Abstract
Associative knowledge networks are often explored by using the so-called spreading activation model to find their key items and their rankings. The spreading activation model is based on the idea of diffusion- or random walk -like spreading of activation in the network. Here, we propose a generalisation, which relaxes an assumption of simple Brownian-like random walk (or equally, ordinary diffusion process) and takes into account nonlocal jump processes, typical for superdiffusive processes, by using fractional graph Laplacian. In addition, the model allows a nonlinearity of the diffusion process. These generalizations provide a dynamic equation that is analogous to fractional porous medium diffusion equation in a continuum case. A solution of the generalized equation is obtained in the form of a recently proposed q-generalized matrix transformation, the so-called q-adjacency kernel, which can be adopted as a systemic state describing spreading activation. Based on the systemic state, a new centrality measure called activity centrality is introduced for ranking the importance of items (nodes) in spreading activation. To demonstrate the viability of analysis based on systemic states, we use empirical data from a recently reported case of a university students’ associative knowledge network about the history of science. It is shown that, while a choice of model does not alter rankings of the items with the highest rank, rankings of nodes with lower ranks depend essentially on the diffusion model.
Highlights
Associative knowledge networks are kinds of semantic networks connecting words, terms or concepts, representing mutual dependency of items that consists of the network [1,2,3]
We have introduced here a model that embodies and quantifies the spreading activation theory related to exploration of semantic networks, in particular as it has been applied in describing the associative knowledge networks (AKNs) [10,11,12]
The assumption that only conventional diffusion or a Brownian random walk should be of interest for AKNs is restrictive and not necessarily the best option from the point of view that what is known about cognitive processes spreading activation is meant to describe
Summary
Associative knowledge networks are kinds of semantic networks connecting words, terms or concepts, representing mutual dependency of items that consists of the network [1,2,3]. A widely used approach for that purpose is a so-called spreading activation model [8,9,10,11,12,13,14,15,16], which assumes that importance of items in an associative network is related to capacity of the item (node) to channel information or messages to activate other nodes within the network. In a recent study [17], we suggested a systemic state approach to model spreading activation, where systemic states correspond to dynamic states of network in spreading activation. This study is a continuation of the previous work [17] and introduces further generalisations that take into account a possibility of non-locality and nonlinearity of the spreading process. Before discussing the generalised model in detail, we briefly summarise main features of the spreading activation approach, key ideas of a generalised model suggested here, and, a context of application [18], which is the same as in the previous study [17]
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