Biased Random Walk Research Articles

Local Structural Aware Heterogeneous Information Network Embedding Based on Relational Self-Attention Graph Neural Network

Heterogeneous Information Networks (HINs) are ubiquitous in our daily life, as they can describe complex interactions among various types of objects. Heterogeneous information network embedding aims to project the network elements of HINs into low-dimensional node representation vectors, which can facilitate effective analyze of HINs. To learn appropriate HIN embeddings, most existing methods usually adopt meta-paths to capture the heterogeneous semantic information, which require domain knowledge and trial-and-error to find suitable meta-paths. Besides, most existing methods fail to preserve high-order local structural information, and pay little attention to the implicit semantics in HINs. In this paper, we propose a local structural aware heterogeneous information network embedding model named LSA-HNE. Specifically, we first design a relational self-attention graph neural network model to aggregate heterogeneous information and automatically extract semantic similarity without using meta-paths. In addition, we employ a biased random walk based sampling method to extract the local structural information and preserve the implicit semantics in HINs. The experiments conducted on four real-world datasets show that our proposed model is effective compared with the state-of-the-art methods.

Retraction of: The speed of a biased random walk on a Galton-Watson tree is analytic

Retraction of: The speed of a biased random walk on a Galton-Watson tree is analytic

Closed-form solutions to the dynamics of confined biased lattice random walks in arbitrary dimensions.

Biased lattice random walks (BLRW) are used to model random motion with drift in a variety of empirical situations in engineering and natural systems such as phototaxis, chemotaxis, or gravitaxis. When motion is also affected by the presence of external borders resulting from natural barriers or experimental apparatuses, modelling biased random movement in confinement becomes necessary. To study these scenarios, confined BLRW models have been employed but so far only through computational techniques due to the lack of an analytic framework. Here, we lay the groundwork for such an analytical approach by deriving the Green's functions, or propagators, for the confined BLRW in arbitrary dimensions and arbitrary boundary conditions. By using these propagators we construct explicitly the time-dependent first-passage probability in one dimension for reflecting and periodic domains, while in higher dimensions we are able to find its generating function. The latter is used to find the mean first-passage passage time for a d-dimensional box, d-dimensional torus or a combination of both. We show the appearance of surprising characteristics such as the presence of saddles in the spatiotemporal dynamics of the propagator with reflecting boundaries, bimodal features in the first-passage probability in periodic domains and the minimization of the mean first-return time for a bias of intermediate strength in rectangular domains. Furthermore, we quantify how in a multitarget environment with the presence of a bias shorter mean first-passage times can be achieved by placing fewer targets close to boundaries in contrast to many targets away from them.

Identifying Key Classes Algorithm in Directed Weighted Class Interaction Network Based on the Structure Entropy Weighted LeaderRank

Identifying key classes can help software maintainers quickly understand software systems. The existing key class recognition algorithms consider the weight of class interaction, but the weight mechanism is single or arbitrary. In this paper, the multitype weighting mechanism is considered, and the key classes are accurately identified by using four kinds of interaction. By abstracting the software system into the directed weighted class interaction network, a novel Structure Entropy Weighted LeaderRank of identifying key classes algorithm is proposed. First, considering multiple types and directions of interactions between every pair of classes, the directed weighted class interaction software network (DWCIS-Network) is built. Second, Class Entropy of each class is initialized by the software structural entropy in DWCIS-Network; the Structure Entropy Weighted LeaderRank applies the biased random walk process to iterate Class Entropy. Finally, the iteration is completed to obtain the Final Class Entropy (FCE) of each class as the importance score of each class, top-k classes are obtained, and key classes are identified. For two sets of experiments on Ant and JHotDraw, our approach effectively identifies key classes in class-level software networks for different top-k of classes, and the recall rates of our approach are the highest, 80% and 100%, respectively. From top-15% to top-5%, the precision of our approach is improved by 13.39%, which is the highest in comparison with the precisions of the other two classical approaches. Compared with the best performance of the two classical approaches, the RankingScore of our approach is improved by 16.51% in JHotDraw.

Extreme-value statistics of stochastic transport processes

We derive exact expressions for the finite-time statistics of extrema (maximum and minimum) of the spatial displacement and the fluctuating entropy flow of biased random walks. Our approach captures key features of extreme events in molecular motor motion along linear filaments. For one-dimensional biased random walks, we derive exact results which tighten bounds for entropy production extrema obtained with martingale theory and reveal a symmetry between the distribution of the maxima and minima of entropy production. Furthermore, we show that the relaxation spectrum of the full generating function, and hence of any moment, of the finite-time extrema distributions can be written in terms of the Marčenko–Pastur distribution of random-matrix theory. Using this result, we obtain efficient estimates for the extreme-value statistics of stochastic transport processes from the eigenvalue distributions of suitable Wishart and Laguerre random matrices. We confirm our results with numerical simulations of stochastic models of molecular motors.

