Novel Recommendation System for Tourist Spots Based on Hierarchical Sampling Statistics and SVD++

Recommendation system for tourist spots has very high potential value including social and economic benefits. The traditional clustering algorithms were usually used to build a recommendation system. However, clustering algorithms have the risk on falling into local minimums, which may decrease the final recommendation performance heavily. Few works focused their research on tourist spots recommendation and few recommendation systems consider the population attributes information for fitting the user implicit preference. To address the problem, we focused our research work on designing a novel recommendation system for tourist spots. First a new dataset named “Smart Travel” is created for the following experiments. Then hierarchical sampling statistics (HSS) model is used to acquire the user preference for different population attributes. A new recommendation list named 𝐿 A is generated in turn by fitting the excavated the user preference. More importantly, SVD++ algorithm rather than those traditional clustering algorithms is used to predict the user ratings. And a new recommendation list named 𝐿 B is generated in turn on the basis of rating predictions. Finally, the two lists 𝐿 A and 𝐿 B are fused together to boost the final recommendation performance. Experimental results demonstrate that the mean precision, mean recall, and mean F1 values of the proposed recommendation system improve about 7.5%, 6.2%, and 6.5%, respectively, compared to the best competitor. The novel recommendation system is especially better at recommending a group of tourist spots, which means it has higher practical value.


Introduction
The rapid development of the Web: people are now stepping into an "information overload" era.Not only the information consumers (online websites users) but the information producers (online websites managers) should face a big challenge: website managers strive to generate valid information of their products and recommending them to their users, which may bring them lots of economic benefits, whereas website users want to know whether the recommended information can satisfy their preference.Recently, a tourism wave has emerged, and tourists (travelers) are smart to retrieve and use valid tourism information to appropriate plan their travel.Obviously, lots of traveling tips are helpful.Hence, statistics show that approximately three-quarters of tourists prefer retrieve travel reviews or ratings of their destinations.As previously mentioned, tourists are often given excessive information due to the dawn of the "information overload" era.Addressing the problem has become increasingly important.As it is known, recommendation system is an effective method which can resolve the "information overload" problem to some extent.However, few works focused their research on tourist spots recommendation and few recommendation systems consider the population attributes information for fitting the user implicit preference.To address the problem, we focus our research work on designing a novel recommendation system for tourist spots: a new dataset named "Smart Travel" is created initially for the following experiments.Then, a hierarchical sampling statistics (HSS) model is utilized to acquire the user implicit preference 2 Mathematical Problems in Engineering for different population attributes.Thirdly a novel SVD++ algorithm is designed to complete the final recommendation.More importantly, the excavated the user preference is fused into the collaborative filtering-based recommendation framework to more effectively generate recommendation results.
The rest of this paper is organized as follows.Section 2 introduces the preliminaries and related works.Section 3 presents the architecture and some details of the proposed recommendation system.Section 4 provides relevant experimental results and discussions.Finally, Section 5 presents the concluding remarks and future works.

