Adding algorithm for implicit feedback data to ALS

This commit is contained in:
Nick Pentreath 2013-09-06 14:45:05 +02:00
parent a106ed8b97
commit 737f01a1ef
3 changed files with 296 additions and 54 deletions

View file

@ -21,7 +21,8 @@ import scala.collection.mutable.{ArrayBuffer, BitSet}
import scala.util.Random
import scala.util.Sorting
import org.apache.spark.{HashPartitioner, Partitioner, SparkContext}
import org.apache.spark.broadcast.Broadcast
import org.apache.spark.{Logging, HashPartitioner, Partitioner, SparkContext}
import org.apache.spark.storage.StorageLevel
import org.apache.spark.rdd.RDD
import org.apache.spark.serializer.KryoRegistrator
@ -61,6 +62,12 @@ case class Rating(val user: Int, val product: Int, val rating: Double)
/**
* Alternating Least Squares matrix factorization.
*
* ALS attempts to estimate the ratings matrix `R` as the product of two lower-rank matrices,
* `X` and `Y`, i.e. `Xt * Y = R`. Typically these approximations are called 'factor' matrices.
* The general approach is iterative. During each iteration, one of the factor matrices is held
* constant, while the other is solved for using least squares. The newly-solved factor matrix is
* then held constant while solving for the other factor matrix.
*
* 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
@ -70,11 +77,21 @@ case class Rating(val user: Int, val product: Int, val rating: Double)
* 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.
*
* For implicit preference data, the algorithm used is based on
* "Collaborative Filtering for Implicit Feedback Datasets", available at
* [[http://research.yahoo.com/pub/2433]], adapted for the blocked approach used here.
*
* Essentially instead of finding the low-rank approximations to the rating matrix `R`,
* this finds the approximations for a preference matrix `P` where the elements of `P` are 1 if r > 0
* and 0 if r = 0. The ratings then act as 'confidence' values related to strength of indicated user
* preferences rather than explicit ratings given to items.
*/
class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var lambda: Double)
extends Serializable
class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var lambda: Double,
var implicitPrefs: Boolean, var alpha: Double)
extends Serializable with Logging
{
def this() = this(-1, 10, 10, 0.01)
def this() = this(-1, 10, 10, 0.01, false, 1.0)
/**
* Set the number of blocks to parallelize the computation into; pass -1 for an auto-configured
@ -103,6 +120,16 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
this
}
def setImplicitPrefs(implicitPrefs: Boolean): ALS = {
this.implicitPrefs = implicitPrefs
this
}
def setAlpha(alpha: Double): ALS = {
this.alpha = alpha
this
}
/**
* Run ALS with the configured parameters on an input RDD of (user, product, rating) triples.
* Returns a MatrixFactorizationModel with feature vectors for each user and product.
@ -147,19 +174,24 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
}
}
for (iter <- 0 until iterations) {
for (iter <- 1 to iterations) {
// perform ALS update
products = updateFeatures(users, userOutLinks, productInLinks, partitioner, rank, lambda)
users = updateFeatures(products, productOutLinks, userInLinks, partitioner, rank, lambda)
logInfo("Re-computing I given U (Iteration %d/%d)".format(iter, iterations))
// YtY / XtX is an Option[DoubleMatrix] and is only required for the implicit feedback model
val YtY = computeYtY(users)
val YtYb = ratings.context.broadcast(YtY)
products = updateFeatures(users, userOutLinks, productInLinks, partitioner, rank, lambda,
alpha, YtYb)
logInfo("Re-computing U given I (Iteration %d/%d)".format(iter, iterations))
val XtX = computeYtY(products)
val XtXb = ratings.context.broadcast(XtX)
users = updateFeatures(products, productOutLinks, userInLinks, partitioner, rank, lambda,
alpha, XtXb)
}
// 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))
}
val usersOut = unblockFactors(users, userOutLinks)
val productsOut = unblockFactors(products, productOutLinks)
usersOut.persist()
productsOut.persist()
@ -167,6 +199,41 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
new MatrixFactorizationModel(rank, usersOut, productsOut)
}
/**
* Computes the (`rank x rank`) matrix `YtY`, where `Y` is the (`nui x rank`) matrix of factors
* for each user (or product), in a distributed fashion. Here `reduceByKeyLocally` is used as
* the driver program requires `YtY` to broadcast it to the slaves
* @param factors the (block-distributed) user or product factor vectors
* @return Option[YtY] - whose value is only used in the implicit preference model
*/
def computeYtY(factors: RDD[(Int, Array[Array[Double]])]) = {
implicitPrefs match {
case true => {
Option(
factors.flatMapValues{ case factorArray =>
factorArray.map{ vector =>
val x = new DoubleMatrix(vector)
x.mmul(x.transpose())
}
}.reduceByKeyLocally((a, b) => a.addi(b))
.values
.reduce((a, b) => a.addi(b))
)
}
case false => None
}
}
/**
* Flatten out blocked user or product factors into an RDD of (id, factor vector) pairs
*/
def unblockFactors(blockedFactors: RDD[(Int, Array[Array[Double]])],
outLinks: RDD[(Int, OutLinkBlock)]) = {
blockedFactors.join(outLinks).flatMap{ case (b, (factors, outLinkBlock)) =>
