Graph Diffusion Research Articles

BGMSDDA: a bipartite graph diffusion algorithm with multiple similarity integration for drug-disease association prediction.

Drug repositioning, a method that relies on the information from the original drug-disease association matrix, aims to identify new indications for existing drugs and is expected to greatly reduce the cost and time of drug development. However, most current drug repositioning methods make use of the original drug-disease association matrix directly without preconditioning. As relatively only a few associations between drugs and diseases have been determined from actual observations, the original drug-disease association matrix used in the prediction is sparse, which affects the performance of the prediction method. A method for mining similar features of drugs and diseases is still lacking. To solve these problems, we developed a bipartite graph diffusion algorithm with multiple similarity integration for drug-disease association prediction (BGMSDDA). First, the weight K nearest known neighbors (WKNKN) algorithm was used to reconstruct the drug-disease association matrix. Secondly, an effective method was designed to extract similar characteristics of drugs and diseases based on integrating linear neighborhood similarity and Gaussian kernel similarity. Finally, bipartite graph diffusion was used to infer undiscovered drug-disease associations. After carrying out 10-fold cross-validation experiments, BGMSDDA showed excellent performance on two datasets, specifically with AUC values of 0.939 (Fdataset) and 0.954 (Cdataset), and AUPR values of 0.466 (Fdataset) and 0.565 (Cdataset). Furthermore, to evaluate the accuracy of the results of BGMSDDA, we conducted case studies on three medically used drugs selected from Fdataset and Cdataset and validated the predictive associated diseases of each drug with some databases. Based on the results obtained, BGMSDDA was demonstrated to be useful for predicting drug-disease associations.

Adaptive Graph Filters in Reproducing Kernel Hilbert Spaces: Design and Performance Analysis

This paper develops adaptive graph filters that operate in reproducing kernel Hilbert spaces. We consider both centralized and fully distributed implementations. We first define nonlinear graph filters that operate on graph-shifted versions of the input signal. We then propose a centralized graph kernel least mean squares (GKLMS) algorithm to identify nonlinear graph filters' model parameters. To reduce the dictionary size of the centralized GKLMS, we apply the principles of coherence check and random Fourier features (RFF). The resulting algorithms have performance close to that of the GKLMS algorithm. Additionally, we leverage the graph structure to derive the distributed graph diffusion KLMS (GDKLMS) algorithms. We show that, unlike the coherence check-based approach, the GDKLMS based on RFF avoids the use of a pre-trained dictionary through its data-independent fixed structure. We conduct a detailed performance study of the proposed RFF-based GDKLMS, and the conditions for its convergence both in mean and mean-squared senses are derived. Extensive numerical simulations show that GKLMS and GDKLMS can successfully identify nonlinear graph filters and adapt to model changes. Furthermore, RFF-based strategies show faster convergence for model identification and exhibit better tracking performance in model-changing scenarios.

Accurately modeling the human brain functional correlations with hypergraph Laplacian

The relationship between the structural connectivity (SC) of human brain networks and their functional connectivity (FC) is of immense importance in understanding brain cognition and disorders and has gained significant attention in the neuroscience over the past decade. However, the underlying mechanism of how SC gives rise to the whole pattern of FC especially the negative correlations still remains poorly understood. In this paper, we propose a model that can accurately simulate the resting-state human brain functional correlations based on hypergraph Laplacian, including the negative correlations. We firstly assume that, for each brain region, there are some links showing positive correlations and some other links showing negative correlations. Then we derive a hypergraph model with the two matrices indicating positive and negative correlations respectively using the SC of human brain network. We apply the model to two empirical datasets and the results show that the simulated FC can achieve higher Pearson correlations with the empirical FC, outperforming the state-of-art graph diffusion (GD) model.