Related Works
In general, recommendation results can be generated on the basis of the user preference, the item features, and other environmental factors such as time, season, and location.In recent recommendation literatures [1,2], recommendation systems are usually categorized into three categories, namely, content-based, collaborative filteringbased, and hybrid recommendation systems.A contentbased recommendation system focuses on selecting those objects with similar characteristics according to the objects that users have browsed.A collaborative filtering-based recommendation system has been widely used in some real websites like Amazon and YouTube.It can generate lots of personalized recommendation results for users.As it is known, collaborative filtering theory was proposed by Goldberg [3] and was first used in "Tapestry," which is a famous recommendation system.However, "Tapestry" only offered recommendation services for fewer users.The ratingbased collaborative filtering recommendation system was presented by Resnick [4], who designed another famous recommendation system called "GroupLens." "GroupLens" predicted user implicit preference on the basis of all user ratings.Traditional clustering algorithms are usually used to mine users who have same or similar preference.Finally, both news and films are recommended to those target users according to semantic similarity computing.On the basis of "GroupLens", Konstan [5] and Miller [6] designed a novel recommendation system on an open computing structure.Yu [7] proposed a multilinear interactive matrix factorization algorithm (MLIMF) to model the interactions between the users and each event associated with their final decisions; the model considered not only the user-item ratings but also the pairwise interactions based on some empirically supported factors.In our real world, items will suffer from the sparsity problem more severely than users since items are usually observed by fewer features to support a featurebased or content-based algorithm.To tackle this problem, Yu [8] proposed a new method to study the collaborative retrieval (CR) task from the users' perspective, which aimed to sufficiently explore the sophisticated relationship of each triple as the form is query × user × item.
Recently, researchers paid their attentions on the recommendation system for tourist spots.Li [9] proposed a hybrid recommendation system for tourist spots based on hierarchical sampling statistics and Bayesian personalized ranking (BPR), and the recommendation performance was improved mainly by the BPR algorithm.Fenza [10] proposed a context-aware recommendation system based on the collaborative filtering theory.First, both users and tourist spots are clustered using the traditional fuzzy clustering algorithm, and context information is analyzed by the situational awareness technology.Then, the similarities of the tourist the spots that users prefer to be were calculated and tourist spots were recommended to users in order.The present work provides an adaptive environment in the process of dynamical user clustering and alleviates the cold start problem to some extent.Hsu [11] adopted the traditional collaborative filtering method to construct a novel recommendation system for tourist spots.Bayesian network was used to calculate the user preference for spots, to improve the final predication accuracy.Nilash [12] designed a new recommendation system for tourist spots based on the multistandard collaborative filtering algorithm.Multiobjective collaborative filtering technology was adopted to mine much more valuable user preference.Finally, recommendation accuracy was improved by a Gaussian mixture-based clustering algorithm.
In summary, we can observe: (1) Different kinds of recommendation system [3][4][5][6][7][8][9][10][11][12] have entered into people's daily life and they have played very important roles in changing people's working, living and studying.To the best of our knowledge, few works focused their research on recommendation system for tourist spots.Moreover, the above-mentioned works only used the traditional collaborative filtering algorithm.And they did not consider the population attributes, which may help to represent the deeplevel semantic information of the user preference.Recently, tourism wave has emerged, which indicates recommendation system for tourist spots has very large potential value.It will give us much more economic benefits as well as social benefits.(2) The traditional clustering algorithms have been used in most recommendation systems [3][4][5].But they have several limitations: first they need a good initial value; second, they usually fall into local minimums; third outliers will interfere with the final clustering results.So the traditional clustering algorithms are not suitable for designing our novel recommendation system.(3) Additional information such as visual content and user personal information [13] could help to improve the final recommendation performance.However, most recommendation systems only used user ratings rather than other additional information to build their models.The paper is an extended version of the reference [9].Our contributions in the paper are two folds: (1) A novel dataset named "Smart Travel" is created by combining a well-designed questionnaire survey and automatic data crawling on the Web.On the basis of the new dataset, the hierarchical sampling statistics (HSS) model [14] is utilized to acquire the user preference for different population attributes, namely, travel season, travel interest, and travel method are used to describe users, which are a good supplement to the traditional collaborative filteringbased recommendation model.
(2) A new recommendation list called  A is generated on the basis of the user preference.Then a novel collaborative  filtering-based model called SVD++ algorithm [15,16] is designed to generate a new recommendation list called  B . A and  B were fused together to obtain the hybrid recommendation system.The hybrid recommendation system could better fit the user preference.More importantly, it was especially better at recommending a group of tourist spots, which means it has higher practical value.

