Graph Diffusion Research Articles

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%.

Characterization and Inference of Graph Diffusion Processes from Observations of Stationnary Signals

Characterization and Inference of Graph Diffusion Processes from Observations of Stationnary Signals

Local network community detection with continuous optimization of conductance and weighted kernel K-means

Local network community detection is the task of finding a single community of nodes concentrated around few given seed nodes in a localized way. Conductance is a popular objective function used in many algorithms for local community detection. This paper studies a continuous relaxation of conductance. We show that continuous optimization of this objective still leads to discrete communities. We investigate the relation of conductance with weighted kernel k-means for a single community, which leads to the introduction of a new objective function, σ-conductance. Conductance is obtained by setting σ to 0. Two algorithms, EMc and PGDc, are proposed to locally optimize σ-conductance and automatically tune the parameter σ. They are based on expectation maximization and projected gradient descent, respectively. We prove locality and give performance guarantees for EMc and PGDc for a class of dense and well separated communities centered around the seeds. Experiments are conducted on networks with ground-truth communities, comparing to state-of-the-art graph diffusion algorithms for conductance optimization. On large graphs, results indicate that EMc and PGDc stay localized and produce communities most similar to the ground, while graph diffusion algorithms generate large communities of lower quality.

Image re-ranking with an alternating optimization

In this work, we propose an efficient image re-ranking method, without regional information of each indexed feature stored in the inverted file, to re-rank all retrieved images. The motivation of the proposed method is that, there are usually many visual words in the query image that only give votes to irrelevant images. With this observation, we propose to use visual words which are actually useful in finding relevant images to re-rank the retrieved images. To achieve this goal, we first initialize some images similar to the query by maximizing a quadratic function when giving an initial ranking of the retrieved images. The quadratic function is constructed by storing the similarities among a short-list of top ranked images into an affinity matrix, where the similarity between any two images is computed by the proposed graph diffusion. Then, we select a subset of visual words in the query with an alternating optimization strategy: (1) at each iteration, visual words are selected based on the set of similar images that we have found, (2) and in turn, the set of similar images is updated with the set of selected words. These two steps are repeated until convergence. Experimental results on standard benchmark datasets show that the proposed method achieves an order of magnitude speedups over the state-of-the-art spatial based re-ranking techniques, and obtains much better retrieval quality as well.

Subject-Motion Correction in HARDI Acquisitions: Choices and Consequences.

Diffusion-weighted imaging (DWI) is known to be prone to artifacts related to motion originating from subject movement, cardiac pulsation, and breathing, but also to mechanical issues such as table vibrations. Given the necessity for rigorous quality control and motion correction, users are often left to use simple heuristics to select correction schemes, which involves simple qualitative viewing of the set of DWI data, or the selection of transformation parameter thresholds for detection of motion outliers. The scientific community offers strong theoretical and experimental work on noise reduction and orientation distribution function (ODF) reconstruction techniques for HARDI data, where post-acquisition motion correction is widely performed, e.g., using the open-source DTIprep software (1), FSL (the FMRIB Software Library) (2), or TORTOISE (3). Nonetheless, effects and consequences of the selection of motion correction schemes on the final analysis, and the eventual risk of introducing confounding factors when comparing populations, are much less known and far beyond simple intuitive guessing. Hence, standard users lack clear guidelines and recommendations in practical settings. This paper reports a comprehensive evaluation framework to systematically assess the outcome of different motion correction choices commonly used by the scientific community on different DWI-derived measures. We make use of human brain HARDI data from a well-controlled motion experiment to simulate various degrees of motion corruption and noise contamination. Choices for correction include exclusion/scrubbing or registration of motion corrupted directions with different choices of interpolation, as well as the option of interpolation of all directions. The comparative evaluation is based on a study of the impact of motion correction using four metrics that quantify (1) similarity of fiber orientation distribution functions (fODFs), (2) deviation of local fiber orientations, (3) global brain connectivity via graph diffusion distance (GDD), and (4) the reproducibility of prominent and anatomically defined fiber tracts. Effects of various motion correction choices are systematically explored and illustrated, leading to a general conclusion of discouraging users from setting ad hoc thresholds on the estimated motion parameters beyond which volumes are claimed to be corrupted.

Multi-Label Learning With Fused Multimodal Bi-Relational Graph

The problem of multi-label image classification using multiple feature modalities is considered in this work. Given a collection of images with partial labels, we first model the association between different feature modalities and the images labels. These associations are then propagated with a graph diffusion kernel to classify the unlabeled images. Towards this objective, a novel Fused Multimodal Bi-relational Graph representation is proposed, with multiple graphs corresponding to different feature modalities, and one graph corresponding to the image labels. Such a representation allows for effective exploitation of both feature complementariness and label correlation. This contrasts with previous work where these two factors are considered in isolation. Furthermore, we provide a solution to learn the weight for each image graph by estimating the discriminative power of the corresponding feature modality. Experimental results with our proposed method on two standard multi-label image datasets are very promising.

