Multi-dimensional Aggregation Recommendation Algorithm Based on Average Prediction

Traditional collaborative filtering recommendation algorithm uses single dimensional data to calculate the similarity between users or items, ignoring the user’s preference, thus affect the recommendation accuracy. To this end, an averaging forecasting based multi-dimensional aggregation recommendation algorithm was proposed in this paper, which constructs the relationship aggregation function by user’s total score and dimension scores firstly, then apply the aggregation function to the initial multi-dimensional score that calculated by the modified averaging forecasting algorithm. The experiment result shows that compared with the previous collaborative filtering based recommendation algorithm, it has higher recommendation accuracy.


Introduction
The collaborative filtering algorithm is a kind of most commonly used algorithms in the recommender system.It mainly include user-based collaborative filtering algorithm and item-based collaborative filtering algorithm [1][2][3][4], they searching "Neighbor" for achieving rating forecast [5].The collaborative filtering algorithm was applied in many fields.However, the similarity measure is based on the assumption that users have only one score for each item [6,7], which ignores user's preference thus affects the accuracy of recommendation.
To fill this research gap, this paper proposes a MDAA (Multi-Dimension Aggregation recommendation based on Average forecasting) algorithm.Firstly, MDAA algorithm uses the multi-dimensional score to reduce the impact of data sparsity on recommendation.Secondly, it adds the average measure to the traditional prediction algorithm, which reduces the impact of user preference on the recommendation.Finally, the algorithm achieves multi-dimensional score aggregation.After experimental verification, the algorithm can effectively improve the accuracy of the recommendation.

Collaborative filtering recommendation algorithms
Collaborative filtering recommendation algorithm is mainly divided into three steps: get user-item rating matrix, find nearest neighbor, and calculate unknown scoring [8][9][10].
The input is a scoring matrix as shown in Table 1, m is the number of users, n is the number of items, and the element in the matrix Rui represents the rating of user u on item i .The collaborative filtering recommendation algorithm uses each row in the rating matrix as the user scoring eigenvector, and gets the top-N user sets which is closest to the target user (the nearest neighbor sets) by cosine similarity calculation.The calculation of similarity between users as follows:

Table1. User-item Rating Matrix
, Where ,m u s the similarity between user u and user m is, , ui R denotes the rating of user u on item i , , mi R is the rating of user m on item i .
According to the top-N neighbor sets, the item ratings of target user are calculated by: Where () Nu represents the set of users that is similar to user u, the set is called neighbour group, and ( , ) sim u m represents the similarity between user u and user m, () Ru refers to the average score of users in all items.

MDAA recommend algorithm
Traditional collaborative filtering recommendation algorithm uses single dimensional data to calculate the similarity between users or items, on the contrast, the MDAA recommendation algorithm is add additional rating information for original users [11][12][13][14] and consider the user's rating preferences at the same time, then increase the accuracy of recommendations.

Get the user-item rating matrix
The difference of one-dimensional recommendation and multi-dimensional recommendation is that the latter has more user rating information and can be used effectively during the recommendation process.The process can be represented as: Where r1-rk are the user's rating on k-dimensions of each item.The user-item multidimensional rating matrix is shown in Table 2.

Calculate the rating similarity
This paper uses multidimensional distance to measure the similarity between users.The smaller distance between two users means the higher similarity between two users.The calculation of similarity is mainly divided into the following three steps: The calculation of multi-dimensional rating distance at the same project of two users.
The calculation of average rating distance of two users.
( ) Where ( , ) I u m the number of products is scored jointly by user u and user m, The calculation of user rating similarity.

Calculate initial multidimensional rating
The mean-based prediction algorithm proposed in this paper mainly uses the rating regularization technique to predict the user's initial multidimensional score on the items.It is reduce the impact of user preferences on the score prediction initially.
Where z is a regularization factor to regularize scores of 1-5, s is to deconcentrate to solve the user's scoring habits on the prediction results, ( , ) R m i represents the rating of user m at item i .