The Proposed Recommendation System
3.1.Fundamental Theory.The above-mentioned collaborative filtering theory has been widely used in recommendation system.As it is known, a collaborative filtering-based recommendation system has several apparent advantages: it can process unstructured objects, and it does not need any domain knowledge to discover new user preference.It can generate lots of personalized recommendation results for users.Hence, we adopt the popular collaborative filtering theory into the proposed recommendation system.It first analyzes the tourist spots other users have rated, then it predicts the ratings of the target users for all spots.Therefore, the matrix of users' ratings is factorized into two matrices (user matrix and spot matrix).They all contain a group of latent factors.The user vector is associated with the user matrix while the spot vector is associated with the spot matrix.Dot product between these two vectors is computed to complete the final rating prediction.Meanwhile, the hierarchical sampling statistics model is used to mine users' preference.
In general, the proposed recommendation system for tourist spots has several components, user data collection, hierarchical sampling statistics, SVD++ algorithm, collaborative filtering model, and hybrid recommendation list.Figure 1 illustrates the recommendation framework.
In Figure 1, travel preference is collected through a well-designed questionnaire survey because we cannot grab travelers' personal information from web.Users' ratings of different tourist spots are crawled from a tourist website (its URL link is http://www.ctrip.com)automatically.Then a data preprocessing strategy is designed to discretize all users' ratings: "0∼5" is used to represent users' satisfaction."5" means the highest positive rating while "0" means the lowest negative rating.Then, the user preference is acquired by using the hierarchical sampling statistics model.The crawled rating data (rated tourist spots) and users' travel preference are matched automatically to create the "Smart Travel" dataset.Based on the users' preference, a new recommendation list called  A is generated from the statistical perspective.Meanwhile, based on the preprocessed users' ratings, SVD++ algorithm is introduced to complete matrix factorization and both a user matrix and a spot matrix are obtained in turn.The user matrix is also called users' embedding, which represents the latent semantic information of users.The spot matrix is also called spots' embeddings, which represents the latent semantic information of spots.With the help of these two embeddings, it is easy to predict the ratings of the target users for all spots: dot product between these them is computed to complete rating prediction.And a novel recommendation list called  B is generated on the basis of the rating prediction.Finally, a hybrid recommendation result called  Mix is acquired by fusing  A and  B .

Hierarchical Sampling Statistics
Model.The HSS model completes the sampling procedure from different hierarchies randomly on the basis of different proportions.First, the target samples (users) are divided into num disjoint subsets in proportion.Second, the sampling procedure is completed independently in each subset.Each subset (e.g.,  1 ,  2 , . . .,  푛푢푚 ) is called a "hierarchy."Finally, num subsets are merged into an overall distribution of the target samples.The proposed sampling procedure is described in detail as follows.
Step 1 (select target random variables).Target random variables are introduced to reflect the differences of tourism preference among different kinds of users.They are the key factors for hierarchical sampling statistics.Several target random variables, such as travel season, travel interest, and travel method, are utilized to instruct the following sampling procedure.
Step 2 (divide the target samples into different hierarchies).On the basis of the previously selected target random variables, all target samples are divided into num disjoint hierarchies (subsets).If  푖 users exist in the i-th ( = 1, . . ., ) hierarchy, then the overall distribution of the target samples is obtained by merging all num hierarchies, as shown as formula (1).
Step 3 (determine the sampling number of each hierarchy).
M is defined as the overall sample size, and num is defined as the total number of hierarchies.E i is defined as the total number of the target users in the i-th hierarchy.On the basis of the definitions, X i is defined as the number of sampled users in the i-th hierarchy by the proposed HSS model.
.. = 1, . . ., Now the target samples are divided into several disjoint hierarchies by the HSS model, which helps decrease the differences within a homogeneous hierarchy and increase the differences between heterogeneous hierarchies.Hence the HSS model strives to sample a certain number of target samples (E i ) to describe the feature space of the current hierarchy and construct the overall distribution of all target samples (E).All classified results are determined through a well-designed questionnaire survey, which can represent the actual tourism preference of users.
On the basis of the subjective weighting method [14], the weight of each population attribute is tuned by the analytic hierarchy process, which means the relative importance of each population attribute should be compared pairwise and a discriminant matrix is established.The weight of each population attribute is illustrated in the discriminant matrix.According to experts' suggestion, six attributes, namely, gender (C 1 ), district (C 2 ), age (C 3 ), education (C 4 ), job (C 5 ), and wage (C 6 ), are chosen for creating the discriminant matrix.These attributes depict users' preference from diverse perspectives.So appropriate weight for each attribute can fit the proposed sampling results.The importance scale of each indicator A relative to index B is as follows: very important = 6, important = 4, slightly important =2, equally important = 1, slightly minor = 1/2, minor = 1/4, and very minor = 1 / 6.Then a discriminant matrix called G can be constructed as follows.(Note: other values have ever been used, but relative worse recommendation performance was obtained.) The weight of the k-th population attribute ( = 1 ∼ 6) is calculated on the basis of the matrix G. Thus each target random variable introduced above can be described by six weighted population attributes.The weight of each population attribute is expressed as follows.
Finally, all population attributes are ranked by their weights and the corresponding prerecommendation results are generated according to the ranked attributes.In summary, the proposed HSS model for recommendation is described as in Algorithm 1. [15,16] is an improved algorithm based on the traditional SVD [17] (Singular Value Decomposition) algorithm.It regards the users' rating matrix R as a product of two matrices P and Q.And it also maps both all users and all tourist spots into a K dimensional latent semantic space.The semantic space is made up of a group of latent factors.As described above, the users' rating matrix R is factorized as follows:

