Good websites should be easy to navigate via hyperlinks, yet maintaining a high-quality link structure is difficult. Identifying pairs of pages that should be linked may be hard for human editors, especially if the site is large and changes frequently. Further, given a set of useful link candidates, the task of incorporating them into the site can be expensive, since it typically involves humans editing pages. In the light of these challenges, it is desirable to develop data-driven methods for automating the link placement task. Here we develop an approach for automatically finding useful hyperlinks to add to a website. We show that passively collected server logs, beyond telling us which existing links are useful, also contain implicit signals indicating which nonexistent links would be useful if they were to be introduced. We leverage these signals to model the future usefulness of yet nonexistent links. Based on our model, we define the problem of link placement under budget constraints and propose an efficient algorithm for solving it. We demonstrate the effectiveness of our approach by evaluating it on Wikipedia, a large website for which we have access to both server logs (used for finding useful new links) and the complete revision history (containing a ground truth of new links). As our method is based exclusively on standard server logs, it may also be applied to any other website, as we show with the example of the biomedical research site Simtk.
Our random walk model ( sec:random walks ) builds on a long tradition of Markovian web navigation models @cite_6 @cite_29 @cite_5 . Among other things, Markov chains have been used to predict users' next clicks @cite_6 @cite_33 as well as their ultimate navigation targets @cite_34 . Our model might be improved by using a higher order Markov model, based on work by Chierichetti al @cite_1 , who found that human browsing is around 10 Further literature on human navigation includes information foraging @cite_0 @cite_26 @cite_15 @cite_34 , decentralized network search @cite_8 @cite_28 @cite_2 , and the analysis of click trails from search result pages @cite_22 @cite_16 @cite_7 .
@cite_26 @cite_33 @cite_22 @cite_8 @cite_28 @cite_7 @cite_29 @cite_1 @cite_6 @cite_16 @cite_0 @cite_2 @cite_5 @cite_15 @cite_34
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One of the most frequently used models for understanding human navigation on the Web is the Markov chain model, where Web pages are represented as states and hyperlinks as probabilities of navigating from one page to another. Predominantly, human navigation on the Web has been thought to satisfy the memoryless Markov property stating that the next page a user visits only depends on her current page and not on previously visited ones. This idea has found its way in numerous applications such as Google's PageRank algorithm and others. Recently, new studies suggested that human navigation may better be modeled using higher order Markov chain models, i.e., the next page depends on a longer history of past clicks. Yet, this finding is preliminary and does not account for the higher complexity of higher order Markov chain models which is why the memoryless model is still widely used. In this work we thoroughly present a diverse array of advanced inference methods for determining the appropriate Markov chain order. We highlight strengths and weaknesses of each method and apply them for investigating memory and structure of human navigation on the Web. Our experiments reveal that the complexity of higher order models grows faster than their utility, and thus we confirm that the memoryless model represents a quite practical model for human navigation on a page level. However, when we expand our analysis to a topical level, where we abstract away from specific page transitions to transitions between topics, we find that the memoryless assumption is violated and specific regularities can be observed. We report results from experiments with two types of navigational datasets (goal-oriented vs. free form) and observe interesting structural differences that make a strong argument for more contextual studies of human navigation in future work. In this paper, we formulate visual tracking as random walks on graph models with nodes representing superpixels and edges denoting relationships between superpixels. We integrate two novel graphs with the theory of Markov random walks, resulting in two Markov chains. First, an ergodic Markov chain is enforced to globally search for the candidate nodes with similar features to the template nodes. Second, an absorbing Markov chain is utilized to model the temporal coherence between consecutive frames. The final confidence map is generated by a structural model which combines both appearance similarity measurement derived by the random walks and internal spatial layout demonstrated by different target parts. The effectiveness of the proposed Markov chains as well as the structural model is evaluated both qualitatively and quantitatively. Experimental results on challenging sequences show that the proposed tracking algorithm performs favorably against state-of-the-art methods. Search engines can record which documents were clicked for which query, and use these query-document pairs as "soft" relevance judgments. However, compared to the true judgments, click logs give noisy and sparse relevance information. We apply a Markov random walk model to a large click log, producing a probabilistic ranking