Network diffusion accurately models the relationship between structural and functional brain connectivity networks

The relationship between anatomic connectivity of large-scale brain networks and their functional connectivity is of immense importance and an area of active research. Previous attempts have required complex simulations which model the dynamics of each cortical region, and explore the coupling between regions as derived by anatomic connections. While much insight is gained from these non-linear simulations, they can be computationally taxing tools for predicting functional from anatomic connectivities. Little attention has been paid to linear models. Here we show that a properly designed linear model appears to be superior to previous non-linear approaches in capturing the brain's long-range second order correlation structure that governs the relationship between anatomic and functional connectivities. We derive a linear network of brain dynamics based on graph diffusion, whereby the diffusing quantity undergoes a random walk on a graph. We test our model using subjects who underwent diffusion MRI and resting state fMRI. The network diffusion model applied to the structural networks largely predicts the correlation structures derived from their fMRI data, to a greater extent than other approaches. The utility of the proposed approach is that it can routinely be used to infer functional correlation from anatomic connectivity. And since it is linear, anatomic connectivity can also be inferred from functional data. The success of our model confirms the linearity of ensemble average signals in the brain, and implies that their long-range correlation structure may percolate within the brain via purely mechanistic processes enacted on its structural connectivity pathways.

Going the Distance for Protein Function Prediction: A New Distance Metric for Protein Interaction Networks

In protein-protein interaction (PPI) networks, functional similarity is often inferred based on the function of directly interacting proteins, or more generally, some notion of interaction network proximity among proteins in a local neighborhood. Prior methods typically measure proximity as the shortest-path distance in the network, but this has only a limited ability to capture fine-grained neighborhood distinctions, because most proteins are close to each other, and there are many ties in proximity. We introduce diffusion state distance (DSD), a new metric based on a graph diffusion property, designed to capture finer-grained distinctions in proximity for transfer of functional annotation in PPI networks. We present a tool that, when input a PPI network, will output the DSD distances between every pair of proteins. We show that replacing the shortest-path metric by DSD improves the performance of classical function prediction methods across the board.

An Efficient Framework for Predicting and Recommending M-Commerce Patterns Based on Graph Diffusion Method

An Efficient Framework for Predicting and Recommending M-Commerce Patterns Based on Graph Diffusion Method

Detecting recurrent gene mutation in interaction network context using multi-scale graph diffusion

BackgroundDelineating the molecular drivers of cancer, i.e. determining cancer genes and the pathways which they deregulate, is an important challenge in cancer research. In this study, we aim to identify pathways of frequently mutated genes by exploiting their network neighborhood encoded in the protein-protein interaction network. To this end, we introduce a multi-scale diffusion kernel and apply it to a large collection of murine retroviral insertional mutagenesis data. The diffusion strength plays the role of scale parameter, determining the size of the network neighborhood that is taken into account. As a result, in addition to detecting genes with frequent mutations in their genomic vicinity, we find genes that harbor frequent mutations in their interaction network context.ResultsWe identify densely connected components of known and putatively novel cancer genes and demonstrate that they are strongly enriched for cancer related pathways across the diffusion scales. Moreover, the mutations in the clusters exhibit a significant pattern of mutual exclusion, supporting the conjecture that such genes are functionally linked. Using multi-scale diffusion kernel, various infrequently mutated genes are found to harbor significant numbers of mutations in their interaction network neighborhood. Many of them are well-known cancer genes.ConclusionsThe results demonstrate the importance of defining recurrent mutations while taking into account the interaction network context. Importantly, the putative cancer genes and networks detected in this study are found to be significant at different diffusion scales, confirming the necessity of a multi-scale analysis.

Affinity Learning with Diffusion on Tensor Product Graph

In many applications, we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples. Often the pairwise similarities (which are also called affinities) are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples. As observed in several recent approaches, more reliable similarities can be obtained if the original similarities are diffused in the context of other data points, where the context of each point is a set of points most similar to it. Compared to the existing methods, our approach differs in two main aspects. First, instead of diffusing the similarity information on the original graph, we propose to utilize the tensor product graph (TPG) obtained by the tensor product of the original graph with itself. Since TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities. However, it comes at the price of higher order computational complexity and storage requirement. The key contribution of the proposed approach is that the information propagation on TPG can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph. We prove that a graph diffusion process on TPG is equivalent to a novel iterative algorithm on the original graph, which is guaranteed to converge. After its convergence we obtain new edge weights that can be interpreted as new, learned affinities. We stress that the affinities are learned in an unsupervised setting. We illustrate the benefits of the proposed approach for data manifolds composed of shapes, images, and image patches on two very different tasks of image retrieval and image segmentation. With learned affinities, we achieve the bull's eye retrieval score of 99.99 percent on the MPEG-7 shape dataset, which is much higher than the state-of-the-art algorithms. When the data- points are image patches, the NCut with the learned affinities not only significantly outperforms the NCut with the original affinities, but it also outperforms state-of-the-art image segmentation methods.