Who is the boss? Identifying key roles in telecom fraud network via centrality-guided deep random walk

PurposeTelecommunication (telecom) fraud is one of the most common crimes and causes the greatest financial losses. To effectively eradicate fraud groups, the key fraudsters must be identified and captured. One strategy is to analyze the fraud interaction network using social network analysis. However, the underlying structures of fraud networks are different from those of common social networks, which makes traditional indicators such as centrality not directly applicable. Recently, a new line of research called deep random walk has emerged. These methods utilize random walks to explore local information and then apply deep learning algorithms to learn the representative feature vectors. Although effective for many types of networks, random walk is used for discovering local structural equivalence and does not consider the global properties of nodes.Design/methodology/approachThe authors proposed a new method to combine the merits of deep random walk and social network analysis, which is called centrality-guided deep random walk. By using the centrality of nodes as edge weights, the authors’ biased random walks implicitly consider the global importance of nodes and can thus find key fraudster roles more accurately. To evaluate the authors’ algorithm, a real telecom fraud data set with around 562 fraudsters was built, which is the largest telecom fraud network to date.FindingsThe authors’ proposed method achieved better results than traditional centrality indices and various deep random walk algorithms and successfully identified key roles in a fraud network.Research limitations/implicationsThe study used co-offending and flight record to construct a criminal network, more interpersonal relationships of fraudsters, such as friendships and relatives, can be included in the future.Originality/valueThis paper proposed a novel algorithm, centrality-guided deep random walk, and applied it to a new telecom fraud data set. Experimental results show that the authors’ method can successfully identify the key roles in a fraud group and outperform other baseline methods. To the best of the authors’ knowledge, it is the largest analysis of telecom fraud network to date.

A framework for quantifying controversy of social network debates using attributed networks: biased random walk (BRW)

All societies have been much more bipolar over the past few years, particularly after the emergence of online social networks and media. In fact, the gap between the two ends of social spectrum is going to be even deeper after the spread of new media. In this circumstance, social polarization has been a growing concern among socialists and computer science experts because of the detrimental impact which online social networks can have on societies by adding fuel to the fire of extremism. Several types of research were conducted for proposing measures to calculate the controversy level in social networks, afterward, to reduce controversy among contradicting viewpoints, for example, by exposing opinions of one side to other side's members. Most of the attempts for quantifying social networks' controversy have considered the networks in their most primary forms, without any attributes. Although these kinds of researches provide platform-free algorithms to be used in different social networks, they are not able to take into account a great deal of useful information provided by users (node attributes).To surmount this shortcoming, we propose a framework to be utilized in different networks with different attributes. We propelled some Biased Random Walks (BRW) to find their path from start point to an initially unknown endpoint with respect to initial energy of start node and energy loss of nodes on the path. We extracted structural attribute of networks, using node2vec, and compared it with state-of-the-art algorithms, and showed its accuracy. Then, we extracted some content attributes of user and analyze their effects on the results of our algorithm. BRW is compared with another state-of-the-art controversy measuring algorithm. Then, its changes in different level of controversy in Persian Twitter is considered to show how it works in different circumstance.

Analysis of node2vec random walks on networks.

Random walks have been proven to be useful for constructing various algorithms to gain information on networks. Algorithm node2vec employs biased random walks to realize embeddings of nodes into low-dimensional spaces, which can then be used for tasks such as multi-label classification and link prediction. The performance of the node2vec algorithm in these applications is considered to depend on properties of random walks that the algorithm uses. In the present study, we theoretically and numerically analyse random walks used by the node2vec. Those random walks are second-order Markov chains. We exploit the mapping of its transition rule to a transition probability matrix among directed edges to analyse the stationary probability, relaxation times in terms of the spectral gap of the transition probability matrix, and coalescence time. In particular, we show that node2vec random walk accelerates diffusion when walkers are designed to avoid both backtracking and visiting a neighbour of the previously visited node but do not avoid them completely.

Biased Continuous-Time Random Walks with Mittag-Leffler Jumps

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps time-changed with an independent (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a “well-scaled” diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the ‘state density kernel’ solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time Mittag-Leffler process. The approach of constructing good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.

