SMCCA:

Sparse multiple/multiview/multiset canonical correlation analysis
 NC:

Normal controls
 AV45:

18F florbetapir PET
 VBM:

Voxelbased morphometry
 PET:

Positron emission tomography
 fMRI:

Functional magnetic resonance imaging
References
Goedert M, Spillantini MG. A century of Alzheimerâ€™s disease. Science. 2006;314(5800):777â€“81.
Grellmann C, Bitzer S, Neumann J, Westlye LT, Andreassen OA, Villringer A, Horstmann A. Comparison of variants of canonical correlation analysis and partial least squares for combined analysis of MRI and genetic data. Neuroimage. 2015;107:289â€“310.
Association A. Alzheimerâ€™s disease facts and figures. Alzheimerâ€™s Dement. 2019;15(3):321â€“87.
Xiao E, Chen Q, Goldman AL, Tan HY, Healy K, Zoltick B, et al. Lateonset Alzheimerâ€™s disease polygenic risk profile score predicts hippocampal function. Biol Psychiatry Cogn Neurosci Neuroimaging. 2017;2(8):673â€“9.
Bakkour A, Morris JC, Wolk DA, Dickerson BC. The effects of aging and Alzheimerâ€™s disease on cerebral cortical anatomy: specificity and differential relationships with cognition. Neuroimage. 2013;76:332â€“44.
Rathore S, Habes M, Iftikhar MA, Shacklett A, Davatzikos C. A review on neuroimagingbased classification studies and associated feature extraction methods for Alzheimerâ€™s disease and its prodromal stages. Neuroimage. 2017;155:530â€“48.
Shivamurthy VK, Tahari AK, Marcus C, Subramaniam RM. Brain FDG PET and the diagnosis of dementia. Am J Roentgenol. 2015;204(1):76â€“85.
Nakao T, Radua J, Rubia K, MataixCols D. Gray matter volume abnormalities in ADHD: voxelbased metaanalysis exploring the effects of age and stimulant medication. Am J Psychiatry. 2011;168(11):1154â€“63.
Woodward M, Rowe CC, Jones G, Villemagne VL, Varos T. Differentiating the frontal presentation of Alzheimerâ€™s disease with FDGPET. J Alzheimers Dis. 2015;44(1):233â€“42.
Stuss DT, Gow CA, Hetherington CR. â€œno longer gageâ€™â€™: frontal lobe dysfunction and emotional changes. J Consult Clin Psychol. 1992;60(3):349.
Lorenzi M, Simpson IJ, Mendelson AF, Vos SB, Cardoso MJ, Modat M, Schott JM, Ourselin S. Multimodal image analysis in Alzheimerâ€™s disease via statistical modelling of nonlocal intensity correlations. Sci Rep. 2016;6(1):1â€“8.
Sui J, Adali T, Yu Q, Chen J, Calhoun VD. A review of multivariate methods for multimodal fusion of brain imaging data. J Neurosci Methods. 2012;204(1):68â€“81.
Zhang D, Wang Y, Zhou L, Yuan H, Shen D. Multimodal classification of Alzheimerâ€™s disease and mild cognitive impairment. Neuroimage. 2011;55(3):856â€“67.
Ball G, Aljabar P, Nongena P, Kennea N, GonzalezCinca N, Falconer S, Chew AT, Harper N, Wurie J, Rutherford MA, et al. Multimodal image analysis of clinical influences on preterm brain development. Ann Neurol. 2017;82(2):233â€“46.
Oxtoby NP, Alexander DC. Imaging plus x: multimodal models of neurodegenerative disease. Curr Opin Neurol. 2017;30(4):371.
Zhang D, Shen D. Multimodal multitask learning for joint prediction of multiple regression and classification variables in Alzheimerâ€™s disease. Neuroimage. 2012;59(2):895â€“907.
Fan C, Cheng Y, Gou H, Liu C, Deng S, Liu C, Chen X, Bu J, Zhang X. Neuroimaging and intervening in memory reconsolidation of human drug addiction. Sci China Inf Sci. 2020;63(7):1â€“11.
Xu C, Wang Z, Fan M, Liu B, Song M, Zhen X, Jiang T, Initiative ADN, et al. Effects of BDNF val66met polymorphism on brain metabolism in Alzheimerâ€™s disease. NeuroReport. 2010;21(12):802.
Timmers T, Ossenkoppele R, Wolters EE, Verfaillie SC, Visser D, Golla SS, Barkhof F, Scheltens P, Boellaard R, Van Der Flier WM, et al. Associations between quantitative [18 F] flortaucipir tau pet and atrophy across the Alzheimerâ€™s disease spectrum. Alzheimerâ€™s Res Ther. 2019;11(1):60.