of documents for a given query. A key advantage of the model is its ability to retrieve relevant documents that have not yet been clicked for that query and rank those effectively. We conduct experiments on click logs from image search, comparing our ("backward") random walk model to a different ("forward") random walk, varying parameters such as walk length and self-transition probability. The most effective combination is a long backward walk with high self-transition probability. The website wheresgeorge.com invites its users to enter the serial numbers of their US dollar bills and track them across America and beyond. Why? “For fun and because it had not been done yet”, they say. But the dataset accumulated since December 1998 has provided the ideal raw material to test the mathematical laws underlying human travel, and that has important implications for the epidemiology of infectious diseases. Analysis of the trajectories of over half a million dollar bills shows that human dispersal is described by a ‘two-parameter continuous-time random walk’ model: our travel habits conform to a type of random proliferation known as ‘superdiffusion’. And with that much established, it should soon be possible to develop a new class of models to account for the spread of human disease. The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronize populations of interacting species, stabilize them, and diversify gene pools1,2,3. Human travel, for example, is responsible for the geographical spread of human infectious disease4,5,6,7,8,9. In the light of increasing international trade, intensified human mobility and the imminent threat of an influenza A epidemic10, the knowledge of dynamical and statistical properties of human travel is of fundamental importance. Despite its crucial role, a quantitative assessment of these properties on geographical scales remains elusive, and the assumption that humans disperse diffusively still prevails in models. Here we report on a solid and quantitative assessment of human travelling statistics by analysing the circulation of bank notes in the United States. Using a comprehensive data set of over a million individual displacements, we find that dispersal is anomalous in two ways. First, the distribution of travelling distances decays as a power law, indicating that trajectories of bank notes are reminiscent of scale-free random walks known as Levy flights. Second, the probability of remaining in a small, spatially confined region for a time T is dominated by algebraically long tails that attenuate the superdiffusive spread. We show that human travelling behaviour can be described mathematically on many spatiotemporal scales by a two-parameter continuous-time random walk model to a surprising accuracy, and conclude that human travel on geographical scales is an ambivalent and effectively superdiffusive process. Recent literature has presented evidence that the study of navigation in complex networks is useful to understand their dynamics and topology. Two main approaches are usually considered: navigation of random walkers and navigation of directed walkers. Unlike these approaches ours supposes that a traveler walks optimally in order to minimize the cost of the walking. If this happens, two extreme regimes arise—one dominated by directed walkers and the other by random walkers. We try to characterize the critical point of the transition from one regime to the other in function of the connectivity and the size of the network. Furthermore, we show that this approach can be used to generalize several concepts presented in the literature concerning random navigation and direct navigation. Finally, we defend that investigating the extreme regimes dominated by random walkers and directed walkers is not sufficient to correctly assess the characteristics of navigation in complex networks. Abstract We consider random walks in dynamic random environments given by Markovian dynamics on Z d . We assume that the environment has a stationary distribution μ and satisfies the Poincare inequality w.r.t. μ . The random walk is a perturbation of another random walk (called “unperturbed”). We assume that also the environment viewed from the unperturbed random walk has stationary distribution μ . Both perturbed and unperturbed random walks can depend heavily on the environment and are not assumed to be finite-range. We derive a law of large numbers, an averaged invariance principle for the position of the walker and a series expansion for the asymptotic speed. We also provide a condition for non-degeneracy of the diffusion, and describe in some details equilibrium and convergence properties of the environment seen by the walker. All these results are based on a more general perturbative analysis of operators that we derive in the context of L 2 - bounded perturbations of Markov processes by means of the so-called Dyson–Phillips expansion. We study properties of multiple random walks on a graph under various assumptions of interaction between the particles. To give precise results, we make the analysis for random regular graphs. The cover time of a random walk on a random @math -regular graph was studied in [C. Cooper and A. Frieze, SIAM J. Discrete Math., 18 (2005), pp. 728-740], where it was shown with high probability (whp) that for @math the cover time is asymptotic to @math , where @math . In this paper we prove the following (whp) results, arising from the study of multiple random walks on a random