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https://issues.apache.org/jira/browse/SPARK-2426?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14377357#comment-14377357
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Debasish Das commented on SPARK-2426:
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[~acopich] From your comment before "Anyway, l2 regularized stochastic matrix
decomposition problem is defined as follows
Minimize w.r.t. W and H : ||R - W*H|| + \lambda(||W|| + ||H||)
under non-negativeness and normalization constraints.
||.|| stands for Frobenius norm (or l1).", could you please point me to a good
reference with application to collaborative filtering/topic modeling ?
Stochastic matrix decomposition is what we can do in this PR now
https://github.com/apache/spark/pull/3221....
For MAP loss, I will open up a PR in a week through JIRA
https://issues.apache.org/jira/browse/SPARK-6323...I am very curious how much
slower we get compared to stochastic matrix decomposition using ALS
> Quadratic Minimization for MLlib ALS
> ------------------------------------
>
> Key: SPARK-2426
> URL: https://issues.apache.org/jira/browse/SPARK-2426
> Project: Spark
> Issue Type: New Feature
> Components: MLlib
> Affects Versions: 1.3.0
> Reporter: Debasish Das
> Assignee: Debasish Das
> Original Estimate: 504h
> Remaining Estimate: 504h
>
> Current ALS supports least squares and nonnegative least squares.
> I presented ADMM and IPM based Quadratic Minimization solvers to be used for
> the following ALS problems:
> 1. ALS with bounds
> 2. ALS with L1 regularization
> 3. ALS with Equality constraint and bounds
> Initial runtime comparisons are presented at Spark Summit.
> http://spark-summit.org/2014/talk/quadratic-programing-solver-for-non-negative-matrix-factorization-with-spark
> Based on Xiangrui's feedback I am currently comparing the ADMM based
> Quadratic Minimization solvers with IPM based QpSolvers and the default
> ALS/NNLS. I will keep updating the runtime comparison results.
> For integration the detailed plan is as follows:
> 1. Add QuadraticMinimizer and Proximal algorithms in mllib.optimization
> 2. Integrate QuadraticMinimizer in mllib ALS
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