Learn the aggregation function
In order to reflect the user's personalization, the paper presents the user's preference by setting the weight in each dimension of the project, and uses the support vector regression machine (SVR) to realize the relationship learning between the total score and each dimension score.This paper assumes that in the original space, the sample set S is linearly inseparable, so a non-linear mapping is used to map the data into a high-dimensional space, so that there is a very good linear regression feature in the feature space H, Linear regression, and then returned to the original space [15].Given the training sample data sets {( , , 1, 2,3,..., )} ii S x y i q == , ( , ) ii xy refers to the user's score pair, r , q represent the sum of the number of user comment items.Relational learning is achieved in the high-dimensional scoring space, according to the given score on the construction of the optimal linear function.
( ) The import of  insensitive loss function, slack ( ) Using the Lagrange  Derive the partial derivatives of , b , i  , i   , then we can get an optimal Lagrange coefficient [17].
) Where ( 13) contains the inequality constraint, so it is need to use the KTT (Karush-Kuhn-Tucker) to get Therefore, a kernel function is introduced to get the regression decision function, ( , ) i K x x is kernel functions in SVR [18].

Experiments
In order to verify the performance of the MDAA algorithm, the experimental compares it with the traditional collaborative filtering recommendation algorithm on two data sets which are got from TripAdvisor.Dataset1 and Dataset2 are users' feedback for Paris Hotel and Beijing Hotel from 2015 to 2017.The detailed information is shown in Table3.

Evaluation
The accuracy of the recommendation system is the basic indicator for evaluating the recommendation algorithm.RMSE (Root Mean Squared Error) measures the accuracy of the prediction by calculating the deviation between the predicted user score and the actual user score [8].
( ) Where ui r represent the true rating user u on item i , ' ui r is the prediction rating of user u on item I, p E is test data set.

Experiment design
In the experiment, the user rating value is between 0 and 5, and the score of 0 indicates that the user does not rate the hotel.This paper mainly compares the recommended results between MDAA recommendation and traditional recommendation algorithms in two aspects: (1) Comparing the recommended results of single-dimension recommendation algorithm, multidimension recommendation algorithm and MDAA recommendation algorithm; (2) Comparing the prediction effects of traditional prediction algorithm and the improved mean prediction algorithm in this paper.

Result Analysis
In the experiment, each algorithm is applied to two datasets, comparing the traditional recommendation algorithm with MDAA recommendation algorithm, traditional prediction algorithm and mean prediction algorithm.
The interpretation of character in the figures is shown in Table 4.In order to better reflect the recommended results of the MDAA algorithm, this paper uses RMSE error backwash method to achieve the proposed algorithm comparison.Analysis of Figure 1, Figure 2 and Figure 3, we can get the following conclusions: (1) In Figure 1 and Figure 2, the line charts obtained by the M-Prediction algorithm are located below the line chart obtained by the T-Prediction algorithm in both data sets, draw a conclusion, not only single dimension recommendation but also multidimension recommendation, the M-Prediction algorithm proposed in this paper all improve the accuracy of the prediction. (2) In Figure 3, comparing the experiment results obtained by the three recommended algorithms, it is obvious for us to find that on the experimental data sets, the MDAA recommendation algorithm has a lower recommendation error than the original single-dimension recommendation algorithm.

Conclusions
In order to make up the shortcoming of the traditional collaborative filtering recommendation algorithm that ignores the user's preference.A recommendation algorithm which considers the impact of data sparsity, non-positive scoring information and user personalization on recommendation was proposed in this paper.This algorithm can improve the recommendations accurate by introduction the multidimensional user-item rating matrix, aggregation function and average forecasting technique.
The experiment result shows that compared with the traditional collaborative filtering recommendation algorithm, the MDAA algorithm can provide a good user experience by consider the user's personalization.The next improvement direction of this paper is to consider the external factors such as time and region comprehensively and incorporate the economic model [19] into the recommendation process to achieve a better recommendation.
scoring distance of two users on item dimension i.
user's total score in the corresponding project 0 penalty factor c. The original function problem transform into optimization problem.