Lane Marking Regression From Confidence Area Detection to Field Inference

Lane marking detection is a fundamental yet challenging task for traffic scene understanding. Previous works generally predict traffic line segmentation and obtain lane marking coordinates with a post-processing step, which are vulnerable to various challenging environments including occlusion, illumination variation, shadow, background clutter. In this paper, we propose a novel method, named as Lane marking Regression Network (LRN), which can simultaneously consider confidence area detection and field inference for producing more precise lane markings in an unified encoder-decoder framework. For obtaining confidence detection of lane area, we introduce the graph diffusion mechanism to aggregate the contextual information for better detecting hard areas. The field inference considers the geometric relationship between lane area and lane markings by adopting a novel constraint regression function. Comprehensive evaluations on CULane and GD datasets well demonstrate the significant superiority of our proposed LRN over other state-of-the-arts for lane marking detection.

CGD: Multi-View Clustering via Cross-View Graph Diffusion

Graph based multi-view clustering has been paid great attention by exploring the neighborhood relationship among data points from multiple views. Though achieving great success in various applications, we observe that most of previous methods learn a consensus graph by building certain data representation models, which at least bears the following drawbacks. First, their clustering performance highly depends on the data representation capability of the model. Second, solving these resultant optimization models usually results in high computational complexity. Third, there are often some hyper-parameters in these models need to tune for obtaining the optimal results. In this work, we propose a general, effective and parameter-free method with convergence guarantee to learn a unified graph for multi-view data clustering via cross-view graph diffusion (CGD), which is the first attempt to employ diffusion process for multi-view clustering. The proposed CGD takes the traditional predefined graph matrices of different views as input, and learns an improved graph for each single view via an iterative cross diffusion process by 1) capturing the underlying manifold geometry structure of original data points, and 2) leveraging the complementary information among multiple graphs. The final unified graph used for clustering is obtained by averaging the improved view associated graphs. Extensive experiments on several benchmark datasets are conducted to demonstrate the effectiveness of the proposed method in terms of seven clustering evaluation metrics.

Identification of FMR1-regulated molecular networks in human neurodevelopment.

RNA-binding proteins (RNA-BPs) play critical roles in development and disease to regulate gene expression. However, genome-wide identification of their targets in primary human cells has been challenging. Here, we applied a modified CLIP-seq strategy to identify genome-wide targets of the FMRP translational regulator 1 (FMR1), a brain-enriched RNA-BP, whose deficiency leads to Fragile X Syndrome (FXS), the most prevalent inherited intellectual disability. We identified FMR1 targets in human dorsal and ventral forebrain neural progenitors and excitatory and inhibitory neurons differentiated from human pluripotent stem cells. In parallel, we measured the transcriptomes of the same four cell types upon FMR1 gene deletion. We discovered that FMR1 preferentially binds long transcripts in human neural cells. FMR1 targets include genes unique to human neural cells and associated with clinical phenotypes of FXS and autism. Integrative network analysis using graph diffusion and multitask clustering of FMR1 CLIP-seq and transcriptional targets reveals critical pathways regulated by FMR1 in human neural development. Our results demonstrate that FMR1 regulates a common set of targets among different neural cell types but also operates in a cell type–specific manner targeting distinct sets of genes in human excitatory and inhibitory neural progenitors and neurons. By defining molecular subnetworks and validating specific high-priority genes, we identify novel components of the FMR1 regulation program. Our results provide new insights into gene regulation by a critical neuronal RNA-BP in human neurodevelopment.

Semi-supervised classification on graphs using explicit diffusion dynamics

Classification tasks based on feature vectors can be significantly improved by including within deep learning a graph that summarises pairwise relationships between the samples. Intuitively, the graph acts as a conduit to channel and bias the inference of class labels. Here, we study classification methods that consider the graph as the originator of an explicit graph diffusion. We show that appending graph diffusion to feature-based learning as an a posteriori refinement achieves state-of-the-art classification accuracy. This method, which we call Graph Diffusion Reclassification (GDR), uses overshooting events of a diffusive graph dynamics to reclassify individual nodes. The method uses intrinsic measures of node influence, which are distinct for each node, and allows the evaluation of the relationship and importance of features and graph for classification. We also present diff-GCN, a simple extension of Graph Convolutional Neural Network (GCN) architectures that leverages explicit diffusion dynamics, and allows the natural use of directed graphs. To showcase our methods, we use benchmark datasets of documents with associated citation data.