regular graph @math . For @math independent walks on @math , the cover time @math is asymptotic to @math , where @math is the cover time of a single walk. For most starting positions, the expected number of steps before any of the walks meet is @math . If the walks can communicate when meeting at a vertex, we show that, for most starting positions, the expected time for @math walks to broadcast a single piece of information to each other is asymptotic to @math as @math . We also establish properties of walks where there are two types of particles, predator and prey, or where particles interact when they meet at a vertex by coalescing or by annihilating each other. For example, the expected extinction time of @math explosive particles ( @math even) tends to @math as @math . The case of @math coalescing particles, where one particle is initially located at each vertex, corresponds to a voter model defined as follows: Initially each vertex has a distinct opinion, and at each step each vertex changes its opinion to that of a random neighbor. The expected time for a unique opinion to emerge is the same as the expected time for all the particles to coalesce, which is asymptotic to @math . Combining results from the predator-prey and multiple random walk models allows us to compare expected detection times of all prey in the following scenarios: Both the predator and the prey move randomly, the prey moves randomly and the predators stay fixed, and the predators move randomly and the prey stays fixed. In all cases, with @math predators and @math prey the expected detection time is @math , where @math is the @math th harmonic number. A method for predicting pedestrian movement on the basis of a mixed Markov-chain model (MMM) is proposed. MMM takes into account a pedestrian's personality as an unobservable parameter. It also takes into account the effects of the pedestrian's previous status. A promotional experiment in a major shopping mall demonstrated that the highest prediction accuracy of the MMM method is 74.4 . In comparison with methods based on a Markov-chain model (MM) and a hidden-Markov model (HMM) (i.e., prediction rates of about 45 and 2 , respectively), the proposed MMM-based prediction method is substantially more accurate. This pedestrian-movement prediction based on MMM using tracking data will make it possible to provide so-called "adaptive mobile services" with proactive functions. We quantify the effectiveness of random walks for searching and construction of unstructured peer-to-peer (P2P) networks. We have identified two cases where the use of random walks for searching achieves better results than flooding: a) when the overlay topology is clustered, and h) when a client re-issues the same query while its horizon does not change much. For construction, we argue that an expander can he maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk can achieve statistical properties similar to independent sampling (if the second eigenvalue of the transition matrix is hounded away from 1, which translates to good expansion of the network; such connectivity is desired, and believed to hold, in every reasonable network and network model). This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead. As humans we possess an intuitive ability for navigation which we master through years of practice; however existing approaches to model this trait for diverse tasks including monitoring pedestrian flow and detecting abnormal events have been limited by using a variety of hand-crafted features. Recent research in the area of deep-learning has demonstrated the power of learning features directly from the data; and related research in recurrent neural networks has shown exemplary results in sequence-to-sequence problems such as neural machine translation and neural image caption generation. Motivated by these approaches, we propose a novel method to predict the future motion of a pedestrian given a short history of their, and their neighbours, past behaviour. The novelty of the proposed method is the combined attention model which utilises both "soft attention" as well as "hard-wired" attention in order to map the trajectory information from the local neighbourhood to the future positions of the pedestrian of interest. We illustrate how a simple approximation of attention weights (i.e hard-wired) can be merged together with soft attention weights in order to make our model applicable for challenging real world scenarios with hundreds of neighbours. The navigational capability of the proposed method is tested on two challenging publicly available surveillance databases where our model outperforms the current-state-of-the-art methods. Additionally, we illustrate how the proposed architecture can be directly applied for the task of abnormal event detection without handcrafting the features. In this paper, we study the safe navigation of a mobile robot through crowds of dynamic agents with uncertain trajectories. Existing algorithms suffer from the “freezing robot” problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused on reducing the predictive uncertainty for individual agents by employing more informed models or heuristically limiting the predictive covariance to prevent this overcautious behavior. In this work, we demonstrate that both the individual prediction and the predictive uncertainty have little to do with the frozen robot problem. Our key insight is that dynamic agents solve the frozen robot problem by