arXiv subjects

Mark Levene

Publications and source records attributed to Mark Levene.

At least 37 records · Page 2Linked to original sources

arXiv2015

A stochastic evolutionary model for capturing human dynamics

The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis, traditionally employed in clinical trials and reliability analysis in engineering. We derive a general solution for the model in the form of a product, and then a continuous approximation to the solution via the renewal equation describing age-structured population dynamics. This enables us to model a wide range of survival distributions, according to the choice of the mortality distribution. We provide empirical evidence for the validity of the model from a longitudinal data set of popular search engine queries over 114 months, showing that the survival function of these queries is closely matched by the solution for our model with power-law mortality.

physics.soc-ph↗

arXiv2014

A stochastic evolutionary model for survival dynamics

The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis, traditionally employed in clinical trials and reliability analysis in engineering. In our model, the only implicit assumption made is that the longer an actor has been in the system, the more likely it is to have failed. We derive a power-law distribution for the process and provide preliminary empirical evidence for the validity of the model from two well-known survival analysis data sets.

physics.soc-ph↗

arXiv2013

A bibliometric index based on the complete list of cited publications

We propose a new index, the $j$-index, which is defined for an author as the sum of the square roots of the numbers of citations to each of the author's publications. The idea behind the $j$-index it to remedy a drawback of the $h$-index $-$ that the $h$-index does not take into account the full citation record of a researcher. The square root function is motivated by our desire to avoid the possible bias that may occur with a simple sum when an author has several very highly cited papers. We compare the $j$-index to the $h$-index, the $g$-index and the total citation count for three subject areas using several association measures. Our results indicate that that the association between the $j$-index and the other indices varies according to the subject area. One explanation of this variation may be due to the proportion of citations to publications of the researcher that are in the $h$-core. The $j$-index is {\em not} an $h$-index variant, and as such is intended to complement rather than necessarily replace the $h$-index and other bibliometric indicators, thus providing a more complete picture of a researcher's achievements.

cs.DL↗

arXiv2011

A Discrete Evolutionary Model for Chess Players' Ratings

The Elo system for rating chess players, also used in other games and sports, was adopted by the World Chess Federation over four decades ago. Although not without controversy, it is accepted as generally reliable and provides a method for assessing players' strengths and ranking them in official tournaments. It is generally accepted that the distribution of players' rating data is approximately normal but, to date, no stochastic model of how the distribution might have arisen has been proposed. We propose such an evolutionary stochastic model, which models the arrival of players into the rating pool, the games they play against each other, and how the results of these games affect their ratings. Using a continuous approximation to the discrete model, we derive the distribution for players' ratings at time $t$ as a normal distribution, where the variance increases in time as a logarithmic function of $t$. We validate the model using published rating data from 2007 to 2010, showing that the parameters obtained from the data can be recovered through simulations of the stochastic model. The distribution of players' ratings is only approximately normal and has been shown to have a small negative skew. We show how to modify our evolutionary stochastic model to take this skewness into account, and we validate the modified model using the published official rating data.

physics.soc-ph↗

arXiv2009

A Methodology for Learning Players' Styles from Game Records

We describe a preliminary investigation into learning a Chess player's style from game records. The method is based on attempting to learn features of a player's individual evaluation function using the method of temporal differences, with the aid of a conventional Chess engine architecture. Some encouraging results were obtained in learning the styles of two recent Chess world champions, and we report on our attempt to use the learnt styles to discriminate between the players from game records by trying to detect who was playing white and who was playing black. We also discuss some limitations of our approach and propose possible directions for future research. The method we have presented may also be applicable to other strategic games, and may even be generalisable to other domains where sequences of agents' actions are recorded.

cs.AI↗

arXiv2007

Modelling the Navigation Potential of a Web Page

Suppose that you are navigating in ``hyperspace'' and you have reached a web page with several outgoing links you could choose to follow. Which link should you choose in such an online scenario? When you are not sure where the information you require resides, you will initiate a navigation session. This involves pruning some of the links and following one of the others, where more pruning is likely to happen the deeper you navigate. In terms of decision making, the utility of navigation diminishes with distance until finally the utility drops to zero and the session is terminated. Under this model of navigation, we call the number of nodes that are available after pruning, for browsing within a session, the {\em potential gain} of the starting web page. Thus the parameters that effect the potential gain are the local branching factor with respect to the starting web page and the discount factor. We first consider the case when the discounting factor is geometric. We show that the distribution of the effective number of links that the user can follow at each navigation step after pruning, i.e. the number of nodes added to the potential gain at that step, is given by the {\em erf} function. We derive an approximation to the potential gain of a web page and show that this is numerically a very accurate estimate. We then consider a harmonic discounting factor and show that, in this case, the potential gain at each step is closely related to the probability density function for the Poisson distribution. The potential gain has been applied to web navigation where it helps the user to choose a good starting point for initiating a navigation session. Another application is in social network analysis, where the potential gain could provide a novel measure of centrality.