基于图和多特征传播的图像显著性检测

基于图和多特征传播的图像显著性检测

Online Distributed Learning Over Graphs With Multitask Graph-Filter Models

In this article, we are interested in adaptive and distributed estimation of graph filters from streaming data. We formulate this problem as a consensus estimation problem over graphs, which can be addressed with diffusion LMS strategies. Most popular graph-shift operators such as those based on the graph Laplacian matrix, or the adjacency matrix, are not energy preserving. This may result in an ill-conditioned estimation problem, and reduce the convergence speed of the distributed algorithms. To address this issue and improve the transient performance, we introduce a preconditioned graph diffusion LMS algorithm. We also propose a computationally efficient version of this algorithm by approximating the Hessian matrix with local information. Performance analyses in the mean and mean-square sense are provided. Finally, we consider a more general problem where the filter coefficients to estimate may vary over the graph. To avoid a large estimation bias, we introduce an unsupervised clustering method for splitting the global estimation problem into local ones. Numerical results show the effectiveness of the proposed algorithms and validate the theoretical results.

Diffusion induced graph representation learning

Nowadays, graph representation learning has aroused a lot of research interest, which aims to learn the latent low-dimensional representations of graph nodes, while preserving the graph structure. Based on the local smooth assumption, some existing methods have achieved significant success. However, although the structure information of data has been taken into consideration, these models fail to capture enough connectivity pattern such as high-order connections. To alleviate this issue, we propose a Graph Diffusion Network (GDN) that can dynamically preserve local and global consistency of graph. More specifically, Graph Diffusion Auto-encoder is utilized as the main framework in GDN to nonlinearly maintain global information volume. Different from simple auto-encoders, the forward propagation in our model is conducted through Graph Diffusion System which can guide the random walk of information flow to sense the high-order local relationships on graph. Furthermore, to discover a customized graph structure that reveals the similarities between nodes, the connection relationship between nodes are refined by learned metrics with the preservation of scale-free property. By the dynamically self-refining on the graph structure, it can be promoted towards learning the intrinsic node representations in a progressive way. Experimental results on node classification tasks demonstrate the effectiveness of the proposed GDN model.

Graph MBO on Star Graphs and Regular Trees. With Corrections to DOI 10.1007/s00032-014-0216-8

The graph Merriman–Bence–Osher scheme produces, starting from an initial node subset, a sequence of node sets obtained by iteratively applying graph diffusion and thresholding to the characteristic (or indicator) function of the node subsets. One result in [14] gives sufficient conditions on the diffusion time to ensure that the set membership of a given node changes in one iteration of the scheme. In particular, these conditions only depend on local information at the node (information about neighbors and neighbors of neighbors of the node in question). In this paper we show that there does not exist any graph which satisfies these conditions. To make up for this negative result, this paper also presents positive results regarding the Merriman–Bence–Osher dynamics on star graphs and regular trees. In particular, we present sufficient (and in some cases necessary) results for the set membership of a given node to change in one iteration.

A Regularization Framework for Learning Over Multitask Graphs

This letter proposes a general regularization framework for inference over multitask networks. The optimization approach relies on minimizing a global cost consisting of the aggregate sum of individual costs regularized by a term that allows to incorporate global information about the graph structure and the individual parameter vectors into the solution of the inference problem. An adaptive strategy, which responds to streaming data and employs stochastic approximations in place of actual gradient vectors, is devised and studied. Methods allowing the distributed implementation of the regularization step are also discussed. This letter shows how to blend real-time adaptation with graph filtering and a generalized regularization framework to result in a graph diffusion strategy for distributed learning over multitask networks.

A longitudinal model for tau aggregation in Alzheimer's disease based on structural connectivity.

