Improvements on Recommender System Based on Mathematical Principles

The main goal of this article is to give optimization methods of the algorithms of the Recommender System in calculation acceleration and accuracy based on mathematical theory. We first introduce the Collaborative Filtering Algorithm and the similarity function used in this algorithm. Both the weakness and the strength of two different mathematical distance used to describe the similarity will be illustrated detailedly in this article. And both nonparametric and parametric methods will be applied to improve it. After that, we introduce BM25 Algorithm in search engines and accommodate it to Recommender System. In this article, we will give the result of performing quantile estimation in Collaborative Filtering Algorithm on the MovieLens Datasets. It is shown that it not only skips the classification process and thus accelerates calculation but also gives accurate recommendation results.