Hedden T, Mormino EC, Amariglio RE, Younger AP, Schultz AP, Becker JA, Buckner RL, Johnson KA, Sperling RA, Rentz DM. Cognitive profile of amyloid burden and white matter hyperintensities in cognitively normal older adults. J Neurosci. 2012;32(46):16233â€“42.
Hardoon DR, ShaweTaylor J. Sparse canonical correlation analysis. Mach Learn. 2011;83(3):331â€“53.
Du L, Huang H, Yan JE. Structured sparse canonical correlation analysis for brain imaging genetics: an improved graphnet method. Bioinformatics. 2016;32(10):1544â€“51.
Shen L, Risacher SL, Du L, Moore JH, Huang H, Inlow M, Kim S, Saykin AJ, Yan J. A novel structureaware sparse learning algorithm for brain imaging genetics. Med Image Comput Comput Assist Interv. 2014;17(3):329â€“36.
Du L, et al. Identifying associations between brain imaging phenotypes and genetic factors via a novel structured SCCA approach. In: International conference on information processing in medical imaging. Springer. 2017. p. 543â€“55.
Wilms I, Croux C. Sparse canonical correlation analysis from a predictive point of view. Biom J. 2015;57(5):834â€“51.
Du L, Liu K, Yao X, Risacher SL, Shen L. Detecting genetic associations with brain imaging phenotypes in Alzheimerâ€™s disease via a novel structured SCCA approach. Med Image Anal. 2020;61:101656.
Chen M, Gao C, Ren Z, Zhou HH. Sparse cca via precision adjusted iterative thresholding. 2013. arXiv preprint. arXiv:1311.6186.
Witten DM, Tibshirani RJ. Extensions of sparse canonical correlation analysis with applications to genomic data. Stat Appl Genet Mol Biol. 2009;8(1):28.
Du L, Zhang J, Liu F, Wang H, Guo L, Han J, Initiative ADN, et al. Identifying associations among genomic, proteomic and imaging biomarkers via adaptive sparse multiview canonical correlation analysis. Med Image Anal. 2021;70:102003.
Hao X, et al. Mining outcomerelevant brain imaging genetic associations via threeway sparse canonical correlation analysis in Alzheimerâ€™s disease. Sci Rep. 2017;7:44272.
Fang J, Lin D, Schulz C, Xu Z, Calhoun VD, Wang YP. Joint sparse canonical correlation analysis for detecting differential imaging genetics modules. Bioinformatics. 2011;32:3480â€“8.
Tibshirani R. Regression shrinkage and selection via the lasso. J R Stat Soc. 1996;58(1):267â€“88.
Liu J, Ji S, Ye J. Multitask feature learning via efficient l2,1norm minimization. 2012. arXiv preprint. arXiv:1205.2631.
Wang H, Nie F, Huang H, Kim S, Nho K, Risacher SL, Saykin AJ, Shen L, Initiative ADN. Identifying quantitative trait loci via groupsparse multitask regression and feature selection: an imaging genetics study of the ADNI cohort. Bioinformatics. 2012;28(2):229â€“37.
Harper L, Bouwman F, Burton EJ, Barkhof F, Scheltens P, TÂ Oâ€™Brien J, et al. Patterns of atrophy in pathologically confirmed dementias: a voxelwise analysis. Journal of Neurology, Neurosurgery, & Psychiatry, 908â€“916 (2017).
Wang W, Yu J, Liu Y, Yin R, Wang H, Wang J, Tan L, Radua J, Tan L. Voxelbased metaanalysis of grey matter changes in Alzheimerâ€™s disease. Transl Neurodegener. 2015;4(1):6.
Potkin SG, Guffanti G, Lakatos A, Turner JA, Kruggel F, Fallon JH, et al. Hippocampal atrophy as a quantitative trait in a genomewide association study identifying novel susceptibility genes for Alzheimerâ€™s disease. PLoS ONE. 2009;4(8):e6501.
Galton C, GomezAnson B, Antoun N, Scheltens P, Patterson K, Graves M, Sahakian B, Hodges J. Temporal lobe rating scale: application to Alzheimerâ€™s disease and frontotemporal dementia. J Neurol Neurosurg Psychiatry. 2001;70(2):165â€“73.
Altmann A, Ng B, Landau SM, Jagust WJ, Greicius MD. Regional brain hypometabolism is unrelated to regional amyloid plaque burden. Brain. 2015;138(12):3734â€“46.
Sepulcre J, Grothe MJ, Uquillas FD, OrtizTerÃ¡n L, Diez I, Yang HS, Jacobs HI, Hanseeuw BJ, Li Q, ElFakhri G, et al. Neurogenetic contributions to amyloid beta and tau spreading in the human cortex. Nat Med. 2018;24(12):1910â€“8.
