Detecting Memory and Structure in Human Navigation Patterns Using Markov Chain Models of Varying Order

Abstract

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.

Mapping Higher-Order Network Flows in Memory and Multilayer Networks with Infomap

“…The standard approach of modeling dynamical processes on networks with first-order flows oversimplifies the real dynamics and sets a limit of what can actually be detected in the system (Figure 1). Capturing critical phenomena in the dynamics and function of complex systems therefore often requires models of higher-order network flows [5][6][7][23][24][25][26][27][28].…”

When is a Network a Network?

“…Considering the graph-analytic view taken by ranking algorithms like PageRank [17], a number of works addressed the question whether the modeling of human click paths based on the topology of the underlying Web graph is justi ed [4,22,28,34]. Chieriche i et al [4] study whether the Markovian assumption underlying such models is justi ed.…”

“…Similarly, West and Leskovec [34] model navigation paths of users playing the Wikispeedia game, nding that incorporating correlations not captured by the topology of the Wikipedia graph improves the performance of a target prediction algorithm. Taking a model selection approach, Singer et al [28] argue that correlations in click streams do not justify Markov models of higher orders when modeling navigation pa erns at the page level, while they are warranted for coarse-grained data at the level of topics or categories.…”

“…Higher-order network modeling techniques building on higher-or variable-order Markov models have been proposed to address this problem [18,20,21,25,26,36]. While there is agreement about the need for such techniques, principled methods to decide (i) when the use of network-based methods is invalid, and (ii) which higher-order model should be used for a given data set were investigated only recently [18,28]. Moreover, using state-of-the-art Markov chain inference techniques, previous works did not account for special characteristics of data on multiple, independent paths with varying lengths that are observed in a graph.…”

“…e degrees of freedom of a Markov chain of order k over a state space |V | are commonly given as |V | k (|V | − 1) [1,27,28,30]. is re ects that (i) the transition matrix of a Markov chain of order k has |V | k +1 entries, and (ii) the rows in this matrix must sum to one.…”