Mining Web Graphs for Recommendations

As the exponential explosion of various contents generated on the Web, Recommendation techniques have become increasingly indispensable. Innumerable different kinds of recommendations are made on the Web every day, including movies, music, images, books recommendations, query suggestions, tags recommendations, etc. No matter what types of data sources are used for the recommendations, essentially these data sources can be modeled in the form of various types of graphs. In this paper, aiming at providing a general framework on mining Web graphs for recommendations, (1) we first propose a novel diffusion method which propagates similarities between different nodes and generates recommendations; (2) then we illustrate how to generalize different recommendation problems into our graph diffusion framework. The proposed framework can be utilized in many recommendation tasks on the World Wide Web, including query suggestions, tag recommendations, expert finding, image recommendations, image annotations, etc. The experimental analysis on large data sets shows the promising future of our work.

Fast Semantic Diffusion for Large-Scale Context-Based Image and Video Annotation

Exploring context information for visual recognition has recently received significant research attention. This paper proposes a novel and highly efficient approach, which is named semantic diffusion, to utilize semantic context for large-scale image and video annotation. Starting from the initial annotation of a large number of semantic concepts (categories), obtained by either machine learning or manual tagging, the proposed approach refines the results using a graph diffusion technique, which recovers the consistency and smoothness of the annotations over a semantic graph. Different from the existing graph-based learning methods that model relations among data samples, the semantic graph captures context by treating the concepts as nodes and the concept affinities as the weights of edges. In particular, our approach is capable of simultaneously improving annotation accuracy and adapting the concept affinities to new test data. The adaptation provides a means to handle domain change between training and test data, which often occurs in practice. Extensive experiments are conducted to improve concept annotation results using Flickr images and TV program videos. Results show consistent and significant performance gain (10 +% on both image and video data sets). Source codes of the proposed algorithms are available online.

Transport and dephasing in a quantum dot: Multiply connected graph model

AbstractUsing the theory of diffusion in graphs, we propose a model to study mesoscopic transport through a diffusive quantum dot. The graph consists of three quasi‐1D regions: a central region describing the dot, and two identical left‐ and right‐ wires connected to leads, which mimic contacts of a real system. We find the exact solution of the diffusion equation for this graph and evaluate the conductance including quantum corrections. Our model is complementary to the RMT‐models describing quantum dots. Firstly, it reproduces the universal limit at zero temperature. But the main advantage compared to RMT‐models is that it allows one to take into account interaction‐induced dephasing at finite temperatures. Besides, the crossovers from open to almost closed quantum dots and between different regimes of dephasing can be described within a single framework. We present results for the temperature dependence of the weak localization correction to the conductance for the experimentally relevant parameter range and discuss the possibility to observe the elusive 0D‐regime of dephasing in different mesoscopic systems.

Resolving the structure of interactomes with hierarchical agglomerative clustering

BackgroundGraphs provide a natural framework for visualizing and analyzing networks of many types, including biological networks. Network clustering is a valuable approach for summarizing the structure in large networks, for predicting unobserved interactions, and for predicting functional annotations. Many current clustering algorithms suffer from a common set of limitations: poor resolution of top-level clusters; over-splitting of bottom-level clusters; requirements to pre-define the number of clusters prior to analysis; and an inability to jointly cluster over multiple interaction types.ResultsA new algorithm, Hierarchical Agglomerative Clustering (HAC), is developed for fast clustering of heterogeneous interaction networks. This algorithm uses maximum likelihood to drive the inference of a hierarchical stochastic block model for network structure. Bayesian model selection provides a principled method for collapsing the fine-structure within the smallest groups, and for identifying the top-level groups within a network. Model scores are additive over independent interaction types, providing a direct route for simultaneous analysis of multiple interaction types. In addition to inferring network structure, this algorithm generates link predictions that with cross-validation provide a quantitative assessment of performance for real-world examples.ConclusionsWhen applied to genome-scale data sets representing several organisms and interaction types, HAC provides the overall best performance in link prediction when compared with other clustering methods and with model-free graph diffusion kernels. Investigation of performance on genome-scale yeast protein interactions reveals roughly 100 top-level clusters, with a long-tailed distribution of cluster sizes. These are in turn partitioned into 1000 fine-level clusters containing 5 proteins on average, again with a long-tailed size distribution. Top-level clusters correspond to broad biological processes, whereas fine-level clusters correspond to discrete complexes. Surprisingly, link prediction based on joint clustering of physical and genetic interactions performs worse than predictions based on individual data sets, suggesting a lack of synergy in current high-throughput data.

