mathorcup数学建模挑战赛获奖论文-第四届B题_10342e.pdf
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Book Recommendation Model based on Collaborative Filtering
Book Recommendation Model based on
Collaborative Filtering
【Abstract】The paper has proposed five models in total on the basis of collaborative filtering. By
full understanding of the questions and full use of the data provided, we optimized the model one
by one, and computer program results show that the model indeed reflects the actual situation.
For question 1, two factors are taken into consideration in the evaluation of a book: the
preference for book tags of the users, the grade provided by the friends of the users. Linear fitting
model has been proposed to study the weight of any tag when the users are giving their scores, and
the model is solved with gradient decent algorithm. On the basis of this, Preference Similarity
is defined to study the similarity in choosing books in a quantitative way, and it’s regarded as
another weight index to study the impact of friends’ score on the evaluation of one book. Then,
the influence index is defined to reflect the overall influence of user’s friends on his evaluation.
Results of MATLAB program shows that the influence index of the user’s friends is high enough.
Ultimately, the conclusion is deduced: the book preference and the friend’s scores have an
significant impact on the scores.
For question 2, one significant fact is taken into consideration: costumers with similar
preference will grade in a similar way. And the model of collaborative filtering has been built on
the precondition of this hypothesis. Firstly, Pearson correlation coefficient is used to describe the
similarity of two users and the prediction model of collaborative filtering based on users is built
afterwards. Second, the situation that the intersection of the book sets of two users is not large
enough to reflect the fact is taken into account. And Jaccard-Pearson correlation coefficient is
proposed to further describe the similarity of two users, and the corresponding model is then
proposed.
Subsequently, another hypothesis that similar books will get similar scores from the same
user is employed to optimize the former model. PCC is again used to describe the similarity of two
books, and the prediction model of collaborative filtering based on items is proposed. Solving the
model with MATLAB program, 20 percent of the data in file‘user_book_score.txt’ is picked out to
serve as the testing set, and the results show that the prediction accuracy of three models are
0.8347,0.9151 and 0.9319, respectively. Model 3 is eventually used for the prediction.
For question 3, the model is built based on two significant points: the preferred tags and the
predicted scores. Taking full use of the users’ historical data of reading, finding out the frequency
of one certain tag appearing in the books the users once used to read, preference index is defined
to describe quantitatively the level how the users prefer one certain kind of books. Based on the
definition of preference index, the Top5 tags are selected from all the tags, and the candidate item
set which contains all the possible recommended books is put forward. The elements of the
candidate item set are books which has one or more Top5 tags. With the former discussion of
problem 2, the predicted scores of the books in the candidate item set are calculated. Finally, the
product of the overall preference index and the predicted score is regarded as the final reference of
which book is to be recommended. 3 books with the top 3 final value are to be recommended to
the user.
At last, objective evaluation is given on the strengths and weaknesses of all the models, and
optimization proposals are provided.
【 Key Words 】 Collaborative filtering; Pearson correlation coefficient; Linear fitting;
Preference index; Gradient decent
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