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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package spark.mllib.recommendation
import scala.collection.mutable.{ArrayBuffer, BitSet}
import scala.util.Random
import scala.util.Sorting
import spark.{HashPartitioner, Partitioner, SparkContext, RDD}
import spark.storage.StorageLevel
import spark.KryoRegistrator
import spark.SparkContext._
import com.esotericsoftware.kryo.Kryo
import org.jblas.{DoubleMatrix, SimpleBlas, Solve}
/**
* Out-link information for a user or product block. This includes the original user/product IDs
* of the elements within this block, and the list of destination blocks that each user or
* product will need to send its feature vector to.
*/
private[recommendation] case class OutLinkBlock(
elementIds: Array[Int], shouldSend: Array[BitSet])
/**
* In-link information for a user (or product) block. This includes the original user/product IDs
* of the elements within this block, as well as an array of indices and ratings that specify
* which user in the block will be rated by which products from each product block (or vice-versa).
* Specifically, if this InLinkBlock is for users, ratingsForBlock(b)(i) will contain two arrays,
* indices and ratings, for the i'th product that will be sent to us by product block b (call this
* P). These arrays represent the users that product P had ratings for (by their index in this
* block), as well as the corresponding rating for each one. We can thus use this information when
* we get product block b's message to update the corresponding users.
*/
private[recommendation] case class InLinkBlock(
elementIds: Array[Int], ratingsForBlock: Array[Array[(Array[Int], Array[Double])]])
/**
* A more compact class to represent a rating than Tuple3[Int, Int, Double].
*/
private[recommendation] case class Rating(user: Int, product: Int, rating: Double)
/**
* Alternating Least Squares matrix factorization.
*
* This is a blocked implementation of the ALS factorization algorithm that groups the two sets
* of factors (referred to as "users" and "products") into blocks and reduces communication by only
* sending one copy of each user vector to each product block on each iteration, and only for the
* product blocks that need that user's feature vector. This is achieved by precomputing some
* information about the ratings matrix to determine the "out-links" of each user (which blocks of
* products it will contribute to) and "in-link" information for each product (which of the feature
* vectors it receives from each user block it will depend on). This allows us to send only an
* array of feature vectors between each user block and product block, and have the product block
* find the users' ratings and update the products based on these messages.
*/
class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var lambda: Double)
extends Serializable
{
def this() = this(-1, 10, 10, 0.01)
/**
* Set the number of blocks to parallelize the computation into; pass -1 for an auto-configured
* number of blocks. Default: -1.
*/
def setBlocks(numBlocks: Int): ALS = {
this.numBlocks = numBlocks
this
}
/** Set the rank of the feature matrices computed (number of features). Default: 10. */
def setRank(rank: Int): ALS = {
this.rank = rank
this
}
/** Set the number of iterations to run. Default: 10. */
def setIterations(iterations: Int): ALS = {
this.iterations = iterations
this
}
/** Set the regularization parameter, lambda. Default: 0.01. */
def setLambda(lambda: Double): ALS = {
this.lambda = lambda
this
}
/**
* Run ALS with the configured parmeters on an input RDD of (user, product, rating) triples.
* Returns a MatrixFactorizationModel with feature vectors for each user and product.
*/
def train(ratings: RDD[(Int, Int, Double)]): MatrixFactorizationModel = {
val numBlocks = if (this.numBlocks == -1) {
math.max(ratings.context.defaultParallelism, ratings.partitions.size / 2)
} else {
this.numBlocks
}
val partitioner = new HashPartitioner(numBlocks)
val ratingsByUserBlock = ratings.map{ case (u, p, r) => (u % numBlocks, Rating(u, p, r)) }
val ratingsByProductBlock = ratings.map{ case (u, p, r) => (p % numBlocks, Rating(p, u, r)) }
val (userInLinks, userOutLinks) = makeLinkRDDs(numBlocks, ratingsByUserBlock)
val (productInLinks, productOutLinks) = makeLinkRDDs(numBlocks, ratingsByProductBlock)
// Initialize user and product factors randomly
val seed = new Random().nextInt()
var users = userOutLinks.mapValues(_.elementIds.map(u => randomFactor(rank, seed ^ u)))
var products = productOutLinks.mapValues(_.elementIds.map(p => randomFactor(rank, seed ^ ~p)))
for (iter <- 0 until iterations) {
// perform ALS update
products = updateFeatures(users, userOutLinks, productInLinks, partitioner, rank, lambda)
users = updateFeatures(products, productOutLinks, userInLinks, partitioner, rank, lambda)
}
// Flatten and cache the two final RDDs to un-block them
val usersOut = users.join(userOutLinks).flatMap { case (b, (factors, outLinkBlock)) =>
for (i <- 0 until factors.length) yield (outLinkBlock.elementIds(i), factors(i))
}
val productsOut = products.join(productOutLinks).flatMap { case (b, (factors, outLinkBlock)) =>
for (i <- 0 until factors.length) yield (outLinkBlock.elementIds(i), factors(i))
}
usersOut.persist()
productsOut.persist()
new MatrixFactorizationModel(rank, usersOut, productsOut)
}
/**
* Make the out-links table for a block of the users (or products) dataset given the list of
* (user, product, rating) values for the users in that block (or the opposite for products).
