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In the previous exercise, we introduced collaborative filtering. However collaborative filtering can be further classified into two major subclasses: memory-based methods (also called neighborhood-based methods) and model-based methods.

Memory-based methods work through the concept of similarity. Fundamentally, memory-based methods work in one of two ways:

1. The algorithm finds similar users to the target users, and recommends items those similar users liked. This approach is known as user-user collaborative filtering.

2. The algorithm finds similar items to ones the target user liked by measuring the similarity of how users rated items. This approach is known as item-item collaborative filtering.

In contrast, model-based methods work by building models that attempt to predict a rating for a user-item pair by using ratings as features. One particular method that is often used in practice is matrix factorization. This method models the user-item ratings matrix as the product of a set of users vector and product vectors. The rating of any user-item pair can then be predicted by multiplying the relevant user vector by the relevant product vector.

After creating a ratings matrix, various data transformations may be performed on the ratings matrix. These transformations are done generally to improve model performance, similar to how normalizing features in a machine learning model can help improve performance.

One such transformation is ratings normalization. Ratings normalization is a technique where the value of each rating for a given row is adjusted based on the statistical properties of that row. The primary reason this transformation is done is because different users may have different approaches to rating something. For example, some users may give a 5-star rating to any positive experience they have. Other users may be more selective, and only give 5 star ratings very rarely. Ratings normalization provides a way to control for these differences.

### Instructions

One of two approaches is usually used for normalizing ratings. The first, mean centering, involves subtracting the mean rating of a row from every value of the row. The other method, z-score normalization, involves using the mean and standard deviation of each row to calculate a z-score for each element of the row. Can you think of other ways to make sure that the ratings between different users and items can be meaningfully compared?