Computes the (rank x rank
) matrix YtY
, where Y
is the (nui x rank
) matrix of factors
for each user (or product), in a distributed fashion.
Computes the (rank x rank
) matrix YtY
, where Y
is the (nui x rank
) matrix of factors
for each user (or product), in a distributed fashion. Here reduceByKeyLocally
is used as
the driver program requires YtY
to broadcast it to the slaves
the (block-distributed) user or product factor vectors
Option[YtY] - whose value is only used in the implicit preference model
Run ALS with the configured parameters on an input RDD of (user, product, rating) triples.
Run ALS with the configured parameters on an input RDD of (user, product, rating) triples. Returns a MatrixFactorizationModel with feature vectors for each user and product.
Set the number of blocks to parallelize the computation into; pass -1 for an auto-configured number of blocks.
Set the number of blocks to parallelize the computation into; pass -1 for an auto-configured number of blocks. Default: -1.
Set the number of iterations to run.
Set the number of iterations to run. Default: 10.
Set the regularization parameter, lambda.
Set the regularization parameter, lambda. Default: 0.01.
Set the rank of the feature matrices computed (number of features).
Set the rank of the feature matrices computed (number of features). Default: 10.
Sets a random seed to have deterministic results.
Flatten out blocked user or product factors into an RDD of (id, factor vector) pairs
Compute the new feature vectors for a block of the users matrix given the list of factors it received from each product and its InLinkBlock.
Alternating Least Squares matrix factorization.
ALS attempts to estimate the ratings matrix
R
as the product of two lower-rank matrices,X
andY
, i.e.X * Yt = R
. Typically these approximations are called 'factor' matrices. The general approach is iterative. During each iteration, one of the factor matrices is held constant, while the other is solved for using least squares. The newly-solved factor matrix is then held constant while solving for the other factor matrix.This is a blocked implementation of the ALS factorization algorithm that groups the two sets of factors (referred to as "users" and "products") into blocks and reduces communication by only sending one copy of each user vector to each product block on each iteration, and only for the product blocks that need that user's feature vector. This is achieved by precomputing some information about the ratings matrix to determine the "out-links" of each user (which blocks of products it will contribute to) and "in-link" information for each product (which of the feature vectors it receives from each user block it will depend on). This allows us to send only an array of feature vectors between each user block and product block, and have the product block find the users' ratings and update the products based on these messages.
For implicit preference data, the algorithm used is based on "Collaborative Filtering for Implicit Feedback Datasets", available at http://dx.doi.org/10.1109/ICDM.2008.22, adapted for the blocked approach used here.
Essentially instead of finding the low-rank approximations to the rating matrix
R
, this finds the approximations for a preference matrixP
where the elements ofP
are 1 if r > 0 and 0 if r = 0. The ratings then act as 'confidence' values related to strength of indicated user preferences rather than explicit ratings given to items.