We propose a computational model to synthesise individual-level user profiles from scarce populationlevel data in tourism domain. Namely, our model exploits, as input, summary information about the items (and item attributes) selected by users, and, as output, builds individual-level user profiles that respect the provided input. As a key contribution, we utilise discrete choice behavioural model to conjoin (via chi-square divergence minimisation) the choices made by the synthesised population of users with the choices observed in the real data. To showcase our idea, we release a code and a dataset that includes synthesised profiles of 10,000 users that interacted with circa 200 items.
Our research on user profiles synthesis relates to the class of Synthetic Reconstruction techniques
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Our model requires structured input that can be tweaked depending on target constraints of the tourism environment. In general, the computational model relies on (1) prior knowledge about the environment presented in a form of summary tables, (2) POI attributes model, and (3) choice model that determines which POIs a tourist with a given profile will visit. As output, the computational model generates tourist profiles that set tourist preferences towards POIs. We discuss the algorithm that links input and output together in a unified optimisation framework.
The computational model by design relies on two marginal distributions that provide a summary of tourist behaviour. The first marginal sum is a POIs visit popularity distribution q∗ . We model a distribution q∗ as a long-tail with probabilities q∗j ∝ 1/rj, where rj is an assigned rank for j-th POI and the most popular one has rank 1. In a population of N users and J POIs on average q∗j N users visit the j-th POI. Importantly, probabilities do not sum to 1, as users can visit more than one POI. Second marginal sum is a tourist level of activity a∗ . This is the percentage of tourists who visit a given number of POIs during a trip. We model a discrete distribution a∗ as a non-negative probability mass vector over possible number of visited POIs. Similarly, we assume that on average a∗tN users visit exactly t POIs during a trip (see Figure 1 and Table 1).
Each POI j has a unique representation fj that we model as a vector with d components
(fj1, fj2, . . . , fjd) ∈ [
Each tourist n has a unique representation zn that we model as a vector with d components
(zn1, zn2, . . . , znd) in the same vector space as POIs. Components of this vector represent
preferences towards corresponding POI attributes. From tourism literature, tourists can be
grouped on the basis of their preferences [
Each user, choosing an items, tries to maximise their own utility. Choice protocol is as follows, user n estimates a linear utility unj = zTnfj for each item j in the collection of POIs and then selects top t (in terms of utility) items from this collection. Parameter t reflects how many items will be selected by the user during his/her trip (in our example Figure 1 it can be from 1 to 5). This parameter usually depends on available time budget, time required to visit a POI, and distances between POIs. Even this simple choice model makes synthesis of tourist profiles – our main goal in this study – very dificult, since user decisions are based on a non-diferentiable operator arg max. In the next section we discuss an approach to relax this operator and, as a consequence, simplify the synthesis problem.
The aim of this research is to synthesise a population of N users {zn} that interact with a collection of J items {fj} in accordance with utility unj = zTnfj maximisation framework. It can be considered as an optimisation problem over dN parameters. Namely, we are searching for user profiles such that user choices are compatible with POIs visit popularity distribution q∗ : popular items appear more often in the top choices because the utility of popular items should be higher than the utility of long-tail items. To fit the population we optimise the quadratic loss:
J Lz = ∑︂(pj − q∗j )2/q∗j + Rz →− min j=1 z1,z2,...,zN
G N G Rz = ∑︂ λ wg ∑︂ 1{n∈g} · ∥ zn − z¯g∥2 + λ bg ∑︂ cossim(z¯g, z¯h).
g=1 n=1 h>g pj is the probability that the j-th item is chosen. We approximate pj as the fraction of users who prefer the j-th item based on utility maximising choice model. Regularisation Rz contains two parts: the first part imposes Gaussian prior on user profiles within each cluster g with centroid z¯g, and the second part penalises for similarities between each two cluster centroids z¯g and z¯h. To optimise this quadratic loss with standard gradient-based techniques we re-parameterise (to relax arg max structure of choice model) probability vector for each component pk as:
N T pk = N1 ∑︂ ∑︂ a∗t · (︂ 1 + un(j) means that the sum is taken over an ordered in decreasing order subsequence of un(1), un(2), . . . , un(J) starting from index t + 1. For high β values, this estimates the share of users for whom item k belongs to top-t choices, i.e., unk > un(t+1). Expectation over distribution a∗ (over a possible number of visits t) reflects the fact that users, even with the same preferences zn, may visit diferent number of POIs during a trip depending on the available time budget.
To showcase our approach, we synthesised tourist profiles. Table 1 summarises experimental setup. Figure 2 shows correlation structure of the synthesised tourist profiles. Figure 3 shows reconstructed tourist choices: each black dot is a POI (choice) favoured by a particular tourist according to his/her utility model, while the right side portrays marginalised over all tourists choices. Marginalised fit – our measure of goodness of fit – is consistent: proposed computational model learned tourist profiles in such a way that corresponding tourist choices match with the ground truth visit popularity distribution, small deviations are due to substitution of combinatorial hard-argmax optimisation problem (that is intractable) with a diferentiable problem with soft-argmax indicators. The source code is available on Github1.
We have proposed a computational model to synthesise tourist profiles from aggregated data and released a synthetic dataset with a source code to generate it. Table 1 shows our configuration, which can be tweaked based on the target tourism environment. Our model exploits gradientbased optimisation, making it scalable to very large environments (millions of tourists and thousands of POIs). Further extensions require the close collaboration with experts in the domain to expand knowledge about the tourist population: improve user generation process (enforce correlation structure), and support context-aware user behaviour. 1https://github.com/pashaPASHaa/tourist-profiles-data-generation