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Valeriy Avanesov edited comment on SPARK-2426 at 12/2/14 11:47 AM: ------------------------------------------------------------------- I'm not sure if I understand your question... As far as I can see, w_i stands for a row of the matrix w and h_j stands for a column of the matrix h. \sum_i \sum_j ( r_ij - w_i*h_j) -- is not a matrix norm. Probably, you either miss abs or square -- \sum_i \sum_j |r_ij - w_i*h_j| or \sum_i \sum_j ( r_ij - w_i*h_j)^2 It looks like l2 regularized stochastic matrix decomposition with respect to Frobenius (or l1) norm. But I don't understand why do you consider k optimization problems (do you? What does k \in {1 ... 25} stand for?). 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). By the way: is the matrix of ranks r stochastic? Stochastic matrix decomposition doesn't seem reasonable if it's not. was (Author: acopich): I'm not sure if I understand your question... As far as I can see, w_i stands for a row of the matrix w and h_j stands for a column of the matrix h. \sum_i \sum_j ( r_ij - w_i*h_j) -- is not a matrix norm. Probably, you either miss abs or square -- \sum_i \sum_j |r_ij - w_i*h_j| or \sum_i \sum_j ( r_ij - w_i*h_j)^2 It looks like l2 regularized stochastic matrix decomposition with respect to Frobenius (or l1) norm. But I don't understand why do you consider k optimization problems (do you? What does k \in {1 ... 25} stand for?). 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). By the way: is the matrix of ranks r stochastic? Stochastic matrix decomposition doesn't seem reasonable if it's not. > 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 -- This message was sent by Atlassian JIRA (v6.3.4#6332) --------------------------------------------------------------------- To unsubscribe, e-mail: issues-unsubscr...@spark.apache.org For additional commands, e-mail: issues-h...@spark.apache.org