## 4 Experiments and Results
### Evaluation Metrics  
The metrics were modelled as suggested by [PERSON] and [PERSON] ([PERSON] and [PERSON] (2018)). Let \(U\) be the set of users in the test set, \(R\) the set of POIs recommended to the users in \(U\), \(R_{u}\) the set of POIsrecommended to a particular user \(u\), \(V\) the set of POIs visited by users in the test set, \(V_{u}\) the set of POIs visited by a specific user \(u\), and \(P\) the set of all possible recommendable POIs. * **Average Precision (AP)**: It is the ratio of _correct_ POI recommendations made to the users in the test set. A correct recommendation was determined by the user's degree of preference in the category of the POI. AP is formulated as follows: \[AP=\frac{1}{|U|\mid\mid R_{u}\mid}\sum_{u\in U}\sum_{r\in R_{u}}1_{CAT_{prf}}( \psi(r))\] (8) The function \(\psi(. )\) gets the category of a POI. \(1_{CAT_{prf}}\) is an indicator function that has value 1 if \(\psi(. )\) returns a category that is preferred by the user and 0 otherwise. A category is preferred by a user if at least one of the user's tweets has been associated with it. * **Average Category Recall (ACR)**: It is the ratio of _preferred_ recommendable POIs that are actually recommended. ACR is formulated as: \[ACR=\frac{1}{|U|}\sum_{u\in U}\frac{\mid R_{u}\cap PREF_{u}\mid}{\mid PREF_{u} \mid}\] (9) where \(PREF_{u}\) is the set of POIs preferred by a concrete user \(u\) in the test set. Preference is determined by the user's interest in the activity category to which the POI belongs. A category is preferred if at least one of the user's tweets has been associated to it. * **Average Item Recall (AIR)**: It is the ratio of visited POIs that are actually recommended. AIR is formulated as: \[AIR=\frac{1}{|U|}\sum_{u\in U}\frac{\mid R_{u}\cap V_{u}\mid}{\mid V_{u}\mid}\] (10)
* **Unified Item Recall (UIR)**: It is the unified fraction of times in which the POIs recommended to a user were among the POIs actually visited by the user. The UIR is formulated as: \[UIR=\frac{\mid\bigcup_{u\in U}R_{u}\cap V_{u}\mid}{\mid\bigcup_{u\in U}V_{u}\mid}\] (11)
* **Similarity**: It measures how similar the POIs recommended to a user and the POIs visited by the user are in terms of their paths in the activity tree. It is formulated as: \[similarity=\frac{1}{|U|\mid R\mid\mid V\mid}\sum_{u\in U}\sum_{r\in R_{u}}\sum_{ v\in V_{u}}sim(\rho(r),\rho(v)).\] (12) \(sim(.,. )\) is the Jaccard similarity coefficient that estimates the similarity of two sample sets, and \(\rho(. )\) produces a set representing the path of the POI in the activity tree. * **Coverage**: It measures the width of the recommendations. It is the percentage of items recommended to the users in the test set with respect to the total set of recommendable items. It is formulated as: \[coverage=\frac{\mid\bigcup_{u\in U}R_{u}\mid}{\mid P\mid}\] (13)
* **Popularity**: It measures the degree to which the popularity of recommended POIs matches the user's popularity preference. \(VPOP_{u}\) is the fraction of top 10 POIs visited by the user \(u\), and \(RPOP_{u}\) is the fraction of top 10 POIs recommended to the user. \[VPOP_{u}=\frac{\mid P_{top10}\cap V_{u}\mid}{\mid V_{u}\mid}\] (14) \[RPOP_{u}=\frac{\mid P_{top10}\cap R_{u}\mid}{\mid R_{u}\mid}\] (15)Then, the popularity measure is computed as follows: \[ popularity=\frac{1}{|U|}\sum_{u\in U}1-|VPOP_{u}-RPOP_{u}|\] (16)
* **Personalisation**: It measures the mean dissimilarity of users in the test set, based on their recommended POIs. It is formulated as: \[personalisation=1-\Bigg{(}\frac{1}{C_{2}^{|U|}}\sum_{u,u\in U}cosim(\gamma(u), \gamma(w))\Bigg{)}\] (17) \(C_{2}^{|U|}\) is the set of all pairs of different users without repetitions, \(cosim(.,. )\) is the cosine similarity of two vectors and \(\gamma(. )\) generates one hot vector representing the POIs recommended to a user from all recommendable POIs. * **Diversity**: It is the pairwise dissimilarity of POIs recommended to users in the test set, modelled after the diversity measure used in [61]. [PERSON] et al.