physics.soc-ph↗

arXiv2006

Comparing Typical Opening Move Choices Made by Humans and Chess Engines

The opening book is an important component of a chess engine, and thus computer chess programmers have been developing automated methods to improve the quality of their books. For chess, which has a very rich opening theory, large databases of high-quality games can be used as the basis of an opening book, from which statistics relating to move choices from given positions can be collected. In order to find out whether the opening books used by modern chess engines in machine versus machine competitions are ``comparable'' to those used by chess players in human versus human competitions, we carried out analysis on 26 test positions using statistics from two opening books one compiled from humans' games and the other from machines' games. Our analysis using several nonparametric measures, shows that, overall, there is a strong association between humans' and machines' choices of opening moves when using a book to guide their choices.

cs.AI↗

arXiv2006

A Stochastic Evolutionary Growth Model for Social Networks

We present a stochastic model for a social network, where new actors may join the network, existing actors may become inactive and, at a later stage, reactivate themselves. Our model captures the evolution of the network, assuming that actors attain new relations or become active according to the preferential attachment rule. We derive the mean-field equations for this stochastic model and show that, asymptotically, the distribution of actors obeys a power-law distribution. In particular, the model applies to social networks such as wireless local area networks, where users connect to access-points, and peer-to-peer networks where users connect to each other. As a proof of concept, we demonstrate the validity of our model empirically by analysing a public log containing traces from a wireless network at Dartmouth College over a period of three years. Analysing the data processed according to our model, we demonstrate that the distribution of user accesses is asymptotically a power-law distribution.

physics.soc-ph↗

arXiv2006

Evaluating Variable Length Markov Chain Models for Analysis of User Web Navigation Sessions

Markov models have been widely used to represent and analyse user web navigation data. In previous work we have proposed a method to dynamically extend the order of a Markov chain model and a complimentary method for assessing the predictive power of such a variable length Markov chain. Herein, we review these two methods and propose a novel method for measuring the ability of a variable length Markov model to summarise user web navigation sessions up to a given length. While the summarisation ability of a model is important to enable the identification of user navigation patterns, the ability to make predictions is important in order to foresee the next link choice of a user after following a given trail so as, for example, to personalise a web site. We present an extensive experimental evaluation providing strong evidence that prediction accuracy increases linearly with summarisation ability.

cs.AI↗

arXiv2005

A Suffix Tree Approach to Email Filtering

We present an approach to email filtering based on the suffix tree data structure. A method for the scoring of emails using the suffix tree is developed and a number of scoring and score normalisation functions are tested. Our results show that the character level representation of emails and classes facilitated by the suffix tree can significantly improve classification accuracy when compared with the currently popular methods, such as naive Bayes. We believe the method can be extended to the classification of documents in other domains.

cs.AI↗

arXiv2005

Methods for comparing rankings of search engine results

In this paper we present a number of measures that compare rankings of search engine results. We apply these measures to five queries that were monitored daily for two periods of about 21 days each. Rankings of the different search engines (Google, Yahoo and Teoma for text searches and Google, Yahoo and Picsearch for image searches) are compared on a daily basis, in addition to longitudinal comparisons of the same engine for the same query over time. The results and rankings of the two periods are compared as well.

cs.IR↗

arXiv2005

A Model for Collaboration Networks Giving Rise to a Power Law Distribution with an Exponential Cutoff

Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. Despite the generality of the proposed stochastic models, there are still some unexplained phenomena, which may arise due to the limited size of networks such as protein, e-mail, actor and collaboration networks. Such networks may in fact exhibit an exponential cutoff in the power-law scaling, although this cutoff may only be observable in the tail of the distribution for extremely large networks. We propose a modification of the basic stochastic evolutionary model, so that after a node is chosen preferentially, say according to the number of its inlinks, there is a small probability that this node will become inactive. We show that as a result of this modification, by viewing the stochastic process in terms of an urn transfer model, we obtain a power-law distribution with an exponential cutoff. Unlike many other models, the current model can capture instances where the exponent of the distribution is less than or equal to two. As a proof of concept, we demonstrate the consistency of our model empirically by analysing the Mathematical Research collaboration network, the distribution of which is known to follow a power law with an exponential cutoff.

physics.soc-ph↗

arXiv2004

A Stochastic Evolutionary Model Exhibiting Power-Law Behaviour with an Exponential Cutoff

Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. Despite the generality of the proposed stochastic models, there are still some unexplained phenomena, which may arise due to the limited size of networks such as protein and e-mail networks. Such networks may in fact exhibit an exponential cutoff in the power-law scaling, although this cutoff may only be observable in the tail of the distribution for extremely large networks. We propose a modification of the basic stochastic evolutionary model, so that after a node is chosen preferentially, say according to the number of its inlinks, there is a small probability that this node will be discarded. We show that as a result of this modification, by viewing the stochastic process in terms of an urn transfer model, we obtain a power-law distribution with an exponential cutoff. Unlike many other models, the current model can capture instances where the exponent of the distribution is less than or equal to two. As a proof of concept, we demonstrate the consistency of our model by analysing a yeast protein interaction network, the distribution of which is known to follow a power law with an exponential cutoff.

cond-mat.soft↗

arXiv2004

Ranking Pages by Topology and Popularity within Web Sites

We compare two link analysis ranking methods of web pages in a site. The first, called Site Rank, is an adaptation of PageRank to the granularity of a web site and the second, called Popularity Rank, is based on the frequencies of user clicks on the outlinks in a page that are captured by navigation sessions of users through the web site. We ran experiments on artificially created web sites of different sizes and on two real data sets, employing the relative entropy to compare the distributions of the two ranking methods. For the real data sets we also employ a nonparametric measure, called Spearman's footrule, which we use to compare the top-ten web pages ranked by the two methods. Our main result is that the distributions of the Popularity Rank and Site Rank are surprisingly close to each other, implying that the topology of a web site is very instrumental in guiding users through the site. Thus, in practice, the Site Rank provides a reasonable first order approximation of the aggregate behaviour of users within a web site given by the Popularity Rank.

cs.AI↗

arXiv2004

Simulating the conflict between reputation and profitability for online rating portals

We simulate the process of possible interactions between a set of competitive services and a set of portals that provide online rating for these services. We argue that to have a profitable business, these portals are forced to have subscribed services that are rated by the portals. To satisfy the subscribing services, we make the assumption that the portals improve the rating of a given service by one unit per transaction that involves payment. In this study we follow the "what-if" methodology, analysing strategies that a service may choose from to select the best portal for it to subscribe to, and strategies for a portal to accept the subscription such that its reputation loss, in terms of the integrity of its ratings, is minimised. We observe that the behaviour of the simulated agents in accordance to our model is quite natural from the real-would perspective. One conclusion from the simulations is that under reasonable conditions, if most of the services and rating portals in a given industry do not accept a subscription policy similar to the one indicated above, they will lose, respectively, their ratings and reputations, and, moreover the rating portals will have problems in making a profit. Our prediction is that the modern portal-rating based economy sector will eventually evolve into a subscription process similar to the one we suggest in this study, as an alternative to a business model based purely on advertising.

cond-mat.other↗

arXiv2004

A Dynamic Clustering-Based Markov Model for Web Usage Mining

Markov models have been widely utilized for modelling user web navigation behaviour. In this work we propose a dynamic clustering-based method to increase a Markov model's accuracy in representing a collection of user web navigation sessions. The method makes use of the state cloning concept to duplicate states in a way that separates in-links whose corresponding second-order probabilities diverge. In addition, the new method incorporates a clustering technique which determines an effcient way to assign in-links with similar second-order probabilities to the same clone. We report on experiments conducted with both real and random data and we provide a comparison with the N-gram Markov concept. The results show that the number of additional states induced by the dynamic clustering method can be controlled through a threshold parameter, and suggest that the method's performance is linear time in the size of the model.

cs.IR↗

arXiv2004

A Stochastic Model for the Evolution of the Web Allowing Link Deletion

Recently several authors have proposed stochastic evolutionary models for the growth of the web graph and other networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. We present a generalisation of the basic model by allowing deletion of individual links and show that it also gives rise to a power-law distribution. We derive the mean-field equations for this stochastic model and show that by examining a snapshot of the distribution at the steady state of the model, we are able to tell whether any link deletion has taken place and estimate the link deletion probability. Our model enables us to gain some insight into the distribution of inlinks in the web graph, in particular it suggests a power-law exponent of approximately 2.15 rather than the widely published exponent of 2.1.

cond-mat.soft↗

arXiv2003

On the economy of web links: Simulating the exchange process

In the modern web economy hyperlinks have already attained monetary value as incoming links to a web site can increase its visibility on major search engines. Thus links can be viewed as investment instruments that can be the subject of an exchange process. In this study we build a simple model performed by rational agents, whereby links can be bought and sold. Through simulation we achieve consistent economic behaviour of the artificial web community and provide analysis of its micro- and macro-level parameters. In our simulations we take the link economy to its extreme, where a significant number of links are exchanged, concluding that it will lead to a winner take all situation.

cond-mat↗