Research On Matrix Factorization Based Collaborative Filtering Recommendation Algorithms

Today’s society, each person’s side is filled with a lot of information, especially the Internet,vast amounts of information almost contains all the content people need, but the “informationoverload” problem still makes it hard to find what they really needs. The emergence of “searchengine” is a great extent to solve the “information overload” problem, but the search engineprovides for every user is the same service, therefore, people eager to obtain more targetedpersonalized service. In this case, the recommendation system arises at the historic moment, it isable to provide users with personalized information recommendation service.In the1990s people began to research Recommendation system, emerged a large numberof research results about recommendation system, many kinds of recommendation algorithms isproposed, and these recommendation algorithms are used in web browsing, moviesrecommendation, music recommendation and E-Commerce, etc. Currently, recommendersystems also have many successful cases of application, recommendation systems have createda useful value for both merchants and users.The main work in this paper is as follows:1. It comprehensively introduces the research background and research status ofrecommendation system. Furthermore it introduces several kinds of recommendation system,including Content-Based Recommendation, Knowledge-Based Recommendation,Collaborative Filtering Recommendation, Graph Structure-Based Recommendation and HybridRecommendation, especially makes a detailed interpretation of the collaborative filteringrecommendation.2. This paper analyzes Matrix Factorization Based Collaborative FilteringRecommendation Algorithms in detail, do a brief introduction for the gradient descent methodwhich is used by Matrix Factorization. It gives the whole process of Basic MF(Basic MatrixFactorization), Regularized MF(Regularized Matrix Factorization) and Biases MF(BiasesMatrix Factorization). Discusses the difference measurement method of Matrix Factorization,this paper introduces KLDD MF(Kullback-Leibler Divergence and Difference MatrixFactorization) algorithm which containing KL Divergence(Kullback-Leibler Divergence) in thedifference and is different from the general situation.3. In order to improve the prediction accuracy of Matrix Factorization, this paper putsforward several new Matrix Factorization algorithms, they are BV MF(Biases Vector MatrixFactorization), US MF(Users Similar Matrix Factorization), IS MF(Items Similar MatrixFactorization) and USIS MF(Users Similar and Items Similar Matrix Factorization), among them,the US MF and the IS MF are two weakening model of USIS MF. BV MF expands the biases of users and items to each feature, each feature will be specific user bias and specific item bias,variable of BV MF is more than other models. Because of user vector and item vector may notkeep the original similarity relation between users or items after Matrix Factorization, thus losingimportant relationships of the intrinsic similarities, in US MF, IS MF and USIS MF, theycombine the similarity relation of user or item, make the similarity information into objectivefunction of minimizing, to mine deeper information, so that the prediction results will be moreaccurate, US MF only considers user similarity information, IS MF only considers item similarityinformation, USIS MF is a combination of them, considering the similarity of user and iteminformation at the same time. BV MF in the aspect of prediction accuracy is not as good asexpected; US MF and IS MF in accuracy comparing to the Basic MF and Regularized MF allhave improved, but they are poor than Biases MF; USIS MF is one of the most outstandingperformance, in terms of accuracy, comparing to the Biases MF it still has improved greatly.4. It discusses the grading prediction method of Matrix Factorization algorithms, includingDirect Prediction, Near Neighbors Prediction, etc., aiming at the problem of prediction scorebeyond upper and lower limits situations, this paper proposes a new prediction method-MappingPrediction, it maps the prediction scores to between score upper and lower limits, and keep theprediction score is relatively high or low status, the scores handled by Mapping Prediction haveno beyond upper and lower limits situations, the ratings through mapping prediction have certainimprovement on the predicted results.5. This paper introduces several different evaluation standards of recommendationalgorithms, including MAE(Mean Absolute Error), RMSE(Root Mean Square Error), Precisionand Recall. And puts forward a new evaluation metrics-Accuracy. The Accuracy is based on therounded scores to evaluate algorithms, unlike the Precision and the Recall only consider thecorrect probability of items being recommended to the users, it also consider the predictiveaccuracy of items that can’t be recommended to users.6. It does a lot of experiments on the data set, analysis of various recommendationalgorithm operation results.In this paper, aiming at accuracy problem, puts forward several new Matrix Factorizationalgorithms, BV MF、US MF、IS MF and USIS MF, among them, in addition to the BV MF,they all have improved in terms of degree of accuracy. For the rating prediction, this paperproposes a new Mapping Prediction method, compared with the Direct Prediction it has obviouseffect. In the evaluation, this paper presents a new Accuracy evaluating metrics, to a certainextent, it can measure the merits of the algorithm.