for (i <- 0 until factors.length) yield (outLinkBlock.elementIds(i), factors(i))
}
}
/**
* 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).
@ -251,7 +318,9 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
userInLinks: RDD[(Int, InLinkBlock)],
partitioner: Partitioner,
rank: Int,
lambda: Double)
lambda: Double,
alpha: Double,
YtY: Broadcast[Option[DoubleMatrix]])
: RDD[(Int, Array[Array[Double]])] =
{
val numBlocks = products.partitions.size
@ -265,7 +334,9 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
toSend.zipWithIndex.map{ case (buf, idx) => (idx, (bid, buf.toArray)) }
}.groupByKey(partitioner)
.join(userInLinks)
.mapValues{ case (messages, inLinkBlock) => updateBlock(messages, inLinkBlock, rank, lambda) }
.mapValues{ case (messages, inLinkBlock) =>
updateBlock(messages, inLinkBlock, rank, lambda, alpha, YtY)
}
}
/**
@ -273,7 +344,7 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
* it received from each product and its InLinkBlock.
*/
def updateBlock(messages: Seq[(Int, Array[Array[Double]])], inLinkBlock: InLinkBlock,
rank: Int, lambda: Double)
rank: Int, lambda: Double, alpha: Double, YtY: Broadcast[Option[DoubleMatrix]])
: Array[Array[Double]] =
{
// Sort the incoming block factor messages by block ID and make them an array
@ -298,8 +369,14 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
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)))
implicitPrefs match {
case false =>
userXtX(us(i)).addi(tempXtX)
SimpleBlas.axpy(rs(i), x, userXy(us(i)))
case true =>
userXtX(us(i)).addi(tempXtX.mul(alpha * rs(i)))
SimpleBlas.axpy(1 + alpha * rs(i), x, userXy(us(i)))
}
}
}
}
@ -311,7 +388,10 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
// 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
implicitPrefs match {
case false => Solve.solvePositive(fullXtX, userXy(index)).data
case true => Solve.solvePositive(fullXtX.add(YtY.value.get), userXy(index)).data
}
}
}
@ -381,7 +461,7 @@ object ALS {
blocks: Int)
: MatrixFactorizationModel =
{
new ALS(blocks, rank, iterations, lambda).run(ratings)
new ALS(blocks, rank, iterations, lambda, false, 1.0).run(ratings)
}
/**
@ -419,6 +499,68 @@ object ALS {
train(ratings, rank, iterations, 0.01, -1)
}
/**
* Train a matrix factorization model given an RDD of 'implicit preferences' given by users
* to some products, in the form of (userID, productID, preference) 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
* @param alpha confidence parameter (only applies when immplicitPrefs = true)
*/
def trainImplicit(
ratings: RDD[Rating],
rank: Int,
iterations: Int,
lambda: Double,
blocks: Int,
alpha: Double)
: MatrixFactorizationModel =
{
new ALS(blocks, rank, iterations, lambda, true, alpha).run(ratings)
}
/**
* Train a matrix factorization model given an RDD of 'implicit preferences' given by users to
* some products, in the form of (userID, productID, preference) 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 trainImplicit(ratings: RDD[Rating], rank: Int, iterations: Int, lambda: Double, alpha: Double)
: MatrixFactorizationModel =
{
trainImplicit(ratings, rank, iterations, lambda, -1, alpha)
}
/**
* Train a matrix factorization model given an RDD of 'implicit preferences' 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`.
* Model parameters `alpha` and `lambda` are set to reasonable default values
*
* @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 trainImplicit(ratings: RDD[Rating], rank: Int, iterations: Int)
: MatrixFactorizationModel =
{
trainImplicit(ratings, rank, iterations, 0.01, -1, 1.0)
}
private class ALSRegistrator extends KryoRegistrator {
override def registerClasses(kryo: Kryo) {
kryo.register(classOf[Rating])
@ -426,29 +568,37 @@ object ALS {
}
def main(args: Array[String]) {
if (args.length != 5 && args.length != 6) {
println("Usage: ALS <master> <ratings_file> <rank> <iterations> <output_dir> [<blocks>]")
if (args.length < 5 || args.length > 9) {
println("Usage: ALS <master> <ratings_file> <rank> <iterations> <output_dir> " +
"[<lambda>] [<implicitPrefs>] [<alpha>] [<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
val lambda = if (args.length >= 6) args(5).toDouble else 0.01
val implicitPrefs = if (args.length >= 7) args(6).toBoolean else false
val alpha = if (args.length >= 8) args(7).toDouble else 1
val blocks = if (args.length == 9) args(8).toInt else -1
System.setProperty("spark.serializer", "org.apache.spark.serializer.KryoSerializer")
System.setProperty("spark.kryo.registrator", classOf[ALSRegistrator].getName)
System.setProperty("spark.kryo.referenceTracking", "false")
System.setProperty("spark.kryoserializer.buffer.mb", "8")
System.setProperty("spark.locality.wait", "10000")
val sc = new SparkContext(master, "ALS")
val ratings = sc.textFile(ratingsFile).map { line =>
val fields = line.split(',')
val fields = line.split("\\D{2}|\\s|,")
Rating(fields(0).toInt, fields(1).toInt, fields(2).toDouble)
}
val model = ALS.train(ratings, rank, iters, 0.01, blocks)
val model = new ALS(rank = rank, iterations = iters, lambda = lambda,
numBlocks = blocks, implicitPrefs = implicitPrefs, alpha = alpha).run(ratings)
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)
sc.stop()
}
}