engaging in “joint collision avoidance”: They cooperatively make room to create feasible trajectories. We develop IGP, a nonparametric statistical model based on dependent output Gaussian processes that can estimate crowd interaction from data. Our model naturally captures the non-Markov nature of agent trajectories, as well as their goal-driven navigation. We then show how planning in this model can be efficiently implemented using particle based inference. Lastly, we evaluate our model on a dataset of pedestrians entering and leaving a building, first comparing the model with actual pedestrians, and find that the algorithm either outperforms human pedestrians or performs very similarly to the pedestrians. We also present an experiment where a covariance reduction method results in highly overcautious behavior, while our model performs desirably. We develop a criterion for transience for a general model of branching Markov chains. In the case of multi-dimensional branching random walk in random environment (BRWRE) this criterion becomes explicit. In particular, we show that Condition L of Comets and Popov [3] is necessary and sufficient for transience as conjectured. Furthermore, the criterion applies to two important classes of branching random walks and implies that the critical branching random walk is transient resp. dies out locally. We report that human walk patterns contain statistically similar features observed in Levy walks. These features include heavy-tail flight and pause-time distributions and the super-diffusive nature of mobility. Human walks are not random walks, but it is surprising that the patterns of human walks and Levy walks contain some statistical similarity. Our study is based on 226 daily GPS traces collected from 101 volunteers in five different outdoor sites. The heavy-tail flight distribution of human mobility induces the super-diffusivity of travel, but up to 30 min to 1 h due to the boundary effect of people's daily movement, which is caused by the tendency of people to move within a predefined (also confined) area of daily activities. These tendencies are not captured in common mobility models such as random way point (RWP). To evaluate the impact of these tendencies on the performance of mobile networks, we construct a simple truncated Levy walk mobility (TLW) model that emulates the statistical features observed in our analysis and under which we measure the performance of routing protocols in delay-tolerant networks (DTNs) and mobile ad hoc networks (MANETs). The results indicate the following. Higher diffusivity induces shorter intercontact times in DTN and shorter path durations with higher success probability in MANET. The diffusivity of TLW is in between those of RWP and Brownian motion (BM). Therefore, the routing performance under RWP as commonly used in mobile network studies and tends to be overestimated for DTNs and underestimated for MANETs compared to the performance under TLW. Abstract The enormous growth in the number of documents in the World Wide Web increases the need for improved link navigation and path analysis models. Link prediction and path analysis are important problems with a wide range of applications ranging from personalization to Web server request prediction. The sheer size of the World Wide Web coupled with the variation in users' navigation patterns makes this a very difficult sequence modelling problem. In this paper, the notion of probabilistic link prediction and path analysis using Markov chains is proposed and evaluated. Markov chains allow the system to dynamically model the URL access patterns that are observed in navigation logs based on the previous state. Furthermore, the Markov chain model can also be used in a generative mode to automatically obtain tours. The Markov transition matrix can be analysed further using eigenvector decomposition to obtain personalized hubs authorities'. The utility of the Markov chain approach is demonstrated in many domains: HTTP request prediction, system-driven adaptive Web navigation, tour generation, and detection of personalized hubs authorities' from user navigation profiles. The generality and power of Markov chains is a first step towards the application of powerful probabilistic models to Web path analysis and link prediction. We consider a finite random walk on a weighted graph G; we show that the fraction of time spent in a set of vertices A converges to the stationary probability @math with error probability exponentially small in the length of the random walk and the square of the size of the deviation from @math . The exponential bound is in terms of the expansion of G and improves previous results of [D. Aldous, Probab. Engrg. Inform. Sci., 1 (1987), pp. 33--46], [L. Lovasz and M. Simonovits, Random Structures Algorithms , 4 (1993), pp. 359--412], [M. Ajtai, J. Komlos, and E. Szemeredi, Deterministic simulation of logspace, in Proc. 19th ACM Symp. on Theory of Computing, 1987]. We show that taking the sample average from one trajectory gives a more efficient estimate of @math than the standard method of generating independent sample points from several trajectories. Using this more efficient sampling method, we improve the algorithms of Jerrum and Sinclair for approximating the number of perfect matchings in a dense graph and for approximating the partition function of a ferromagnetic Ising system, and we give an efficient algorithm to estimate the entropy of a random walk on an unweighted graph.