SVD++ Algorithm. SVD++
= ( 1 ,  2 , . . .,  푚 ) represents a user set while  = ( 1 ,  2 , . . .,  푛 ) represents a tourist spot set. 푖푘 represents the preference degree of the user i for the k-th latent factor of the tourist spots. 푘푗 represents the distribution of the k-th latent factor among the tourist spot j.So each user is associated with a user vector  푢 ∈  퐾 which is a row of the matrix P.And each tourist spot is associated with a tourist spot vector  푧 ∈  퐾 which is a column of the matrix Q.  푢 describes the preference of a user. 푧 describes the feature space of a tourist spot.They are now located in a homogeneous data space.Hence, the traditional collaborative filtering theory can Input: Results of questionnaire survey (T).Output: Recommendation list ( A ) 1. Target random variables including travel season, travel interest, and travel method are used to depict the user preference.Each variable is described by six population attributes namely gender, district, age, education, job, and wage.2. On the basis of the T, the sampling dataset is obtained by the HSS model.and the sampling number of the i-th hierarchy is obtained.which is expressed as Equation (2). 3. The proportional value of each attribute hierarchy is calculated by  W /N, which can depict the actual distribution of the corresponding attribute.4. On the basis of the preceding proportional values, the relative importance of each attribute is determined by the subjective weighting method, and a discriminant matrix (G) is obtained, which is expressed as Equation (4). 5.The weight of each attribute hierarchy is calculated on the basis of the matrix G and Equation ( 5), and each target random variable is described by the six weighted previously population attributes.6. Population attributes are ranked by their weights and recommendation results are generated according to the ranked attributes.7. Recommendation list  A is generated by matching the above recommendation results and users' population attributes collected from the survey.Algorithm 1: Hierarchical sampling statistics model for recommendation.
be applied here: the dot product between these two vectors is utilized to get the prediction rating r푢푧 which is rated by the user u for the tourist spot z: By analyzing the users' ratings matrix R, we find some users always give high ratings (or low ratings) compared with others.This means the corresponding ratings are biased.However, (7) does not consider the bias.Hence several key bias factors should be taken into account, which contributes to getting more objective ratings.The modified rating equation is shown as follows: b uz represents the overall "bias information" of the user u for the spot z.  is a rating mean.b z represents the "bias information" of the tourist spot z, which is an item offset to the rating mean.b u represents the "bias information" of the user u, which is a user offset to the rating mean.In addition to the "bias information", many implicit parameters are added to the SVD++ algorithm to better reflect users' latent preference for tourist spots.Generally, users' ratings are usually called "explicit information" while users' behaviors are usually called "implicit information".Finally, a novel perspective of users' preference is acquired by combining the above-mentioned "explicit information", "bias information", and "implicit information" together.The final rating equation is shown as follows: N u represents the behavior data of the user u.This means the user u has rated the corresponding tourist spots.| 푢 | is the size of the behavior data.−(1/2) is the contraction factor which is an empirical value.y j represents the implicit parameters used for describing the "implicit information" in recommendation, which indicates that the user u has rated the tourist spot j.Finally, besides "explicit information", the SVD++ algorithm takes both the above-mentioned "bias information" and "implicit information" into account.It firstly analyzes users' preference degree for the latent semantic factors of the tourist spots.Then it obtains the distribution of the latent semantic factors among all tourist spots.Lastly, it takes both the above-mentioned "bias information" and "implicit information" into account.Based on the above analysis, the cost function J of the SVD++ algorithm is shown as follows: Input: Users' rating matrix (R) Output: Rating prediction matrix (D) and Recommendation list ( B ) 1. Compute the mean rating based on the matrix R.
2. Initialize the "bias information" b u and b z .Initialize the user vector p u .Initialize the tourist spot vector  푢 .Initialize the implicit parameters  푗 .
3. User ratings are grouped by user ids. 4. Compute the inner product of the user vector  푢 and the tourist spot vector  푧 by Equation ( 11).User's ratings are predicted.5. Compute the prediction error  푢푧 based on the real rating and the predicted rating.As shown in Equation ( 13)∼( 18), the SGD method is utilized to complete optimization.21)-( 24), respectively) of the hybrid recommendation system.
Algorithm 3: A novel recommendation system for tourist spots.
The first part of J is the loss based on the least square method.The second part of J is the regularization term.The proposed SVD++ algorithm is optimized by the stochastic gradient descent method: e uz is the prediction error,  is the learning rate, and  is the regularization parameter.

