Collaborative Filtering at Spotify

Music recommendations at Spotify Erik Bernhardsson erikbern@spotify.com

Recommendation stuff at Spotify

Collaborative filtering

Collaborative filteringIdea:- If two movies x, y get similar ratings then they are probably similar- If a lot of users all listen to tracks x, y, z, then those tracks are probably similar

Get data

… lots of data

Aggregate dataThrow away temporal information and just look at the number of times

OK, so now we have a big matrix

… very big matrix

Supervised collaborative filtering is pretty much matrix completion

Supervised learning: Matrix completion

Supervised: evaluating rec quality

Unsupervised learning- Trying to estimate the density- i.e. predict probability of future events

Try to predict the future given the past

How can we find similar items

We can calculate correlation coefficient as an item similarity- Use something like Pearson, Jaccard, …

Amazon did this for “customers who bought this also bought”- US patent 7113917

Parallelization is hard though

Can speed this up using various LSH tricks- Twitter: Dimension Independent Similarity Computation (DISCO)

Are there other approaches?

Natural Language Processing has a lot of similar problems…matrix factorization is one idea

Matrix factorization

Matrix factorization- Want to get user vectors and item vectors- Assume f latent factors (dimensions) for each user/item

Probabilistic Latent Semantic Analysis (PLSA)- Hofmann, 1999- Also called PLSI

PLSA, cont.+ a bunch of constraints:

PLSA, cont.Optimization problem: maximize log-likelihood

PLSA, cont.

“Collaborative Filtering for Implicit Feedback Datasets”- Hu, Koren, Volinsky (2008)

“Collaborative Filtering for Implicit Feedback Datasets”, cont.

Here is another method we use

What happens each iteration- Assign all latent vectors small random values- Perform gradient ascent to optimize log-likelihood

Calculate derivative and do gradient ascent- Assign all latent vectors small random values- Perform gradient ascent to optimize log-likelihood

2D iteration example

Vectors are pretty nice because things are now super fast- User-item score is a dot product:- Item-item similarity score is a cosine similarity:- Both cases have trivial complexity in the number of factors f:

Example: item similarity as a cosine of vectors

Two dimensional example for tracks

We can rank all tracks by the user’s vector

So how do we implement this?

One iteration of a matrix factorization algorithm“Google News personalization: scalable online collaborative filtering”

So now we solved the problem of recommendations right?

Actually what we really want is to apply it to other domains

Radio- Artist radio: find related tracks- Optimize ensemble model based on skip/thumbs data

Learning from feedback is actually pretty hard

A/B testing

More applications!!!

Last but not least: we’re hiring!

Thank you

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Collaborative Filtering at Spotify

by Erik Bernhardsson on Jan 25, 2013

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