Gábor Hermann created FLINK-4961:
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Summary: SGD for Matrix Factorization
Key: FLINK-4961
URL: https://issues.apache.org/jira/browse/FLINK-4961
Project: Flink
Issue Type: New Feature
Components: Machine Learning Library
Reporter: Gábor Hermann
Assignee: Gábor Hermann
We have started an implementation of distributed stochastic gradient descent
for matrix factorization based on Gemulla et al. [1].
The main problem with distributed SGD in general is the conflicting updates of
the model variable. In case of matrix factorization we can avoid conflicting
updates by carefully deciding in each iteration step which blocks of the rating
matrix we should use to update the corresponding blocks of the user and item
matrices (see Figure 1. in paper).
Although a general SGD solver might seem relevant for this issue, we can do
much better in the special case of matrix factorization. E.g. in case of a
linear regression model, the model is broadcasted in every iteration. As the
model is typically small in that case, we can only avoid conflicts by having a
"global" model. Based on this, the general SGD solver is a different issue.
To give more details, the algorithm works as follows.
We randomly create user and item vectors, then randomly partition them into
{{k}} user and {{k}} item blocks. Based on these factor blocks we partition the
rating matrix to {{k * k}} blocks correspondingly.
In one iteration step we choose {{k}} non-conflicting rating blocks, i.e. we
should not choose two rating blocks simultaneously with the same user or item
block. This is done by assigning a rating block ID to every user and item
block. We match the user, item, and rating blocks by the current rating block
ID, and update the user and item factors by the ratings locally. We also update
the rating block ID for the factor blocks, thus in the next iteration we use
other rating blocks to update the factors.
In {{k}} iteration we sweep through the whole rating matrix of {{k * k}} blocks
(so instead of {{numberOfIterationSteps}} iterations we should do {{k *
numberOfIterationSteps}} iterations).
[1] [http://people.mpi-inf.mpg.de/~rgemulla/publications]/gemulla11dsgd.pdf
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