The Proposed Collaborative Filtering Model.
As described above, the SVD++algorithm decomposes the users' rating matrix R into two matrices P and Q that contain a group of latent semantic factors.Each user is associated with a user vector that is a row of the matrix P. Each tourist spot is associated with a tourist spot vector that is a column of the matrix Q.By computing the inner product of these two vectors and taking both the above-mentioned "bias information" and "implicit information" into account, the corresponding ratings of users can be predicted.Algorithm 2 shows the details about the proposed SVD++ based collaborative filtering model.

Novel Recommendation System for Tourist Spots.
As described in Section 3.2, the HSS model is used to generate the recommendation list  A from the statistical perspective.As described in Section 3.4, the proposed SVD++ algorithm is used to generate the recommendation list  B from the matrix factorization perspective.On the basis of the two lists, a novel hybrid recommendation system for tourist spots is achieved, which is shown in Algorithm 3.

Experimental Results and Discussions
4.1.The Dataset.All user ratings in the Smart Travel dataset is crawled from http://www.Ctrip.com.approximately 5000 users' ratings of 60 tourist spots are crawled from the website.On the basis of experts' suggestion, we classify the 60 tourist spots into 8 categories: Seashore Island (SI), World Heritage (WH), Blessing Buddha (BB), Cruise Trip (CT), Ancient Town (AT), Family Travel (FT), Health Leisure (HL), and Folk Experience (FE).About 4000 ratings (80%) are select randomly for training while the rest 1000 ratings (20%) are selected for testing.Then a well-designed questionnaire survey is used to collect users' preference from diverse population attributes, namely, gender, age, district, and wage.It is a very important complementary part of user ratings,  which can assist the proposed model in recommending better performance.Finally, all user ratings are discretized: "0∼5" represent users' satisfaction degree, where "5" means the highest positive rating whereas "0" represents the lowest negative rating.Users' population attributes such as gender, age, district, and wage are discretized into integer values too.Generally, some detailed information about the "Smart Travel" dataset and the well-designed questionnaire survey can be found in https://github.com/CVNLP/SmartTravel.

