Overview
One of the standard tools in recommender systems is the rating matrix, which is a matrix which records the ratings of a set of customers for a set of products. In this case, if there are {% m %} customers and {% n %} products, the rating matrix is an {% m \times n %} matrix, where {% r_{i,j} %} is the rating of the {% i^{th} %} customer for product {% j %}.
Ratings should be encoded as a number. That is, if the ratings are discrete cateogories, the values should first be translated into a number.
Ratings matrices are not always completely filled in. That is, a customer may not have provided a rating for a given product. As a matter of implementation, a null value can be placed in the matrix for any rating that is missing.
Processing
- Fill in Missing Values - some algorithms will require a mtrix with no nulls. In this case, there are multiple techniques for filling in Missing Values. A common method is to fill in nulls with the average value of non-null values for either the row or the column that the null resides in.
- Singular Value Decomposition (SVD) - approximate the ratings matrix with truncated SVD.