*/
private def makeOutLinkBlock(numBlocks: Int, ratings: Array[Rating]): OutLinkBlock = {
val userIds = ratings.map(_.user).distinct.sorted
val numUsers = userIds.length
val userIdToPos = userIds.zipWithIndex.toMap
val shouldSend = Array.fill(numUsers)(new BitSet(numBlocks))
for (r <- ratings) {
shouldSend(userIdToPos(r.user))(r.product % numBlocks) = true
}
OutLinkBlock(userIds, shouldSend)
}
/**
* Make the in-links table for a block of the users (or products) dataset given a list of
* (user, product, rating) values for the users in that block (or the opposite for products).
*/
private def makeInLinkBlock(numBlocks: Int, ratings: Array[Rating]): InLinkBlock = {
val userIds = ratings.map(_.user).distinct.sorted
val numUsers = userIds.length
val userIdToPos = userIds.zipWithIndex.toMap
// Split out our ratings by product block
val blockRatings = Array.fill(numBlocks)(new ArrayBuffer[Rating])
for (r <- ratings) {
blockRatings(r.product % numBlocks) += r
}
val ratingsForBlock = new Array[Array[(Array[Int], Array[Double])]](numBlocks)
for (productBlock <- 0 until numBlocks) {
// Create an array of (product, Seq(Rating)) ratings
val groupedRatings = blockRatings(productBlock).groupBy(_.product).toArray
// Sort them by product ID
val ordering = new Ordering[(Int, ArrayBuffer[Rating])] {
def compare(a: (Int, ArrayBuffer[Rating]), b: (Int, ArrayBuffer[Rating])): Int = a._1 - b._1
}
Sorting.quickSort(groupedRatings)(ordering)
// Translate the user IDs to indices based on userIdToPos
ratingsForBlock(productBlock) = groupedRatings.map { case (p, rs) =>
(rs.view.map(r => userIdToPos(r.user)).toArray, rs.view.map(_.rating).toArray)
}
}
InLinkBlock(userIds, ratingsForBlock)
}
/**
* Make RDDs of InLinkBlocks and OutLinkBlocks given an RDD of (blockId, (u, p, r)) values for
* the users (or (blockId, (p, u, r)) for the products). We create these simultaneously to avoid
* having to shuffle the (blockId, (u, p, r)) RDD twice, or to cache it.
*/
private def makeLinkRDDs(numBlocks: Int, ratings: RDD[(Int, Rating)])
: (RDD[(Int, InLinkBlock)], RDD[(Int, OutLinkBlock)]) =
{
val grouped = ratings.partitionBy(new HashPartitioner(numBlocks))
val links = grouped.mapPartitionsWithIndex((blockId, elements) => {
val ratings = elements.map{_._2}.toArray
val inLinkBlock = makeInLinkBlock(numBlocks, ratings)
val outLinkBlock = makeOutLinkBlock(numBlocks, ratings)
Iterator.single((blockId, (inLinkBlock, outLinkBlock)))
}, true)
links.persist(StorageLevel.MEMORY_AND_DISK)
(links.mapValues(_._1), links.mapValues(_._2))
}
/**
* Make a random factor vector with the given seed.
* TODO: Initialize things using mapPartitionsWithIndex to make it faster?
