An illustrative example

Figure 3.4 illustrates an example from Edinburgh. The ground truth is a trajectory of length 4 that starts at a POI of categoryStructures, visits two intermediate POIs of category Structures and Cultural and terminates at a POI of category Structures.

(a) PersTour (b) PoiRank (c) Markov (d) Best Cultural Historical Museums Parks Structures

Figure 3.4: Example of recommendations from different methods. See the main text in Section 3.6.4 for description.

The trajectory recommended by PersTour is a tour with 11 POIs, as shown in Figure 3.4a, with none of the desired intermediate POIs visited. PoiRank(Figure 3.4b) recommended a tour with correct POIs, but with completely different routes. On the other hand, Markov(Figure 3.4c) missed one POI but one of the intermediate routes is consistent with the ground truth. The best recommendation, as shown in Figure 3.4d, with exactly the same points and routes as the ground truth, which in this case is achieved by Rank+MarkovPath.

3.7

Summary

We propose approaches that jointly optimising point preferences and routes to recom- mend trajectories. This is in contrast to related work which looks at only POI or next location recommendation. Point preferences are learned by ranking according to POI and query features, and factorised transition probabilities between POIs are learned from previous trajectories extracted from social media. We investigate the maximum likelihood sequence approach (which may recommend sub-tours) and propose an improved method. Our feature driven approach naturally allows learning the combi- nation of POI ranks and routes. We argue that one should measure performance with respect to the visiting order of POIs, and suggest a new pairs-F1 metric. We empiri- cally evaluate our tour recommendation approaches on five datasets extracted from Flickr photos, and demonstrate that our methods improves on prior work, in terms of both the traditional F1metric and our proposed performance measure. Our promising results from learning points and routes for trajectory recommendation suggests that research in this domain should consider both information sources simultaneously.

Structured Recommendation for

Travel Trajectories

We investigated the path recommendation problem for travel trajectories in Chapter 3. Here, we continue the study of this problem. In contrast to the feature-driven approach that independently learns POI preferences and transition patterns (Section 3.5.2), we propose methods that systematically incorporate both of these information sources by leveraging a substantially modified SSVMs (Section 2.3). Section 4.2 casts path recommendation as a structured prediction problem, and analyses the fundamental challenges in recommending trajectories. Section 4.3 presents a structured recommen- dation approach, which is based on the SSVMs, but with a loss function that accounts for the existence of multiple ground truths, as well as updated training and prediction procedures for recommending paths. Empirical results demonstrate the effectiveness of the proposed approach for travel trajectory recommendation (Section 4.4).

4.1

Introduction

Established techniques for recommendation have focused on a fixed set of individual items such as books or movies (Linden et al., 2003; Koren, 2010; Agarwal et al., 2013; Amatriain and Basilico, 2015; Gomez-Uribe and Hunt, 2015). This does not however capture scenarios where the content is naturally organised withstructures

(e.g., sequence, graph or set). For example, consider recommending linked websites for e-commerce (Antikacioglu et al., 2015), a chemical compound (Dehaspe et al., 1998; Agrafiotis et al., 2007), or a playlist of songs (McFee and Lanckriet, 2011; Chen et al., 2012; Hidasi et al., 2015; Choi et al., 2016). Recall that the problem of recommending travel trajectories is to suggest a trajectory of points-of-interest (POIs) in a city to a visitor (Lu et al., 2010, 2012; Lim et al., 2015; Chen et al., 2016; He et al., 2018), i.e., a sequence of POIs without repeats, which is also known as apath.

Table 4.1: Challenges of travel trajectory recommendation and the proposed solutions.

Challenge Solution

C1. Global cohesion Structured support vector machines (§4.3.2)

C2. Multiple ground truths Ground truths aggregation in structured hinge loss (§4.3.3)

C3. Loop elimination The list Viterbi algorithm or integer linear programming (§4.3.4)

4.2

Problem statement

Suppose we have a set of points-of-interest (POIs)P in a city and historical trajectories visited by travellers_S =_{(x(i),_{y(ij)_}Ni

j=1)}Ni=1, where eachx(i)is a distinct query with {y(ij)_}Ni

j=1an associated set of observed trajectories. Here we define atrajectory query asx = (ps,L)that comprises the start point ps2 P as well as the trip length L(i.e., the desired number of POIs, including ps). Similar to Chapter 3, our task is to learn

a recommender from S that can suggest trajectories for a new query not seen in S. Compared to the definition of trajectory query in Section 3.2, the end location is omitted here, with the aim of accommodating broader scenarios of travel trajectory recommendation in practice. As a remark, we expect most queries to have several distinct trajectories; minimally, for example, there may be two nearby POIs that are visited in interchangeable order by different travellers.

Travel trajectory recommendation brings several challenges, the most immediate of which is the need to ensureglobal cohesionof recommendations. To illustrate, consider a naïve approach which ignores all sequential structure: we could learn a user’s preference for individual POIs, and create a trajectory based on the top ranked items. Such an approach may be sub-optimal, as it is unlikely e.g., a user will want to visit three restaurants in a row; more generally, while a user’s two favourite songs might be in the metal and country genres, a playlist featuring these songs in succession may be jarring. To effectively ensure such global cohesion, we propose to attack the travel trajectory recommendation problem via structured prediction, in particular, leveraging the toolkit of the SSVMs (Section 2.3.1).

However, a vanilla application of such methods does not suffice, owing to two additional challenges: in trajectory recommendation, each input can havemultiple ground truths, since multiple trajectories may be reasonable for a single query; and further, one needs to constrain predictions to avoidrepeatedelements, since users are unlikely to wish to visit the same POI twice. We nonetheless show how to extend the SSVMs to address these challenges, via a novel application of the list Viterbi algorithm (Section 2.4.2), or alternatively, by adapting an integer linear programming formulation of the s-t path TSP (Section 2.4.3). Table 4.1 summaries the three challenges of travel trajectory recommendation and the solutions proposed in this chapter.