The genetic architecture of the human cerebral cortex

The cerebral cortex underlies our complex cognitive capabilities, yet little is known about the specific genetic loci that influence human cortical structure. To identify genetic variants that affect cortical structure, we conducted a genome-wide association meta-analysis of brain magnetic resonance imaging data from 51,665 individuals. We analyzed the surface area and average thickness of the whole cortex and 34 regions with known functional specializations. We identified 199 significant loci and found significant enrichment for loci influencing total surface area within regulatory elements that are active during prenatal cortical development, supporting the radial unit hypothesis. Loci that affect regional surface area cluster near genes in Wnt signaling pathways, which influence progenitor expansion and areal identity. Variation in cortical structure is genetically correlated with cognitive function, Parkinson's disease, insomnia, depression, neuroticism, and attention deficit hyperactivity disorder

Convex clustering: an attractive alternative to hierarchical clustering.

The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its shortcomings in accuracy, hierarchical clustering is the dominant clustering method in bioinformatics. Biologists find the trees constructed by hierarchical clustering visually appealing and in tune with their evolutionary perspective. Hierarchical clustering operates on multiple scales simultaneously. This is essential, for instance, in transcriptome data, where one may be interested in making qualitative inferences about how lower-order relationships like gene modules lead to higher-order relationships like pathways or biological processes. The recently developed method of convex clustering preserves the visual appeal of hierarchical clustering while ameliorating its propensity to make false inferences in the presence of outliers and noise. The solution paths generated by convex clustering reveal relationships between clusters that are hidden by static methods such as k-means clustering. The current paper derives and tests a novel proximal distance algorithm for minimizing the objective function of convex clustering. The algorithm separates parameters, accommodates missing data, and supports prior information on relationships. Our program CONVEXCLUSTER incorporating the algorithm is implemented on ATI and nVidia graphics processing units (GPUs) for maximal speed. Several biological examples illustrate the strengths of convex clustering and the ability of the proximal distance algorithm to handle high-dimensional problems. CONVEXCLUSTER can be freely downloaded from the UCLA Human Genetics web site at http://www.genetics.ucla.edu/software/

Propensity Clustering and Decomposition. Description Details

Description This package implements propensity clustering and decomposition. Propensity decomposition can be viewed on the one hand as a generalization of the eigenvector-based approximation of correlation networks, and on the other hand as a generalization of random multigraph models and conformity-based decompositions

Convex clustering concepts.

<p>For clarity, we present three random data points extracted from the three classes in the Iris dataset. Black points denote the original data points <b><i>X</i></b> and blue points denote the cluster centers <b><i>U</i></b>. At <i>μ</i> = 0, <b><i>X</i></b> and <b><i>U</i></b> coincide. At intermediate <i>μ</i> values (middle figure), <b><i>U</i></b> coalesces towards its cluster center. For sufficiently large <i>μ</i>, <b><i>U</i></b> converges to cluster centers (right figure). Note that in this demonstration, only the left two points have non-zero pairwise weights <i>w</i>_<i>ij</i>. Hence, the two resulting clusters reflect the two graphs defined by the matrix of weights.</p

Convex clustering of the breast cancer samples.

<p>Points on the plot indicate data vectors projected onto the first and third principal components (PCs) of the sample. Lines trace the cluster centers as they traverse the regularization path.</p

Magnified view of the convex clustering results for the HGDP data in Europe and Central Asia.

<p>Magnified view of the convex clustering results for the HGDP data in Europe and Central Asia.</p

Hierarchical clustering of the European populations from the POPRES data.

<p>Hierarchical clustering of the European populations from the POPRES data.</p

Magnified view of the convex clustering results for the HGDP data in East Asia.

<p>Magnified view of the convex clustering results for the HGDP data in East Asia.</p

Convex clustering of the European populations from the POPRES data using <i>ϕ</i> = 10 and <i>k</i> = 40.

<p>Convex clustering of the European populations from the POPRES data using <i>ϕ</i> = 10 and <i>k</i> = 40.</p

Hierarchical clustering of the 52 populations from the HGDP data.

<p>Hierarchical clustering of the 52 populations from the HGDP data.</p