*/
private def randomFactor(rank: Int, seed: Int): Array[Double] = {
val rand = new Random(seed)
Array.fill(rank)(rand.nextDouble)
}
/**
* Compute the user feature vectors given the current products (or vice-versa). This first joins
* the products with their out-links to generate a set of messages to each destination block
* (specifically, the features for the products that user block cares about), then groups these
* by destination and joins them with the in-link info to figure out how to update each user.
* It returns an RDD of new feature vectors for each user block.
*/
private def updateFeatures(
products: RDD[(Int, Array[Array[Double]])],
productOutLinks: RDD[(Int, OutLinkBlock)],
userInLinks: RDD[(Int, InLinkBlock)],
partitioner: Partitioner,
rank: Int,
lambda: Double)
: RDD[(Int, Array[Array[Double]])] =
{
val numBlocks = products.partitions.size
productOutLinks.join(products).flatMap { case (bid, (outLinkBlock, factors)) =>
val toSend = Array.fill(numBlocks)(new ArrayBuffer[Array[Double]])
for (p <- 0 until outLinkBlock.elementIds.length; userBlock <- 0 until numBlocks) {
if (outLinkBlock.shouldSend(p)(userBlock)) {
toSend(userBlock) += factors(p)
}
}
toSend.zipWithIndex.map{ case (buf, idx) => (idx, (bid, buf.toArray)) }
}.groupByKey(partitioner)
.join(userInLinks)
.mapValues{ case (messages, inLinkBlock) => updateBlock(messages, inLinkBlock, rank, lambda) }
}
/**
* Compute the new feature vectors for a block of the users matrix given the list of factors
* it received from each product and its InLinkBlock.
*/
def updateBlock(messages: Seq[(Int, Array[Array[Double]])], inLinkBlock: InLinkBlock,
rank: Int, lambda: Double)
: Array[Array[Double]] =
{
// Sort the incoming block factor messages by block ID and make them an array
val blockFactors = messages.sortBy(_._1).map(_._2).toArray // Array[Array[Double]]
val numBlocks = blockFactors.length
val numUsers = inLinkBlock.elementIds.length
// We'll sum up the XtXes using vectors that represent only the lower-triangular part, since
// the matrices are symmetric
val triangleSize = rank * (rank + 1) / 2
val userXtX = Array.fill(numUsers)(DoubleMatrix.zeros(triangleSize))
val userXy = Array.fill(numUsers)(DoubleMatrix.zeros(rank))
// Some temp variables to avoid memory allocation
val tempXtX = DoubleMatrix.zeros(triangleSize)
val fullXtX = DoubleMatrix.zeros(rank, rank)
// Compute the XtX and Xy values for each user by adding products it rated in each product block
for (productBlock <- 0 until numBlocks) {
for (p <- 0 until blockFactors(productBlock).length) {
val x = new DoubleMatrix(blockFactors(productBlock)(p))
fillXtX(x, tempXtX)
val (us, rs) = inLinkBlock.ratingsForBlock(productBlock)(p)
for (i <- 0 until us.length) {
userXtX(us(i)).addi(tempXtX)
SimpleBlas.axpy(rs(i), x, userXy(us(i)))
}
}
}
// Solve the least-squares problem for each user and return the new feature vectors
userXtX.zipWithIndex.map{ case (triangularXtX, index) =>
// Compute the full XtX matrix from the lower-triangular part we got above
fillFullMatrix(triangularXtX, fullXtX)
// Add regularization
(0 until rank).foreach(i => fullXtX.data(i*rank + i) += lambda)
// Solve the resulting matrix, which is symmetric and positive-definite
Solve.solvePositive(fullXtX, userXy(index)).data
}
}
/**
* Set xtxDest to the lower-triangular part of x transpose * x. For efficiency in summing
* these matrices, we store xtxDest as only rank * (rank+1) / 2 values, namely the values
* at (0,0), (1,0), (1,1), (2,0), (2,1), (2,2), etc in that order.
*/
private def fillXtX(x: DoubleMatrix, xtxDest: DoubleMatrix) {
var i = 0
var pos = 0
while (i < x.length) {
var j = 0
while (j <= i) {
xtxDest.data(pos) = x.data(i) * x.data(j)
pos += 1
j += 1
}
i += 1
}
}
/**
* Given a triangular matrix in the order of fillXtX above, compute the full symmetric square
* matrix that it represents, storing it into destMatrix.
