The increasing importance of the web as a medium for electronic and business transactions has served as a driving force for the development of recommender systems technology. An important catalyst in this regard is the ease with which the web enables users to provide feedback about their likes or dislikes. The basic idea of recommender systems is to utilize these user data to infer customer interests. The entity to which the recommendation is provided is referred to as the user, and the product being recommended is referred to as an item. The basic models for recommender systems works with two kinds of data:

1. User-Item interactions such as ratings
2. Attribute information about the users and items such as textual profiles or relevant keywords Models that use type 1 data are referred to as collaborative filtering methods, whereas models that use type 2 data are referred to as content based methods. In this project, we will build recommendation system using collaborative filtering methods.

Collaborative filtering models use the collaborative power of the ratings provided by multiple users to make recommendations. The main challenge in designing collaborative filtering methods is that the underlying ratings matrices are sparse. Consider an example of a movie application in which users specify ratings indicating their like or dislike of specific movies. Most users would have viewed only a small fraction of the large universe of available movies and as a result most of the ratings are unspecified. The basic idea of collaborative filtering methods is that these unspecified ratings can be imputed because the observed ratings are often highly correlated across various users and items. For example, consider two users named John and Molly, who have very similar tastes. If the ratings, which both have specified, are very similar, then their similarity can be identified by the filtering algorithm. In such cases, it is very likely that the ratings in which only one of them has specified a value, are also likely to be similar. This similarity can be used to make inferences about incompletely specified values. Most of the collaborative filtering methods focuses on leveraging either inter-item correlations or inter-user correlations for the prediction process. In this project, we will implement and analyze the performance of two types of collaborative filtering methods:

1. Neighborhood-based collaborative filtering
2. Model-based collaborative filtering

In this project, we will build a recommendation system to predict the ratings of the movies in the MovieLens dataset. The dataset can be downloaded using the following link: http://files.grouplens.org/datasets/movielens/ml-latest-small.zip Although the dataset contains movie genre information, but we will only use the movie rating information in this project. For the subsequent discussion, we assume that the ratings matrix is denoted by R, and it is an m × n matrix containing m users (rows) and n movies (columns). The (i, j) entry of the matrix is the rating of user i for movie j and is denoted by rij . Before moving on to the collaborative filter implementation, we will analyze and visualize some properties of this dataset.