Mosconi L. Brain glucose metabolism in the early and specific diagnosis of Alzheimerâ€™s disease. Eur J Nucl Med Mol Imaging. 2005;32(4):486â€“510.
Jalali A, Sanghavi S, Ruan C, Ravikumar PK. A dirty model for multitask learning. In: NIPS, 2010. p. 964â€“72.
Du L, Liu K, Yao X, Risacher S, Han J, Saykin A, Guo L, Shen L. Multitask sparse canonical correlation analysis with application to multimodal brain imaging genetics. IEEE/ACM Trans Comput Biol Bioinf. 2021;18(1):227â€“39.
Du L, Liu K, Zhu L, Yao X, Risacher SL, Guo L, Saykin AJ, Shen L, Initiative ADN. Identifying progressive imaging genetic patterns via multitask sparse canonical correlation analysis: a longitudinal study of the ADNI cohort. Bioinformatics. 2019;35(14):474â€“83.
Witten DM, Tibshirani R, Hastie T. A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics. 2009;10(3):515â€“34.
Gorski J, Pfeuffer F, Klamroth K. Biconvex sets and optimization with biconvex functions: a survey and extensions. Math Methods Oper Res. 2007;66(3):373â€“407.
Acknowledgements
Data collection and sharing for this project was funded by the Alzheimerâ€™s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH1220012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimerâ€™s Association; Alzheimerâ€™s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; BristolMyers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. HoffmannLa Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimerâ€™s Therapeutic Research Institute at the University of Southern California. ADNI data are disseminated by the Laboratory for Neuro Imaging at the University of Southern California. Data used in preparation of this article were obtained from the Alzheimerâ€™s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wpcontent/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf.
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This article has been published as part of BMC Bioinformatics Volume 23 Supplement 3, 2022: Selected articles from the International Conference on Intelligent Biology and Medicine (ICIBM 2021): bioinformatics. The full contents of the supplement are available online at https://bmcbioinformatics.biomedcentral.com/articles/supplements/volume23supplement3.
Funding
The data collection and sharing of this project was funded by the Alzheimerâ€™s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH1220012). Publication costs are funded in part by the KeyArea Research and Development Program of Guangdong Province [2019B010110001]; the National Natural Science Foundation of China [61973255, 62136004, 61936007, 62036011, U1801265, 62027813]; the Key R&D Program of Shaanxi Province [2021ZDLGY0108]; the Natural Science Basic Research Program of Shaanxi [2020JM142]; the China Postdoctoral Science Foundation [2020T130537] at Northwestern Polytechnical University. This work was also supported in part by the Shanghai Municipal Science and Technology Major Project [2018SHZDZX01] at LCNBI and ZJLab.
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JZ: methodology, software, writingoriginal draft. HW: visualization, writingreview. YZ: software, investigation. LG: validation, writingreview and editing. LD: conceptualization, writingreview and editing. All authors read and approved the final manuscript.
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Zhang, J., Wang, H., Zhao, Y. et al. Identification of multimodal brain imaging association via a parameter decomposition based sparse multiview canonical correlation analysis method. BMC Bioinformatics 23 (Suppl 3), 128 (2022). https://doi.org/10.1186/s1285902204669z
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DOI: https://doi.org/10.1186/s1285902204669z