隨著網際網路的發展，人們面臨越來越多的選擇，例如購物網站中商品的選擇，影音網站中該看哪些影片的選擇。推薦系統在這些網站中扮演幫人們迅速決定的重要角色。在這篇論文中，我們針對在推薦系統中的知名方法潛在因子模型 (Latent factor model)進行分析與改良，並提出了加權潛在因子模型和多項式潛在因子模型。這兩個模型分別賦予了傳統潛在因子模型權重參數和非線性的特徵組合。我們將這兩個模型對五種開放資料集進行了許多實驗，發現相較於傳統模型，這兩個模型能夠有更好地預測效果。由於我們提出的模型是基於潛在因子模型的變體，我們的模型也可以應用於其他潛在因子模型上，如SVD++模型和NMF模型。

With the development of the Internet, people are faced with more and more choices, such as the choice of products in shopping websites and the choice of which videos to watch in video and audio websites. The recommendation system plays an important role in these sites to help people decide quickly. In this paper, we analyze the well known method -- the latent factor model in the recommendation system, and propose the weighted latent factor model and the polynomial latent factor model. These two models respectively give the traditional latent factor model weights and nonlinear feature combinations. We conducted many experiments on these two models for the five open data sets and found that the two models have better predictive effects than the traditional models. Since our proposed model is based on the latent factor models, our model can also be applied to other latent factor models such as SVD++ model and NMF model.

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