Collaborative Filtering (ML Exam 3)

data

set of users, set of items, some sort of interaction between the users and the items (rating, watch duration, skips, etc.)

represented as a table or matrix

Collaborative Filtering

method for recommender systems that is solely based on feedback that has been recorded between users and items

Neighborhood Models

datapoints are users and axises are items. measure similarity between data points using cosine similarity (can have user based or item based)

Cosine similarity

measures the angle between two datapoints. withstands issues with rating scales

cosine similarity values

-1: 180 angle, exactly opposite

0: 90 angle: no correlation

1: exactly the same

issues with cosine similarity

scaling: can’t predict the rating because rating scales differ

zeroes: fill in missing values with 0, but 0 implies a low rating

data scaling

scale all ratings from a user by their own average (subtract users average rating from all of their ratings). now 0 is average.

centered cosine

the cosine angle between scaled vectors

Predicting ratings

user-user model: find k nearest neighbors using centered cosine similarity. calculate the average of the scaled ratings of the neighbors to find the prediction for the rating for the user.

Latent Factors Model

Assume there exists some unknown set of factors that characterize both the items and the users, and that we can infer these factors from ratings. Can use matrix dependencies to fill holes.

finding matrix dependencies

1. matrix factorization

• matrix with items and characteristics x matrix with users and characteristics

2. multiply to get ratings matrix

how to find the right factorization

machine will guess matrices until their product is close enough (number of latent factors is a hyper parameter). Use SSE to determine how far off the predicted matrix is from the target matrix. take partial derivative of the error with respect to each variable to find downhill slope.