Encoding Multi-Resolution Brain Networks Using Unsupervised Deep Learning

The main goal of this study is to extract a set of brain networks in multiple time-resolutions to analyze the connectivity patterns among the anatomic regions for a given cognitive task. We suggest a deep architecture which learns the natural groupings of the connectivity patterns of human brain in multiple time-resolutions. The suggested architecture is tested on task data set of Human Connectome Project (HCP) where we extract multi-resolution networks, each of which corresponds to a cognitive task. At the first level of this architecture, we decompose the fMRI signal into multiple sub-bands using wavelet decompositions. At the second level, for each sub-band, we estimate a brain network extracted from short time windows of the fMRI signal. At the third level, we feed the adjacency matrices of each mesh network at each time-resolution into an unsupervised deep learning algorithm, namely, a Stacked De- noising Auto-Encoder (SDAE). The outputs of the SDAE provide a compact connectivity representation for each time window at each sub-band of the fMRI signal. We concatenate the learned representations of all sub-bands at each window and cluster them by a hierarchical algorithm to find the natural groupings among the windows. We observe that each cluster represents a cognitive task with a performance of 93% Rand Index and 71% Adjusted Rand Index. We visualize the mean values and the precisions of the networks at each component of the cluster mixture. The mean brain networks at cluster centers show the variations among cognitive tasks and the precision of each cluster shows the within cluster variability of networks, across the subjects.Comment: 6 pages, 3 figures, submitted to The 17th annual IEEE International Conference on BioInformatics and BioEngineerin

Hierarchical Multi-resolution Mesh Networks for Brain Decoding

We propose a new framework, called Hierarchical Multi-resolution Mesh Networks (HMMNs), which establishes a set of brain networks at multiple time resolutions of fMRI signal to represent the underlying cognitive process. The suggested framework, first, decomposes the fMRI signal into various frequency subbands using wavelet transforms. Then, a brain network, called mesh network, is formed at each subband by ensembling a set of local meshes. The locality around each anatomic region is defined with respect to a neighborhood system based on functional connectivity. The arc weights of a mesh are estimated by ridge regression formed among the average region time series. In the final step, the adjacency matrices of mesh networks obtained at different subbands are ensembled for brain decoding under a hierarchical learning architecture, called, fuzzy stacked generalization (FSG). Our results on Human Connectome Project task-fMRI dataset reflect that the suggested HMMN model can successfully discriminate tasks by extracting complementary information obtained from mesh arc weights of multiple subbands. We study the topological properties of the mesh networks at different resolutions using the network measures, namely, node degree, node strength, betweenness centrality and global efficiency; and investigate the connectivity of anatomic regions, during a cognitive task. We observe significant variations among the network topologies obtained for different subbands. We, also, analyze the diversity properties of classifier ensemble, trained by the mesh networks in multiple subbands and observe that the classifiers in the ensemble collaborate with each other to fuse the complementary information freed at each subband. We conclude that the fMRI data, recorded during a cognitive task, embed diverse information across the anatomic regions at each resolution.Comment: 18 page

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

Learning quadrangulated patches for 3D shape parameterization and completion

We propose a novel 3D shape parameterization by surface patches, that are oriented by 3D mesh quadrangulation of the shape. By encoding 3D surface detail on local patches, we learn a patch dictionary that identifies principal surface features of the shape. Unlike previous methods, we are able to encode surface patches of variable size as determined by the user. We propose novel methods for dictionary learning and patch reconstruction based on the query of a noisy input patch with holes. We evaluate the patch dictionary towards various applications in 3D shape inpainting, denoising and compression. Our method is able to predict missing vertices and inpaint moderately sized holes. We demonstrate a complete pipeline for reconstructing the 3D mesh from the patch encoding. We validate our shape parameterization and reconstruction methods on both synthetic shapes and real world scans. We show that our patch dictionary performs successful shape completion of complicated surface textures.Comment: To be presented at International Conference on 3D Vision 2017, 201