🤖 AI / ML

Alternating Least Squares

als · alternating least squares · implicit als · ials · als matrix factorization · als matrix factorisation

Definition

ALS is an iterative matrix factorisation algorithm for collaborative filtering that optimises latent user and item vectors in alternating turns using least squares.

How ALS works

The job of a recommender system is to fill in a sparse user-by-item matrix. Most cells are empty:
any one user has interacted with only a tiny slice of the catalogue. ALS solves this by
decomposing the matrix into two much smaller ones — a matrix of user vectors and a matrix of item
vectors.

The algorithm runs iteratively:

Initialise the user and item vectors with random values
Fix the item vectors, then optimise the user vectors (a least-squares problem)
Fix the user vectors, then optimise the item vectors (a least-squares problem)
Repeat until convergence

At each step the task reduces to a system of linear equations — hence “least squares”.

ALS for implicit data (iALS)

E-commerce has almost no explicit ratings. What it has is behaviour: views, add-to-basket events,
purchases. Implicit ALS reads these as confidence in a preference:

confidence(u, i) = 1 + alpha * frequency(u, i)

where frequency is the number of interactions between user u and item i, and alpha is a scaling
parameter. More interactions mean the model is more confident that the item is relevant.

Signal	Typical weight
Purchase	High
Add to basket	Medium
Product page view	Low
View in a category listing	Very low

Scalability: why ALS is popular in production

On each iteration, updating the user vectors is independent across users, so the work can run in
parallel. That makes ALS a natural fit for Apache Spark (MLlib) and other distributed compute.
Large e-commerce platforms with hundreds of millions of interactions train ALS models in a
reasonable time.

The limits of ALS

Cold start. No history means no useful vector. New users and newly added items need their own
strategies.
No temporal context. Standard ALS does not account for preferences changing over time; that
requires extensions or different architectures such as sequential recommendations and
transformers.
Interpretability. Latent factors carry no human-readable meaning, so the model cannot explain
to a shopper why this particular product was recommended.

Frequently asked questions

What is the advantage of ALS over SGD for recommendations?

ALS parallelises well: at each step, updating the user vectors or the item vectors is independent work, so the model can be trained on a cluster. SGD updates parameters sequentially and scales worse on large datasets. With millions of users and SKUs, ALS is the practical choice.

How does ALS handle implicit data?

Implicit ALS (iALS) treats interactions — a click, a view, a purchase — as confidence signals rather than explicit ratings. The more interactions there are, the higher the confidence in the preference. This is the standard approach in e-commerce, where five-star ratings are rare and behaviour is the richer source of signal.

Which problem does ALS not solve well?

The cold start. For new users or new items with no interaction history, ALS cannot build a usable vector. Those cases need extra machinery: content-based filtering, a fallback to popular products, or a hybrid model.