Uncertainty measurement of the basic probability assignment function has always been a hot issue in Dempster-Shafer evidence. Many existing studies mainly consider the influence of the mass function itself and the size of the frame of discernment, so that the correlation between the subsets is ignored in the power set of the frame of discernment. Without making full use of the information contained in the evidence, the existing methods are less effective in some cases given in the paper. In this paper, inspired by Shannon entropy and Deng entropy, we propose an improved entropy that not only inherits the many advantages of Shannon entropy and Deng entropy, but also fully considers the relationship between subsets, which makes the improved entropy overcome the shortcomings of existing methods and have greater advantages in uncertainty measurement. Many numerical examples are used to demonstrate the validity and superiority of our proposed entropy in this paper.
The recommender systems play an important role in our lives, since it can quickly help users find what they are interested in. Collaborative filtering has become one of the most widely used algorithms in recommender systems due to its simplicity and efficiency. However, when the user's rating data is sparse, the accuracy of the collaborative filtering algorithm for predictive rating is badly reduced. In addition, the similarity calculation method is another important factor that affects the accuracy of the collaborative filtering algorithm recommendation. Faced with these problems, we propose a new collaborative filtering algorithm which based on Gaussian mixture model and improved Jaccard similarity. The proposed model uses Gaussian mixture model to cluster users and items respectively and extracts new features to build a new interaction matrix, which effectively solves the impact of rating data sparsity on collaborative filtering algorithms. Meanwhile, a new similarity calculation method is proposed, which is combined by triangle similarity and Jaccard similarity. Compare our proposed model with four models based on collaborative filtering algorithms on three public datasets. The experimental results show that the proposed model not only mitigates the sparseness of the data, but also improves the accuracy of the rating prediction.INDEX TERMS Recommender systems, collaborative filtering, clustering, Gaussian mixture model, Jaccard similarity.
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