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      Adaptive sparse multiple canonical correlation analysis with application to imaging (epi)genomics study of schizophrenia

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          Abstract

          <p class="first" id="P1">Finding correlations across multiple data sets in imaging and (epi)genomics is a common challenge. Sparse multiple canonical correlation analysis (SMCCA) is a multivariate model widely used to extract contributing features from each data while maximizing the cross-modality correlation. The model is achieved by using the combination of pairwise covariances between any two data sets. However, the scales of different pairwise covariances could be quite different and the direct combination of pairwise covariances in SMCCA is unfair. The problem of ‘unfair combination of pairwise covariances’ restricts the power of SMCCA for feature selection. In this paper, we propose a novel formulation of SMCCA, called adaptive SMCCA, to overcome the problem by introducing adaptive weights when combining pairwise covariances. Both simulation and real data analysis show the outperformance of adaptive SMCCA in terms of feature selection over conventional SMCCA and SMCCA with fixed weights. Large-scale numerical experiments show that adaptive SMCCA converges as fast as conventional SMCCA. When applying it to imaging (epi)genetics study of schizophrenia subjects, we can detect significant (epi)genetic variants and brain regions, which are consistent with other existing reports. In addition, several significant brain-development related pathways, e.g., neural tube development, are detected by our model, demonstrating imaging epigenetic association may be overlooked by conventional SMCCA. All these results demonstrate that adaptive SMCCA are well-suited for detecting three-way or multi-way correlations and thus can find widespread applications in multiple omics and imaging data integration. </p>

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          Stability selection

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            A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis.

            We present a penalized matrix decomposition (PMD), a new framework for computing a rank-K approximation for a matrix. We approximate the matrix X as circumflexX = sigma(k=1)(K) d(k)u(k)v(k)(T), where d(k), u(k), and v(k) minimize the squared Frobenius norm of X - circumflexX, subject to penalties on u(k) and v(k). This results in a regularized version of the singular value decomposition. Of particular interest is the use of L(1)-penalties on u(k) and v(k), which yields a decomposition of X using sparse vectors. We show that when the PMD is applied using an L(1)-penalty on v(k) but not on u(k), a method for sparse principal components results. In fact, this yields an efficient algorithm for the "SCoTLASS" proposal (Jolliffe and others 2003) for obtaining sparse principal components. This method is demonstrated on a publicly available gene expression data set. We also establish connections between the SCoTLASS method for sparse principal component analysis and the method of Zou and others (2006). In addition, we show that when the PMD is applied to a cross-products matrix, it results in a method for penalized canonical correlation analysis (CCA). We apply this penalized CCA method to simulated data and to a genomic data set consisting of gene expression and DNA copy number measurements on the same set of samples.
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              Schizophrenia genes, gene expression, and neuropathology: on the matter of their convergence.

              This review critically summarizes the neuropathology and genetics of schizophrenia, the relationship between them, and speculates on their functional convergence. The morphological correlates of schizophrenia are subtle, and range from a slight reduction in brain size to localized alterations in the morphology and molecular composition of specific neuronal, synaptic, and glial populations in the hippocampus, dorsolateral prefrontal cortex, and dorsal thalamus. These findings have fostered the view of schizophrenia as a disorder of connectivity and of the synapse. Although attractive, such concepts are vague, and differentiating primary events from epiphenomena has been difficult. A way forward is provided by the recent identification of several putative susceptibility genes (including neuregulin, dysbindin, COMT, DISC1, RGS4, GRM3, and G72). We discuss the evidence for these and other genes, along with what is known of their expression profiles and biological roles in brain and how these may be altered in schizophrenia. The evidence for several of the genes is now strong. However, for none, with the likely exception of COMT, has a causative allele or the mechanism by which it predisposes to schizophrenia been identified. Nevertheless, we speculate that the genes may all converge functionally upon schizophrenia risk via an influence upon synaptic plasticity and the development and stabilization of cortical microcircuitry. NMDA receptor-mediated glutamate transmission may be especially implicated, though there are also direct and indirect links to dopamine and GABA signalling. Hence, there is a correspondence between the putative roles of the genes at the molecular and synaptic levels and the existing understanding of the disorder at the neural systems level. Characterization of a core molecular pathway and a 'genetic cytoarchitecture' would be a profound advance in understanding schizophrenia, and may have equally significant therapeutic implications.
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                Author and article information

                Journal
                IEEE Transactions on Biomedical Engineering
                IEEE Trans. Biomed. Eng.
                Institute of Electrical and Electronics Engineers (IEEE)
                0018-9294
                1558-2531
                2017
                : 1
                Article
                10.1109/TBME.2017.2771483
                5826588
                29364120
                4b8908e5-3d0e-4b67-b235-53430d664fa1
                © 2017
                History

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