RNe2Vec: information diffusion popularity prediction based on repost network embedding

With the rapid development in artificial intelligence and mobile networks, the past decade has witnessed the flourish of social media, and information diffusion popularity prediction in social media has attracted wide attention in both academics and industrials. However, existing popularity prediction methods either rely heavily on human experience to handcraft the features, designate the generative model, or largely depend on the underlying user relation network for embedding learning. Motivated by the above observation, this paper studies the precise prediction of the information diffusion popularity only based on early repost information, given that the underlying user relation network is unknown. To solve this problem, we propose RNe2Vec (repost network to vector), a repost network embedding-based diffusion popularity prediction algorithm. Specifically, we first build a repost network from the early repost data, and then use biased random walks to generate node sequences, in which we elaborately design walking rules to capture different repost behaviors. After that we employ the skip-gram method to learn low dimensional node vectors from the node sequences. Finally, we apply PCA (principal component analysis) algorithm on the node vectors for dimensionality reduction, and combine the embedding features with handcrafted features to train the downstream machine learning models. Experimental results on a microblog dataset show that incorporating network embedding features can significantly improve the overall prediction accuracy.

Reaction–subdiffusion equations for the [formula omitted] reaction in space- and time-dependent force fields: A study for the anomalous dielectric relaxation

To describe the anomalous dielectric relaxation of reaction in space- and time-dependent electric field, we derive the possible kinetic equations for describing the distributions of A and B particles in a simple reaction A→B based on the biased continuous time random walk, when the jumping probabilities are evaluated after or before the waiting time, respectively. Different reaction—subdiffusion equations are derived for different cases, in which the properties of A and B particles are the same or different. The reaction and subdiffusion terms can be decoupled if the past is forgotten when B particles are converted by A particles. According to the corresponding kinetic equations in the spherical coordinates, the dielectric polarization of the reaction is derived. By comparing the different expressions of the polarization, it is found that the reaction–subdiffusion equation based on the jumping probabilities, which are independent of time and evaluated before the waiting time, is more reasonable to describe the dielectric relaxation process in the chemical reaction.

Modeling parking search behavior in the city center: A game-based approach

Drivers cruising for scarce on-street parking in city centers create negative externalities, including congestion and pollution. We apply a serious game – PARKGAME – to understand and model drivers' two intertwined instantaneous parking choices: when to quit cruising and where to cruise. Forty-nine participants took part in a lab experiment in which they had to arrive on time to a fictional appointment or face monetary penalties, and had to choose between uncertain but cheap on-street parking or a certain but costly parking lot. Scenarios diverged on the time to appointment and distance between the meeting place and parking lot locations. Participants played a series of 8 or 16 computer games on a Manhattan grid road network with high on-street parking occupancy and a nearby parking lot of unlimited capacity. Players’ parking choices were analyzed with accelerated-failure time (AFT) and multinomial logistic regression models. Results show that drivers are mostly myopic and risk-averse, and quit their on-street parking search long before the optimal moment. Spatially, drivers are attracted by the lot-destination axis, and their turn choices at junctions comply with a second-order biased random walk. The implications of game-based methods for simulation model development and sustainable parking policy are further discussed.

Haloarchaea swim slowly for optimal chemotactic efficiency in low nutrient environments

Archaea have evolved to survive in some of the most extreme environments on earth. Life in extreme, nutrient-poor conditions gives the opportunity to probe fundamental energy limitations on movement and response to stimuli, two essential markers of living systems. Here we use three-dimensional holographic microscopy and computer simulations to reveal that halophilic archaea achieve chemotaxis with power requirements one hundred-fold lower than common eubacterial model systems. Their swimming direction is stabilised by their flagella (archaella), enhancing directional persistence in a manner similar to that displayed by eubacteria, albeit with a different motility apparatus. Our experiments and simulations reveal that the cells are capable of slow but deterministic chemotaxis up a chemical gradient, in a biased random walk at the thermodynamic limit.

Nonlocal biased random walks and fractional transport on directed networks.

In this paper, we study nonlocal random walk strategies generated with the fractional Laplacian matrix of directed networks. We present a general approach to analyzing these strategies by defining the dynamics as a discrete-time Markovian process with transition probabilities between nodes expressed in terms of powers of the Laplacian matrix. We analyze the elements of the transition matrices and their respective eigenvalues and eigenvectors, the mean first passage times and global times to characterize the random walk strategies. We apply this approach to the study of particular local and nonlocal ergodic random walks on different directed networks; we explore circulant networks, the biased transport on rings and the dynamics on random networks. We study the efficiency of a fractional random walker with bias on these structures. Effects of ergodicity loss which occur when a directed network is not any more strongly connected are also discussed.

