Identifying features to represent graphs such as social networks, protein graphs is increasingly common in both research and business communities, thanks to the fact that data has increased not only in quantity but also in complexity. This results in the graphs to be sparser because not all nodes a re fully connected. In addition, if this whole graph is used as input data for learning algorithms e.g. neural network, a lot of training time will be required. Substantial efforts have been made to convert the graphs to better yet compact representations, among of which is graph embedding. The traditional methods used to map the original graph to its embedding representation had not yielded significant results until deep learning was invented. Many good approaches in this direction, as examples, are DeepWalk, node2vec. However, their general weakness is many important connections in the original graph could be lost. In this paper, we propose another approach to retain more edge information while ensuring the embedding graph is still sufficiently small, compared to the original one. Our experiment results show that the method also increases the accuracy of latter learning models.

Large-scale web search engines need to crawl the Web continuously to discover and download newly created web content. The speed at which the new content is discovered and the quality of the discovered content can have a big impact on the coverage and quality of the results provided by the search engine. In this paper, we propose a search-centric solution to the problem of prioritizing the pages in the frontier of a crawler for download. Our approach essentially orders the web pages in the frontier through a random walk model that takes into account the pages' potential impact on user-perceived search quality. In addition, we propose a link graph enrichment technique that extends this solution. Finally, we explore a machine learning approach that combines different frontier prioritization approaches. We conduct experiments using two very large, real-life web datasets to observe various search quality metrics. Comparisons with several baseline techniques indicate that the proposed approaches have the potential to improve the user-perceived quality of web search results considerably.

In this paper, we provide a short review of Retinex and then present a unifying framework. The fundamental assumption of all Retinex models is that the observed image is a multiplication between the illumination and the true underlying reflectance of the object. Starting from Morel's 2010 PDE model, where illumination is supposed to vary smoothly and where the reflectance is thus recovered from a hard-thresholded Laplacian of the observed image in a Poisson equation, we define our unifying Retinex model in two similar, but more general, steps. We reinterpret the gradient thresholding model as variational models with sparsity constraints. First, we look for a filtered gradient that is the solution of an optimization problem consisting of two terms: a sparsity prior of the reflectance and a fidelity prior of the reflectance gradient to the observed image gradient. Second, since this filtered gradient almost certainly is not a consistent image gradient, we then fit an actual reflectance gradient to it, subject to further sparsity and fidelity priors. This generalized formulation allows making connections with other variational or kernel-based Retinex implementations. We provide simple algorithms for the optimization problems resulting from our framework. In particular, in the quadratic case, we can link our model to a plausible neural mechanism through Wilson--Cowan equations. Beyond unifying existing models, we derive entirely novel Retinex flavors by using more interesting non-local versions for the sparsity and fidelity priors. Eventually, we define within a single framework new Retinex applications to shadow detection and removal, nonuniformity correction, cartoon-texture decomposition, as well as color and hyperspectral image enhancement.

Diffusion MRI offers the unique opportunity of assessing the structural connections of human brains in vivo. With the advance of diffusion MRI technology, multi-shell imaging methods are becoming increasingly practical for large scale studies and clinical application. In this work, we propose a novel method for the analysis of multi-shell diffusion imaging data by incorporating compartment models into a spherical deconvolution framework for fiber orientation distribution (FOD) reconstruction. For numerical implementation, we develop an adaptively constrained energy minimization approach to efficiently compute the solution. On simulated and real data from Human Connectome Project (HCP), we show that our method not only reconstructs sharp and clean FODs for the modeling of fiber crossings, but also generates reliable estimation of compartment parameters with great potential for clinical research of neurological diseases. In comparisons with publicly available DSI-Studio and BEDPOSTX of FSL, we demonstrate that our method reconstructs sharper FODs with more precise estimation of fiber directions. By applying probabilistic tractography to the FODs computed by our method, we show that more complete reconstruction of the corpus callosum bundle can be achieved. On a clinical, two-shell diffusion imaging data, we also demonstrate the feasibility of our method in analyzing white matter lesions.

A recently developed approach, called “empirical wavelet transform,” aims to build one-dimensional (1D) adaptive wavelet frames accordingly to the analyzed signal. In this paper, we present several extensions of this approach to two-dimensional (2D) signals (images). We revisit some well-known transforms (tensor wavelets, Littlewood--Paley wavelets, ridgelets, and curvelets) and show that it is possible to build their empirical counterparts. We prove that such constructions lead to different adaptive frames which show some promising properties for image analysis and processing.

Diffusion tensor imaging is widely used in brain connectivity research. As more and more studies recruit large numbers of subjects, it is important to design registration methods which are not only theoretically rigorous, but also computationally efficient. However, the requirement of reorienting diffusion tensors complicates and considerably slows down registration procedures, due to the correlated impacts of registration forces at adjacent voxel locations. Based on the diffeomorphic Demons algorithm (Vercauteren , 2009), we propose a fast local trust region algorithm for handling inseparable registration forces for quadratic energy functions. The method guarantees that, at any time and at any voxel location, the velocity is always within its local trust region. This local regularization allows efficient calculation of the transformation update with numeric integration instead of completely solving a large linear system at every iteration. It is able to incorporate exact reorientation and regularization into the velocity optimization, and preserve the linear complexity of the diffeomorphic Demons algorithm. In an experiment with 84 diffusion tensor images involving both pair-wise and group-wise registrations, the proposed algorithm achieves better registration in comparison with other methods solving large linear systems (Yeo , 2009). At the same time, this algorithm reduces the computation time and memory demand tenfold.