外文：
Introduction to Recommender System
Approaches of Collaborative Filtering: Nearest Neighborhood and Matrix Factorization
“We are leaving the age of information and entering the age of recommendation.”
Like many machine learning techniques, a recommender system makes prediction based on users’ historical behaviors. Specifically, it’s to predict user preference for a set of items based on past experience. To build a recommender system, the most two popular approaches are Content-based and Collaborative Filtering.
Content-based approach requires a good amount of information of items’ own features, rather than using users’ interactions and feedbacks. For example, it can be movie attributes such as genre, year, director, actor etc., or textual content of articles that can extracted by applying Natural Language Processing. Collaborative Filtering, on the other hand, doesn’t need anything else except users’ historical preference on a set of items. Because it’s based o
expressed翻译n historical data, the core assumption here is that the users who have agreed in the past tend to also agree in the future. In terms of user preference, it usually expressed by two categories. Explicit Rating, is a rate given by a user to an item on a sliding scale, like 5 stars for Titanic. This is the most direct feedback from users to show how much they like an item. Implicit Rating, suggests users preference indirectly, such as page views, clicks, purchase records, whether or not listen to a music track, and so on. In this article, I will take a close look at collaborative filtering that is a traditional and powerful tool for recommender systems.
Nearest Neighborhood
The standard method of Collaborative Filtering is known as Nearest Neighborhood algorithm. There are user-based CF and item-based CF. Let’s first look at User-based CF. We have an n × m matrix of ratings, with user uᵢ, i = 1, ...n and item pⱼ, j=1, …m. Now we want to predict the rating rᵢⱼ if target user i did not watch/rate an item j. The process is to calculate the similarities between target user i and all other users, select t
he top X similar users, and take the weighted average of ratings from these X users with similarities as weights.
While different people may have different baselines when giving ratings, some people tend to give high scores generally, some are pretty strict even though they are satisfied with item
s. To avoid this bias, we can subtract each user’s average rating of all items when computing weighted average, and add it back for target user, shown as below.
Two ways to calculate similarity are Pearson Correlation and Cosine Similarity.
Basically, the idea is to find the most similar users to your target user (nearest neighbors) and weight their ratings of an item as the prediction of the rating of this item for target user.
Without knowing anything about items and users themselves, we think two users are similar when they give the same item similar ratings . Analogously, for Item-based CF, we say two items are similar when they received similar ratings from a same user. Then, we will make prediction for a target user on an item by calculating weighted average of ratings on most X similar items from this user. One key advantage of Item-based CF is the stability which is that the ratings on a given item will not change significantly overtime, unlike the tastes of human beings.

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