neighborhood-based collaborative filtering

(Algorithm) (Code Lab)

neighborhood-based collaborative filtering is a specific collaborative filtering algorithm to recommender system. It predict sthe degree of preference for an item of a user based on other similar users’ ratings. Similarity is determined by their preferences for known items.

For example, both users and rate movies 5 stars. Given user also like movie , user might also like it.

Process

1. Mean normalization
2. Cost function
3. gradient descent

Cost function

(Algorithm) The algorithm can learn features based on known user ratings (), then proceed to learn usual parameters .

	numbering	total number
item
user
feature

This cost function can be minimized using gradient descent

Mean normalization

(Mean normalization)

Why transforming utility matrix?

If there is a new user that hasn’t rated any item, cost function above will predict that user will rate all items , which doesn’t make much sense. Here comes mean normalization:

1. Average rating for each item (), arranged them in a matrix
2. Create a new utility matrix: subtract from each user rating for an item.

3. For user , on item the algorithm will predict a rating:

w^{(j)}\cdot x^{(i)} +b^{(j)}+\textcolor{red}{\mu_{i}}