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https://issues.apache.org/jira/browse/SPARK-38816?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Nikolay updated SPARK-38816:
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Attachment: image-2022-04-18-15-54-15-474.png
> Wrong comment in random matrix generator in spark-als algorithm
> ----------------------------------------------------------------
>
> Key: SPARK-38816
> URL: https://issues.apache.org/jira/browse/SPARK-38816
> Project: Spark
> Issue Type: Improvement
> Components: ML
> Affects Versions: 3.1.1, 3.1.2, 3.2.1
> Reporter: Nikolay
> Assignee: Sean R. Owen
> Priority: Minor
> Fix For: 3.1.3, 3.3.0, 3.2.2
>
> Original Estimate: 24h
> Remaining Estimate: 24h
>
> In algorithm Spark ALS we need initialize nonegative factor matricies for
> users and items.
> In ALS:
>
> {code:java}
> private def initialize[ID](
> inBlocks: RDD[(Int, InBlock[ID])],
> rank: Int,
> seed: Long): RDD[(Int, FactorBlock)] = {
> // Choose a unit vector uniformly at random from the unit sphere, but from
> the
> // "first quadrant" where all elements are nonnegative. This can be done by
> choosing
> // elements distributed as Normal(0,1) and taking the absolute value, and
> then normalizing.
> // This appears to create factorizations that have a slightly better
> reconstruction
> // (<1%) compared picking elements uniformly at random in [0,1].
> inBlocks.mapPartitions({ iter =>
> iter.map {
> case (srcBlockId, inBlock) =>
> val random: XORShiftRandom = new XORShiftRandom(byteswap64(seed ^
> srcBlockId))
> val factors: Array[Array[Float]] = Array.fill(inBlock.srcIds.length) {
> val factor = Array.fill(rank)(random.nextGaussian().toFloat)
> val nrm: Float = blas.snrm2(rank, factor, 1)
> blas.sscal(rank, 1.0f / nrm, factor, 1)
> factor
> }
> (srcBlockId, factors)
> }
> }, preservesPartitioning = true)
> } {code}
> In the comments, the author writes that we are generating a matrix filled
> with positive numbers. In the code we use random.nextGaussian().toFloat. But
> if we look at the documentation of the nextGaussian method, we can see that
> it also returns negative numbers:
>
> {code:java}
> /**
> * @return the next pseudorandom, Gaussian ("normally") distributed
> * {@code double} value with mean {@code 0.0} and
> * standard deviation {@code 1.0} from this random number
> * generator's sequence
> */
> synchronized public double nextGaussian() {
> // See Knuth, ACP, Section 3.4.1 Algorithm C.
> if (haveNextNextGaussian) {
> haveNextNextGaussian = false;
> return nextNextGaussian;
> } else {
> double v1, v2, s;
> do {
> v1 = 2 * nextDouble() - 1; // between -1 and 1
> v2 = 2 * nextDouble() - 1; // between -1 and 1
> s = v1 * v1 + v2 * v2;
> } while (s >= 1 || s == 0);
> double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s)/s);
> nextNextGaussian = v2 * multiplier;
> haveNextNextGaussian = true;
> return v1 * multiplier;
> }
> }
> {code}
>
> The result is a matrix with negative values
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