Results of Hierarchical Sampling Statistics Model.
We randomly sent the survey table to 2170 visitors and completed the corresponding statistical analysis by the proposed HSS model.This survey can better cover the key population attributes of the interviewed visitors.In each population attribute, we took 1,000 visitors as sampling objects and got the statistics results of the corresponding preference.Three angles, namely, travel season, travel interest, and travel method, are chosen as the tourist preference.On the basis of this setting, the final HSS statistics can be computed.And several valuable conclusions can be obtained from the HSS statistics [9].Most of them are close to people's cognition: (1) Most interviewees prefer to travel in spring and fall.Tourist spots in spring (or fall) are more attractive than those in other seasons, given the suitable temperature and beautiful scenes; thus, people are willing to embrace nature.Meanwhile, most students (age ≤ 20) prefer to travel in summer during their vacation, which is a good opportunity for them to travel freely and extend their knowledge.(2) Most interviewees prefer to travel with their families, which is especially for the aged people (age >=40).We guess it is due to Chinese traditional culture.Chinese enjoy themselves in a family trip.Surprisingly, males prefer to travel by themselves.(3) Most middle-aged or the elder (age >=50) prefer to choose the tourist spots of "HL" since these tourist spots require less physical strength.(4) Most interviewees from the east district (or the central district) in China prefer to choose the tourist spots of "SI", while most interviewees from the west district (or the north district) in China prefer to choose the tourist spots of "FE" and "AT".We guess this is mainly due to the living habits of the interviewees.(5) Most interviewees with a master's degree or above tend to travel by themselves.

RMSE and MAE Evaluations. We use both Root Mean
Square Error (RMSE) and Mean Absolute Error (MAE) to compute the corresponding rating prediction accuracy.Small RMSE and MAE indicate good recommendation performance.RMSE and MAE are expressed as (19) and (20), respectively, where Test is the testing dataset; || is the number of testing data; (u, z) is a user-spot combination in the user rating matrix, where z and u denote a spot and a user, respectively; r uz represents the actual rating value user u rated spot z in the Wisdom Tourist dataset;and r푢푧 is the predicted rating generated by the recommendation system.
(2) The proposed SVD++ algorithm finds out the latent semantic space which is suitable for depicting the user preference.
(3) The proposed SVD++ algorithm also finds out the latent semantic space which is suitable for depicting different tourist spots.(4) Both the abovementioned "implicit information" and "bias information" also play very important roles in the recommendation procedure.As described in Section 3.2, the proposed SVD++ algorithm plays the most important role in the hybrid recommendation system.So it should be tuned carefully.The SVD++ algorithm has several key parameters such as the regularization parameter (), the learning rate parameter (), and different split ratio.These parameters are tuned by crossvalidation.The corresponding results are shown in Figures 3-4: In Figures 3(a)-3(d), when  = 0.005,  = 0.02 the proposed SVD++ algorithm achieves the best recommendation performance (its MAE = 0.7141 and its RMSE = 0.9306 in Figure 2).Second, in all subfigures, the variation trends of MAE are similar to that of RMSE, which demonstrates that the proposed SVD++ algorithm is more robust.
In Figure 4, different split ratios are utilized to validate the best split method (other parameters are fixed, for example  =0.005 and  =0.02).Obviously,when the train set accounts for 80%, the proposed SVD++ algorithm achieves the best recommendation performance.

