| Summary: | <p>Understanding the relationships between products is an important problem in industry, where two central concepts are complements and substitutes. Complementary products are sold separately but used together, each creating a demand for the other, while substitute products can be used in place of each other, each taking a demand from the other. Hence, such two competing product relationships are also essential in further understanding how the demand change of some products transforms into the change of the whole range of products.</p>
<p>To start with, we capture the information in the sales transaction data through a bipartite network representation, then products of the two competing relationships can be characterised as certain roles in the network. For this reason, the identification of the nature of a relationship between products is directly related to the more general problem of role extraction in network science. Targeting at extracting the two specific roles, we propose a novel customised data-driven role extraction method. With the product relationships, we can consider unipartite networks only of products, and then the change of demand can be modelled as dynamics on top of such networks. Further, the associated decision making can be formulated as optimisation problems with appropriate objectives. In this thesis, we consider the one that is closely related to viral marketing, where we aim to maximise the overall revenue through putting a small range of products on promotion. We model the dynamic of demand changes as information propagating through the network, and the overall change as the influence on each node, thus the problem is then a variant of the influence maximisation, where our objective is a (price-)weighted sum of the influence. Accordingly, we propose a novel class of information propagation model for demand dynamics, unifying the mechanisms underlying the classic models, and a general framework for the associated influence maximisation problem, from simple networks of a single relation to signed networks of two competing relations.</p>
<p>Although inspired by the retail industry, the proposed role extraction method can be applied to other contexts, including trading networks, ecological systems and social networks, where both the identification of cooperative and competitive relations are of interest. Further, the proposed information propagation model and influence maximisation framework are also applicable to more general dynamical processes on either simple or signed networks, including social networks with trust-distrust relationships and brain networks with positive-negative functional connections.</p>
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