Convolutional neural networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite-impulse response filters are learned on a hierarchy of layers, each contributing more abstract information than the previous layer. The simplicity and elegance of the convolutional filtering process makes them perfect for structured problems, such as image, video, or voice, where vertices are homogeneous in the sense of number, location, and strength of neighbors. The vast majority of classification problems, for example in the pharmaceutical, homeland security, and financial domains are unstructured. As these problems are formulated into unstructured graphs, the heterogeneity of these problems, such as number of vertices, number of connections per vertex, and edge strength, cannot be tackled with standard convolutional techniques. We propose a novel neural learning framework that is capable of handling both homogeneous and heterogeneous data while retaining the benefits of traditional CNN successes. Recently, researchers have proposed variations of CNNs that can handle graph data. In an effort to create learnable filter banks of graphs, these methods either induce constraints on the data or require preprocessing. As opposed to spectral methods, our framework, which we term Graph-CNNs, defines filters as polynomials of functions of the graph adjacency matrix. Graph-CNNs can handle both heterogeneous and homogeneous graph data, including graphs having entirely different vertex or edge sets. We perform experiments to validate the applicability of Graph-CNNs to a variety of structured and unstructured classification problems and demonstrate state-of-the-art results on document and molecule classification problems.

Functional connectivity (FC) in resting-state functional magnetic resonance imaging (rs-fMRI) is widely used to find coactivating regions in the human brain. Despite its widespread use, the effects of sex and age on resting FC are not well characterized, especially during early adulthood. Here we apply regression and graph theoretical analyses to explore the effects of sex and age on FC between the 116 AAL atlas parcellations (a total of 6670 FC measures). rs-fMRI data of 494 healthy subjects (203 males and 291 females; age range: 22–36 years) from the Human Connectome Project were analyzed. We report the following findings. (1) Males exhibited greater FC than females in 1352 FC measures (1025 survived Bonferroni correction; \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}$$p < 7.49{ \rm{E}} - 6$$ ). In 641 FC measures, females exhibited greater FC than males but none survived Bonferroni correction. Significant FC differences were mainly present in frontal, parietal, and temporal lobes. Although the average FC values for males and females were significantly different, FC values of males and females exhibited large overlap. (2) Age effects were present only in 29 FC measures and all significant age effects showed higher FC in younger subjects. Age and sex differences of FC remained significant after controlling for cognitive measures. (3) Although sex \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}$$\times$$ age interaction did not survive multiple comparison correction, FC in females exhibited a faster cross-sectional decline with age. (4) Male brains were more locally clustered in all lobes but the cerebellum; female brains had a higher clustering coefficient at the whole-brain level. Our results indicate that although both male and female brains show small-world network characteristics, male brains were more segregated and female brains were more integrated. Findings of this study further our understanding of FC in early adulthood and provide evidence to support that age and sex should be controlled for in FC studies of young adults.

Thirion’s Demons [1] is a popular algorithm for nonrigid image registration because of its linear computational complexity and ease of implementation. It approximately solves the diffusion registration problem [2] by successively estimating force vectors that drive the deformation toward alignment and smoothing the force vectors by Gaussian convolution. In this article, we show how the Demons algorithm can be generalized to allow image-driven locally adaptive regularization [3,4] in a manner that preserves both the linear complexity and ease of implementation of the original Demons algorithm. We show that the proposed algorithm exhibits lower target registration error and requires less computational effort than the original Demons algorithm on the registration of serial chest CT scans of patients with lung nodules.

Since its introduction as a powerful graph-based method for image segmentation, the Normalized Cuts (NCuts) algorithm has been generalized to incorporate expert knowledge about how certain pixels or regions should be grouped, or how the resulting segmentation should be biased to be correlated with priors. Previous approaches incorporate hard must-link constraints on how certain pixels should be grouped as well as hard cannot-link constraints on how other pixels should be separated into different groups. In this paper, we reformulate NCuts to allow both sets of constraints to be handled in a soft manner, enabling the user to tune the degree to which the constraints are satisfied. An approximate spectral solution to the reformulated problem exists without requiring explicit construction of a large, dense matrix, hence, computation time is comparable to that of unconstrained NCuts. Using synthetic data and real imagery, we show that soft handling of constraints yields better results than unconstrained NCuts and enables more robust clustering and segmentation than is possible when the constraints are strictly enforced.

Multi-modal image registration is a challenging problem in medical imaging. The goal is to align anatomically identical structures; however, their appearance in images acquired with different imaging devices, such as CT or MR, may be very different. Registration algorithms generally deform one image, the floating image, such that it matches with a second, the reference image, by maximizing some similarity score between the deformed and the reference image. Instead of using a universal, but a priori fixed similarity criterion such as mutual information, we propose learning a similarity measure in a discriminative manner such that the reference and correctly deformed floating images receive high similarity scores. To this end, we develop an algorithm derived from max-margin structured output learning, and employ the learned similarity measure within a standard rigid registration algorithm. Compared to other approaches, our method adapts to the specific registration problem at hand and exploits correlations between neighboring pixels in the reference and the floating image. Empirical evaluation on CT-MR/PET-MR rigid registration tasks demonstrates that our approach yields robust performance and outperforms the state of the art methods for multi-modal medical image registration.