Tau tangles are a pathological hallmark of Alzheimer?s disease (AD) with strong correlations existing between tau aggregation and cognitive decline. Studies in mouse models have shown that the characteristic patterns of tau spatial spread associated with AD progression are determined by neural connectivity rather than physical proximity between different brain regions. We present here a network diffusion model for tau aggregation based on longitudinal tau measures from positron emission tomography (PET) and structural connectivity graphs from diffusion tensor imaging (DTI). White matter fiber bundles reconstructed via tractography from the DTI data were used to compute normalized graph Laplacians which served as graph diffusion kernels for tau spread. By linearizing this model and using sparse source localization, we were able to identify distinct patterns of propagative and generative buildup of tau at a population level. A gradient descent approach was used to solve the sparsity-constrained optimization problem. Model fitting was performed on subjects from the Harvard Aging Brain Study cohort. The fitted model parameters include a scalar factor controlling the network-based tau spread and a network-independent seed vector representing seeding in different regions-of-interest. This parametric model was validated on an independent group of subjects from the same cohort. We were able to predict with reasonably high accuracy the tau buildup at a future time-point. The network diffusion model, therefore, successfully identifies two distinct mechanisms for tau buildup in the aging brain and offers a macroscopic perspective on tau spread.

Large algebraic connectivity fluctuations in spatial network ensembles imply a predictive advantage from node location information

A Random Geometric Graph (RGG) ensemble is defined by the disordered distribution of its node locations. We investigate how this randomness drives sample-to-sample fluctuations in the dynamical properties of these graphs. We study the distributional properties of the algebraic connectivity which is informative of diffusion and synchronization timescales in graphs. We use numerical simulations to provide the first characterisation of the algebraic connectivity distribution for RGG ensembles. We find that the algebraic connectivity can show fluctuations relative to its mean on the order of $30 \%$, even for relatively large RGG ensembles ($N=10^5$). We explore the factors driving these fluctuations for RGG ensembles with different choices of dimensionality, boundary conditions and node distributions. Within a given ensemble, the algebraic connectivity can covary with the minimum degree and can also be affected by the presence of density inhomogeneities in the nodal distribution. We also derive a closed-form expression for the expected algebraic connectivity for RGGs with periodic boundary conditions for general dimension.

An Euclidean Distance Based on Tensor Product Graph Diffusion Related Attribute Value Embedding for Nominal Data Clustering

Not like numerical data clustering, nominal data clustering is a very difficult problem because there exists no natural relative ordering between nominal attribute values. This paper mainly aims to make the Euclidean distance measure appropriate to nominal data clustering, and the core idea is the attribute value embedding, namely, transforming each nominal attribute value into a numerical vector. This embedding method consists of four steps. In the first step, the weights, which can quantify the amount of information in attribute values, is calculated for each value in each nominal attribute based on each object and its k nearest neighbors. In the second step, an intra-attribute value similarity matrix is created for each nominal attribute by using the attribute value's weights. In the third step, for each nominal attribute, we find another attribute with the maximal dependence on it, and build an inter-attribute value similarity matrix on the basis of the attribute value's weights related to these two attributes. In the last step, a diffusion matrix of each nominal attribute is constructed by the tensor product graph diffusion process, and this step can cause the acquired value embedding to contain simultaneously the intra- and inter-attribute value similarities information. To evaluate the effectiveness of our proposed method, experiments are done on 10 data sets. Experimental results demonstrate that our method not only enables the Euclidean distance to be used for nominal data clustering, but also can acquire the better clustering performance than several existing state-of-the-art approaches.

Characterization and Inference of Graph Diffusion Processes From Observations of Stationary Signals

Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph signal processing tools cannot be used anymore. Researchers have proposed approaches to infer a graph topology from observations of signals on its vertices. Since the problem is ill-posed, these approaches make assumptions, such as smoothness of the signals on the graph, or sparsity priors. In this paper, we propose a characterization of the space of valid graphs, in the sense that they can explain stationary signals. To simplify the exposition in this paper, we focus here on the case where signals were i.i.d. at some point back in time and were observed after diffusion on a graph. We show that the set of graphs verifying this assumption has a strong connection with the eigenvectors of the covariance matrix, and forms a convex set. Along with a theoretical study in which these eigenvectors are assumed to be known, we consider the practical case when the observations are noisy, and experimentally observe how fast the set of valid graphs converges to the set obtained when the exact eigenvectors are known, as the number of observations grows. To illustrate how this characterization can be used for graph recovery, we present two methods for selecting a particular point in this set under chosen criteria, namely graph simplicity and sparsity. Additionally, we introduce a measure to evaluate how much a graph is adapted to signals under a stationarity assumption. Finally, we evaluate how state-of-the-art methods relate to this framework through experiments on a dataset of temperatures.