View file

@ -19,6 +19,7 @@ package org.apache.spark.mllib.recommendation;
import java.io.Serializable;
import java.util.List;
import java.lang.Math;
import scala.Tuple2;
@ -48,7 +49,7 @@ public class JavaALSSuite implements Serializable {
}
void validatePrediction(MatrixFactorizationModel model, int users, int products, int features,
DoubleMatrix trueRatings, double matchThreshold) {
DoubleMatrix trueRatings, double matchThreshold, boolean implicitPrefs, DoubleMatrix truePrefs) {
DoubleMatrix predictedU = new DoubleMatrix(users, features);
List<scala.Tuple2<Object, double[]>> userFeatures = model.userFeatures().toJavaRDD().collect();
for (int i = 0; i < features; ++i) {
@ -68,12 +69,32 @@ public class JavaALSSuite implements Serializable {
DoubleMatrix predictedRatings = predictedU.mmul(predictedP.transpose());
for (int u = 0; u < users; ++u) {
for (int p = 0; p < products; ++p) {
double prediction = predictedRatings.get(u, p);
double correct = trueRatings.get(u, p);
Assert.assertTrue(Math.abs(prediction - correct) < matchThreshold);
if (!implicitPrefs) {
for (int u = 0; u < users; ++u) {
for (int p = 0; p < products; ++p) {
double prediction = predictedRatings.get(u, p);
double correct = trueRatings.get(u, p);
Assert.assertTrue(String.format("Prediction=%2.4f not below match threshold of %2.2f",
prediction, matchThreshold), Math.abs(prediction - correct) < matchThreshold);
}
}
} else {
// For implicit prefs we use the confidence-weighted RMSE to test (ref Mahout's implicit ALS tests)
double sqErr = 0.0;
double denom = 0.0;
for (int u = 0; u < users; ++u) {
for (int p = 0; p < products; ++p) {
double prediction = predictedRatings.get(u, p);
double truePref = truePrefs.get(u, p);
double confidence = 1.0 + /* alpha = */ 1.0 * trueRatings.get(u, p);
double err = confidence * (truePref - prediction) * (truePref - prediction);
sqErr += err;
denom += 1.0;
}
}
double rmse = Math.sqrt(sqErr / denom);
Assert.assertTrue(String.format("Confidence-weighted RMSE=%2.4f above threshold of %2.2f",
rmse, matchThreshold), Math.abs(rmse) < matchThreshold);
}
}
@ -83,12 +104,12 @@ public class JavaALSSuite implements Serializable {
int iterations = 15;
int users = 10;
int products = 10;
scala.Tuple2<List<Rating>, DoubleMatrix> testData = ALSSuite.generateRatingsAsJavaList(
users, products, features, 0.7);
scala.Tuple3<List<Rating>, DoubleMatrix, DoubleMatrix> testData = ALSSuite.generateRatingsAsJavaList(
users, products, features, 0.7, false);
JavaRDD<Rating> data = sc.parallelize(testData._1());
MatrixFactorizationModel model = ALS.train(data.rdd(), features, iterations);
validatePrediction(model, users, products, features, testData._2(), 0.3);
validatePrediction(model, users, products, features, testData._2(), 0.3, false, testData._3());
}
@Test
@ -97,14 +118,46 @@ public class JavaALSSuite implements Serializable {
int iterations = 15;
int users = 20;
int products = 30;
scala.Tuple2<List<Rating>, DoubleMatrix> testData = ALSSuite.generateRatingsAsJavaList(
users, products, features, 0.7);
scala.Tuple3<List<Rating>, DoubleMatrix, DoubleMatrix> testData = ALSSuite.generateRatingsAsJavaList(
users, products, features, 0.7, false);
JavaRDD<Rating> data = sc.parallelize(testData._1());
MatrixFactorizationModel model = new ALS().setRank(features)
.setIterations(iterations)
.run(data.rdd());
validatePrediction(model, users, products, features, testData._2(), 0.3);
validatePrediction(model, users, products, features, testData._2(), 0.3, false, testData._3());
}
@Test
public void runImplicitALSUsingStaticMethods() {
int features = 1;
int iterations = 15;
int users = 40;
int products = 80;
scala.Tuple3<List<Rating>, DoubleMatrix, DoubleMatrix> testData = ALSSuite.generateRatingsAsJavaList(
users, products, features, 0.7, true);
JavaRDD<Rating> data = sc.parallelize(testData._1());
MatrixFactorizationModel model = ALS.trainImplicit(data.rdd(), features, iterations);
validatePrediction(model, users, products, features, testData._2(), 0.4, true, testData._3());
}
@Test
public void runImplicitALSUsingConstructor() {
int features = 2;
int iterations = 15;
int users = 50;
int products = 100;
scala.Tuple3<List<Rating>, DoubleMatrix, DoubleMatrix> testData = ALSSuite.generateRatingsAsJavaList(
users, products, features, 0.7, true);
JavaRDD<Rating> data = sc.parallelize(testData._1());
MatrixFactorizationModel model = new ALS().setRank(features)
.setIterations(iterations)
.setImplicitPrefs(true)
.run(data.rdd());
validatePrediction(model, users, products, features, testData._2(), 0.4, true, testData._3());
}
}