*/
private def fillFullMatrix(triangularMatrix: DoubleMatrix, destMatrix: DoubleMatrix) {
val rank = destMatrix.rows
var i = 0
var pos = 0
while (i < rank) {
var j = 0
while (j <= i) {
destMatrix.data(i*rank + j) = triangularMatrix.data(pos)
destMatrix.data(j*rank + i) = triangularMatrix.data(pos)
pos += 1
j += 1
}
i += 1
}
}
}
/**
* Top-level methods for calling Alternating Least Squares (ALS) matrix factorizaton.
*/
object ALS {
/**
* Train a matrix factorization model given an RDD of ratings given by users to some products,
* in the form of (userID, productID, rating) pairs. We approximate the ratings matrix as the
* product of two lower-rank matrices of a given rank (number of features). To solve for these
* features, we run a given number of iterations of ALS. This is done using a level of
* parallelism given by `blocks`.
*
* @param ratings RDD of (userID, productID, rating) pairs
* @param rank number of features to use
* @param iterations number of iterations of ALS (recommended: 10-20)
* @param lambda regularization factor (recommended: 0.01)
* @param blocks level of parallelism to split computation into
*/
def train(
ratings: RDD[(Int, Int, Double)],
rank: Int,
iterations: Int,
lambda: Double,
blocks: Int)
: MatrixFactorizationModel =
{
new ALS(blocks, rank, iterations, lambda).train(ratings)
}
/**
* Train a matrix factorization model given an RDD of ratings given by users to some products,
* in the form of (userID, productID, rating) pairs. We approximate the ratings matrix as the
* product of two lower-rank matrices of a given rank (number of features). To solve for these
* features, we run a given number of iterations of ALS. The level of parallelism is determined
* automatically based on the number of partitions in `ratings`.
*
* @param ratings RDD of (userID, productID, rating) pairs
* @param rank number of features to use
* @param iterations number of iterations of ALS (recommended: 10-20)
* @param lambda regularization factor (recommended: 0.01)
*/
def train(ratings: RDD[(Int, Int, Double)], rank: Int, iterations: Int, lambda: Double)
: MatrixFactorizationModel =
{
train(ratings, rank, iterations, lambda, -1)
}
/**
* Train a matrix factorization model given an RDD of ratings given by users to some products,
* in the form of (userID, productID, rating) pairs. We approximate the ratings matrix as the
* product of two lower-rank matrices of a given rank (number of features). To solve for these
* features, we run a given number of iterations of ALS. The level of parallelism is determined
* automatically based on the number of partitions in `ratings`.
*
* @param ratings RDD of (userID, productID, rating) pairs
* @param rank number of features to use
* @param iterations number of iterations of ALS (recommended: 10-20)
*/
def train(ratings: RDD[(Int, Int, Double)], rank: Int, iterations: Int)
: MatrixFactorizationModel =
{
train(ratings, rank, iterations, 0.01, -1)
}
private class ALSRegistrator extends KryoRegistrator {
override def registerClasses(kryo: Kryo) {
kryo.register(classOf[Rating])
}
}
def main(args: Array[String]) {
if (args.length != 5 && args.length != 6) {
println("Usage: ALS <master> <ratings_file> <rank> <iterations> <output_dir> [<blocks>]")
System.exit(1)
}
val (master, ratingsFile, rank, iters, outputDir) =
(args(0), args(1), args(2).toInt, args(3).toInt, args(4))
val blocks = if (args.length == 6) args(5).toInt else -1
System.setProperty("spark.serializer", "spark.KryoSerializer")
System.setProperty("spark.kryo.registrator", classOf[ALSRegistrator].getName)
System.setProperty("spark.kryo.referenceTracking", "false")
System.setProperty("spark.locality.wait", "10000")
val sc = new SparkContext(master, "ALS")
val ratings = sc.textFile(ratingsFile).map { line =>
val fields = line.split(',')
(fields(0).toInt, fields(1).toInt, fields(2).toDouble)
}
val model = ALS.train(ratings, rank, iters, 0.01, blocks)
model.userFeatures.map{ case (id, vec) => id + "," + vec.mkString(" ") }
.saveAsTextFile(outputDir + "/userFeatures")
model.productFeatures.map{ case (id, vec) => id + "," + vec.mkString(" ") }
.saveAsTextFile(outputDir + "/productFeatures")
println("Final user/product features written to " + outputDir)
System.exit(0)
}
}
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