Investigation of effect of collagen fiber orientation on tumor cell invasion

Collagen fibers can both inhibit and promote cellular migration, based on their orientation. Physical models such as Random walk can regenerate cellular migration. As such, we proposed a model based on (biased) random walk to study migration on collagen fibers. We took mean squared displacement as the determinant factor for metastatic risk and found that direction of fibers, spatial correlations and migration mode together regulate the risk and we proposed an approach to quantify an existing prognostic approach.

Interplay of various particle acceleration processes in astrophysical environment

AbstractAstrophysical systems possess various sites of particle acceleration, which gives rise to the observed non-thermal spectra. Diffusive shock acceleration (DSA) and stochastic turbulent acceleration (STA) are the candidates for producing very high energy particles in weakly magnetized regions. While DSA is a systematic acceleration process, STA is a random energization process, usually modelled as a biased random walk in energy space with a Fokker-Planck equation. In astrophysical systems, different acceleration processes work in an integrated manner along with various energy losses.Here we study the interplay of both STA and DSA in addition to various energy losses, in a simulated RMHD jet cocoon. Further, we consider a phenomenologically motivated STA timescale and discuss its effect on the emission profile of the RMHD jet. A parametric study on the turbulent acceleration timescale is also conducted to showcase the effect of turbulence damping on the emission structure of the simulated jet.

Cross-Network Skip-Gram Embedding for Joint Network Alignment and Link Prediction

Link prediction and network alignment are two fundamental and interleaved tasks in network analysis. In this paper, we propose a novel cross-network embedding model under the Skip-gram framework, which alternately performs link prediction and network alignment by joint optimization. Vertex sequences, obtained via a biased random walk based on empirical mixture distributions, are used to train a Skip-gram based node embedding model. On one hand, based on the similarity in embedding space, network alignment can be effectively performed either with the initial ground truth alignments as seeds or from scratch. On the other hand, the proposed link prediction model involves training a supervised classifier by sampling a set of positive and negative edges. We also modify and incorporate the Collective Link Fusion (CLF) method under a Skip-gram framework and show that the new method can achieve better results in both tasks. Extensive experimental results show the state-of-the-art performance of our methods.

On biased random walks, corrupted intervals, and learning under adversarial design

We tackle some fundamental problems in probability theory on corrupted random processes on the integer line. We analyze when a biased random walk is expected to reach its bottommost point and when intervals of integer points can be detected under a natural model of noise. We apply these results to problems in learning thresholds and intervals under a new model for learning under adversarial design.

Experimental Realization of Parrondo's Paradox in 1D Quantum Walks

AbstractThe Parrondo effect is a well‐known apparent paradox where a combination of biased random walks displays a counterintuitive reversal in direction. These random walks can be expressed in terms of classical coin tossing games, leading to the surprising result that a combination of losing games can result in a winning game. There is now a large body of literature on quantum walks theoretically analyzing the quantum version of this effect, but to date, there have been no experimental observations of quantum Parrondo walks. Here, the first experimental verification of a quantum Parrondo walk within a quantum optics scenario is demonstrated. Based on the compact large‐scale experimental quantum‐walk platform, two rotation operators are implemented to realize the quantum Parrondo effect. The effect of quantum coherence in a quantum Parrondo walk is also investigated based on a delayed‐choice scheme that cannot be realized with classical light. It is demonstrated that the Parrondo effect vanishes when the quantum walk has a completely decoherent initial state in a delayed‐choice setting. Quantum walks are fundamental to multiple quantum algorithms, and this research provides motivation to expand the results to further explore quantum Parrondo walks.

Nonuniform Hyper-Network Embedding with Dual Mechanism

Network embedding which aims to learn the low-dimensional representations for vertices in networks has been extensively studied in recent years. Although there are various models designed for networks with different properties and different structures for different tasks, most of them are only applied to normal networks which only contain pairwise relationships between vertices. In many realistic cases, relationships among objects are not pairwise and such relationships can be better modeled by a hyper-network in which each edge can connect an uncertain number of vertices. In this article, we focus on two properties of hyper-networks: nonuniform and dual property. In order to make full use of these two properties, we firstly propose a flexible model called Hyper2vec to learn the embeddings of hyper-networks by applying a biased second order random walk strategy to hyper-networks in the framework of Skip-gram. Then, we combine the features of hyperedges by considering the dual hyper-networks to build a further model called NHNE based on 1D convolutional neural networks, and train a tuplewise similarity function for the nonuniform relationships in hyper-networks. Extensive experiments demonstrate the significant effectiveness of our methods for hyper-network embedding.