Precision, Recall, and F1 Evaluations.
As shown in HSS statistics result, different population attributes determine the corresponding travel preference.Based on the fact, a new model called Our HS is created: as described in Section 3.2, the weight of each attribute is set by the subjective weight evaluation method [14]: "gender" is 0.2, "district" is 0.05, "age" is 0.3, "education" is 0.05, "job" is 0.1, and "wage" is 0. In addition to MAE and RMSE, Precision, Recall, and F-Score are often used to evaluate recommendation system.The type that the recommended tourist spots belong to should be determined before computing the corresponding Precision, Recall, and F-Score values.In Table 1, "True-Positive(tp)" indicates the recommended tourist spots are preferred by users, "False-Positive(fp)" indicates the recommended tourist spots are not preferred by users, "False-Negative (fn)" indicates the tourist spots which are not recommended are preferred by users, and "True-Negative(tn)" indicates the tourist spots which are not recommended are not preferred by users.
Based on Table 1, Precision, Recall, and F-Score are computed as follows: F-Score = ( 2 + 1) * Precision * Recall # means the number.The F1 (=1) metric (see (24)) is used to evaluate the overall recommendation performance, when N' tourist spots are recommended to users.A novel metric named P' (see (25)) is used to evaluate the mean performance.
The index (w) represents the evaluation metric described above such as Precision, Recall, and F1.N'=1∼10.Precisions are listed in Table 2, Recalls are listed in Table 3, and F1 values are listed in Table 4.
In Table 2, the "KNN + means" algorithm acquires the best Precision when N'=1; it is better for recommending only one tourist spot.However, this cannot meet users' personalized requirement.Except the SVD, SVD ++, NMF, and KNN algorithms, the Precision cannot obtain significant improvement when more tourist spots are recommended to users because the rating matrix R is sparse.The proposed SVD++ algorithm can obtain higher Precision and beat other baselines when N'≥3.This indicates the proposed SVD++ algorithm is better at recommending more tourist spots.It is very close to people's cognition and it can better meet users' personalized requirement.However, the superiority of the SVD++ algorithm is a margin compared with the best competitor.It still has a large improvement space.
As expected, the proposed Our Mix model wins nine first places among ten results.Figure 5(a) describes the precision improvement between different models with respect to N' .For example, the precision improvement of the proposed Our Mix model is improved about 2.49% when N'=2.Meanwhile, the precision improvements of the proposed Our Mix model are always positive, and it has an increasing trend.On the contrary, the SVD ++ algorithm has a tortuous trend which twists and turns.More importantly, the overall improvement of the SVD++ algorithm is far less than that of the Our Mix model.Hence, when more and more tourist spots are recommended to users, the proposed Our Mix model is more stable than any other baseline.We conclude the proposed SVD++ algorithm plays a major role while the HSS model plays a minor role.They complement each other to obtain the best recommendation performance.
In summary, based on the P' values, we find, compared with the best competitor, the mean precision of the proposed Our Mix model is improved about (65.18%-60.66%)/60.66% ≈7.5%.It is a larger margin, which indicates the proposed hybrid recommendation model is more practical than any other baseline.Moreover, the mean precision descend order of all models is shown as Our Mix>SVD++>"KNN + means"> "KNN + Zscore"> SVD > "KNN Baseline">Slope One>Co-Clustering>NMF>KNN>BPR>Our HS.
In Table 3, several baselines, i.e., SVD++, Co-Clustering and KNN, obtain better recall values.Among ten results, the proposed SVD++ algorithm wins one first place and seven second places.It is better at recommending a group of tourist spots (especially for N'≥5).As expected, the proposed Our Mix model gets the best recall values.When more spots are recommended to users, the proposed Our Mix model is more stable and superior to any other baseline.Figure 5(b) indicates the recall improvement between different models with respect to  耠 .For example, the recall value of the proposed Our Mix model is improved about 2.49% when  耠 =2.The recall improvements of the Our Mix model are always positive and it has an increasing trend.
In summary, based on the P' values, compared with the best competitor, the mean recall of the proposed Our Mix model is improved about (

Figure 2 :
Figure 2: The prediction rating comparisons with baselines.

Figure 3 :
Figure 3: The parameter tuning procedure of the proposed SVD++ algorithm.

F1 = 2 *
Precision * Recall Precision + Recall(24) 7. Repeat the third step and fourth step to get the prediction rating  푢푧 .Update the rating prediction matrix D.7.Generate the recommendation list  B based on the matrix D.
Input: Questionnaire results T, Users' rating matrix R Output: Hybrid recommendation list  Mix 1. Generate the recommendation list  A using Algorithm 1. 2. Generate the recommendation list  B using Algorithm 2. 3. The mix merge method is used to generate the recommendation list  Mix .4. Compute the precision, recall, and F1 values (Equations (

Table 1 :
3.Moreover, a new model called Our Mix is created too: the recommendation list  A generated by the Our HS model is fused with the recommendation list  B generated The classification method of the recommended tourist spots.

Table 2 :
Precisions of different algorithms (the best value of each row is shown as 60.52,

Table 3 :
Recall values of different algorithms (the best value of each row is shown as 16.13, the suboptimal value of each row is shown as 17.89, and unit is %).

Table 4 :
F1 values of different algorithms (the best value of each row is shown as 25.30, the suboptimal value of each row is shown as 27.44, and unit is %).