Predicting functional associations from metabolism using bi-partite network algorithms

BackgroundMetabolic reconstructions contain detailed information about metabolic enzymes and their reactants and products. These networks can be used to infer functional associations between metabolic enzymes. Many methods are based on the number of metabolites shared by two enzymes, or the shortest path between two enzymes. Metabolite sharing can miss associations between non-consecutive enzymes in a serial pathway, and shortest-path algorithms are sensitive to high-degree metabolites such as water and ATP that create connections between enzymes with little functional similarity.ResultsWe present new, fast methods to infer functional associations in metabolic networks. A local method, the degree-corrected Poisson score, is based only on the metabolites shared by two enzymes, but uses the known metabolite degree distribution. A global method, based on graph diffusion kernels, predicts associations between enzymes that do not share metabolites. Both methods are robust to high-degree metabolites. They out-perform previous methods in predicting shared Gene Ontology (GO) annotations and in predicting experimentally observed synthetic lethal genetic interactions. Including cellular compartment information improves GO annotation predictions but degrades synthetic lethal interaction prediction. These new methods perform nearly as well as computationally demanding methods based on flux balance analysis.ConclusionsWe present fast, accurate methods to predict functional associations from metabolic networks. Biological significance is demonstrated by identifying enzymes whose strong metabolic correlations are missed by conventional annotations in GO, most often enzymes involved in transport vs. synthesis of the same metabolite or other enzyme pairs that share a metabolite but are separated by conventional pathway boundaries. More generally, the methods described here may be valuable for analyzing other types of networks with long-tailed degree distributions and high-degree hubs.

GPD: a graph pattern diffusion kernel for accurate graph classification with applications in cheminformatics.

Graph data mining is an active research area. Graphs are general modeling tools to organize information from heterogeneous sources and have been applied in many scientific, engineering, and business fields. With the fast accumulation of graph data, building highly accurate predictive models for graph data emerges as a new challenge that has not been fully explored in the data mining community. In this paper, we demonstrate a novel technique called graph pattern diffusion (GPD) kernel. Our idea is to leverage existing frequent pattern discovery methods and to explore the application of kernel classifier (e.g., support vector machine) in building highly accurate graph classification. In our method, we first identify all frequent patterns from a graph database. We then map subgraphs to graphs in the graph database and use a process we call "pattern diffusion" to label nodes in the graphs. Finally, we designed a graph alignment algorithm to compute the inner product of two graphs. We have tested our algorithm using a number of chemical structure data. The experimental results demonstrate that our method is significantly better than competing methods such as those kernel functions based on paths, cycles, and subgraphs.

Bootstrap Percolation and Diffusion in Random Graphs with Given Vertex Degrees

We consider diffusion in random graphs with given vertex degrees. Our diffusion model can be viewed as a variant of a cellular automaton growth process: assume that each node can be in one of the two possible states, inactive or active. The parameters of the model are two given functions $\theta: {\Bbb N} \rightarrow {\Bbb N}$ and $\alpha:{\Bbb N} \rightarrow [0,1]$. At the beginning of the process, each node $v$ of degree $d_v$ becomes active with probability $\alpha(d_v)$ independently of the other vertices. Presence of the active vertices triggers a percolation process: if a node $v$ is active, it remains active forever. And if it is inactive, it will become active when at least $\theta(d_v)$ of its neighbors are active. In the case where $\alpha(d) =\alpha$ and $\theta(d) =\theta$, for each $d \in {\Bbb N}$, our diffusion model is equivalent to what is called bootstrap percolation. The main result of this paper is a theorem which enables us to find the final proportion of the active vertices in the asymptotic case, i.e., when $n \rightarrow \infty$. This is done via analysis of the process on the multigraph counterpart of the graph model.

Finding friends and enemies in an enemies-only network: A graph diffusion kernel for predicting novel genetic interactions and co-complex membership from yeast genetic interactions

The yeast synthetic lethal genetic interaction network contains rich information about underlying pathways and protein complexes as well as new genetic interactions yet to be discovered. We have developed a graph diffusion kernel as a unified framework for inferring complex/pathway membership analogous to "friends" and genetic interactions analogous to "enemies" from the genetic interaction network. When applied to the Saccharomyces cerevisiae synthetic lethal genetic interaction network, we can achieve a precision around 50% with 20% to 50% recall in the genome-wide prediction of new genetic interactions, supported by experimental validation. The kernels show significant improvement over previous best methods for predicting genetic interactions and protein co-complex membership from genetic interaction data.