Ergodicity in Stationary Graph Processes: A Weak Law of Large Numbers

For stationary signals in time the weak law of large numbers (WLLN) states that ensemble and realization averages are within e of each other with a probability of order O(1/Ne^2) when considering N signal components. The graph WLLN introduced in this paper shows that the same is essentially true for signals supported on graphs. However, the notions of stationarity, ensemble mean, and realization mean are different. Recent papers have defined graph stationary signals as those that satisfy a form of invariance with respect to graph diffusion. The ensemble mean of a graph stationary signal is not a constant but a node-varying signal whose structure depends on the spectral properties of the graph. The realization average of a graph signal is defined here as an average of successive weighted averages of local signal values with signal values of neighboring nodes. The graph WLLN shows that this two node-varying signals are within e of each other with probability of order O(1/Ne^2) in at least some nodes. In stationary time signals, the realization average is not only a consistent estimator of the ensemble mean but also optimal in terms of mean squared error (MSE). This is not true of graph signals. Optimal MSE graph filter designs are also presented. An example problem concerning the estimation of the mean of a Gaussian random field is presented.

Large-scale vocabularies with local graph diffusion and mode seeking

In this work, we propose a large-scale clustering method that captures the intrinsic manifold structure of local features by graph diffusion for image retrieval. The proposed method is a mode seeking like algorithm, and it finds the mode of each data point with the defined stochastic matrix resulted by a same local graph diffusion process. While mode seeking algorithms are normally costly, our method is efficient to generate large-scale vocabularies as it is not iterative, and the major computational steps are done in parallel. Furthermore, unlike other clustering methods, such as k-means and spectral clustering, the proposed clustering algorithm does not need to empirically appoint the number of clusters beforehand, and its time complexity is independent on the number of clusters. Experimental results on standard image retrieval datasets demonstrate that the proposed method compares favorably to previous large-scale clustering methods.

Self-organisation of small-world networks by adaptive rewiring in response to graph diffusion

Complex networks emerging in natural and human-made systems tend to assume small-world structure. Is there a common mechanism underlying their self-organisation? Our computational simulations show that network diffusion (traffic flow or information transfer) steers network evolution towards emergence of complex network structures. The emergence is effectuated through adaptive rewiring: progressive adaptation of structure to use, creating short-cuts where network diffusion is intensive while annihilating underused connections. With adaptive rewiring as the engine of universal small-worldness, overall diffusion rate tunes the systems’ adaptation, biasing local or global connectivity patterns. Whereas the former leads to modularity, the latter provides a preferential attachment regime. As the latter sets in, the resulting small-world structures undergo a critical shift from modular (decentralised) to centralised ones. At the transition point, network structure is hierarchical, balancing modularity and centrality - a characteristic feature found in, for instance, the human brain.

Localization with Graph Diffusion Property.

Node localization is an essential issue in wireless sensor networks (WSNs). Many range-free localization methods have been proposed to satisfy the requirement of low-system cost. However, some range-free methods only depend on network connectivity, and others only utilize the proximity information attached in neighborhood ordering. To employ the strength of the above two aspects, this paper introduces a new metric system called Combined and Weighted Diffusion Distance (CWDD). CWDD is designed to obtain the relative distance among nodes based on both graph diffusion property and neighbor information. We implement our design by embedding CWDD into two well-known localization algorithms and evaluate it by extensive simulations. Results show that our design improves the localization performance in large scale and non-uniform sensor networks, which reduces positioning errors by as much as 26%.