9a5d482e09
This pull request includes a nonnegative least-squares solver (NNLS) tailored to the kinds of small-scale problems that come up when training matrix factorisation models by alternating nonnegative least-squares (ANNLS). The method used for the NNLS subproblems is based on the classical method of projected gradients. There is a modification where, if the set of active constraints has not changed since the last iteration, a conjugate gradient step is considered and possibly rejected in favour of the gradient; this improves convergence once the optimal face has been located. The NNLS solver is in `org.apache.spark.mllib.optimization.NNLSbyPCG`. Author: Tor Myklebust <tmyklebu@gmail.com> Closes #460 from tmyklebu/annls and squashes the following commits: 79bc4b5 [Tor Myklebust] Merge branch 'master' of https://github.com/apache/spark into annls 199b0bc [Tor Myklebust] Make the ctor private again and use the builder pattern. 7fbabf1 [Tor Myklebust] Cleanup matrix math in NNLSSuite. 65ef7f2 [Tor Myklebust] Make ALS's ctor public and remove a couple of "convenience" wrappers. 2d4f3cb [Tor Myklebust] Cleanup. 0cb4481 [Tor Myklebust] Drop the iteration limit from 40k to max(400,20n). e2a01d1 [Tor Myklebust] Create a workspace object for NNLS to cut down on memory allocations. b285106 [Tor Myklebust] Clean up NNLS test cases. 9c820b6 [Tor Myklebust] Tweak variable names. 8a1a436 [Tor Myklebust] Describe the problem and add a reference to Polyak's paper. 5345402 [Tor Myklebust] Style fixes that got eaten. ac673bd [Tor Myklebust] More safeguards against numerical ridiculousness. c288b6a [Tor Myklebust] Finish moving the NNLS solver. 9a82fa6 [Tor Myklebust] Fix scalastyle moanings. 33bf4f2 [Tor Myklebust] Fix missing space. 89ea0a8 [Tor Myklebust] Hack ALSSuite to support NNLS testing. f5dbf4d [Tor Myklebust] Teach ALS how to use the NNLS solver. 6cb563c [Tor Myklebust] Tests for the nonnegative least squares solver. a68ac10 [Tor Myklebust] A nonnegative least-squares solver. |
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