View file

@ -34,16 +34,19 @@ object ALSSuite {
users: Int,
products: Int,
features: Int,
samplingRate: Double): (java.util.List[Rating], DoubleMatrix) = {
val (sampledRatings, trueRatings) = generateRatings(users, products, features, samplingRate)
(seqAsJavaList(sampledRatings), trueRatings)
samplingRate: Double,
implicitPrefs: Boolean): (java.util.List[Rating], DoubleMatrix, DoubleMatrix) = {
val (sampledRatings, trueRatings, truePrefs) =
generateRatings(users, products, features, samplingRate, implicitPrefs)
(seqAsJavaList(sampledRatings), trueRatings, truePrefs)
}
def generateRatings(
users: Int,
products: Int,
features: Int,
samplingRate: Double): (Seq[Rating], DoubleMatrix) = {
samplingRate: Double,
implicitPrefs: Boolean = false): (Seq[Rating], DoubleMatrix, DoubleMatrix) = {
val rand = new Random(42)
// Create a random matrix with uniform values from -1 to 1
@ -52,14 +55,20 @@ object ALSSuite {
val userMatrix = randomMatrix(users, features)
val productMatrix = randomMatrix(features, products)
val trueRatings = userMatrix.mmul(productMatrix)
val (trueRatings, truePrefs) = implicitPrefs match {
case true =>
val raw = new DoubleMatrix(users, products, Array.fill(users * products)(rand.nextInt(10).toDouble): _*)
val prefs = new DoubleMatrix(users, products, raw.data.map(v => if (v > 0) 1.0 else 0.0): _*)
(raw, prefs)
case false => (userMatrix.mmul(productMatrix), null)
}
val sampledRatings = {
for (u <- 0 until users; p <- 0 until products if rand.nextDouble() < samplingRate)
yield Rating(u, p, trueRatings.get(u, p))
}
(sampledRatings, trueRatings)
(sampledRatings, trueRatings, truePrefs)
}
}
@ -85,6 +94,14 @@ class ALSSuite extends FunSuite with BeforeAndAfterAll {
testALS(20, 30, 2, 15, 0.7, 0.3)
}
test("rank-1 matrices implicit") {
testALS(40, 80, 1, 15, 0.7, 0.4, true)
}
test("rank-2 matrices implicit") {
testALS(50, 100, 2, 15, 0.7, 0.4, true)
}
/**
* Test if we can correctly factorize R = U * P where U and P are of known rank.
*
@ -96,11 +113,14 @@ class ALSSuite extends FunSuite with BeforeAndAfterAll {
* @param matchThreshold max difference allowed to consider a predicted rating correct
*/
def testALS(users: Int, products: Int, features: Int, iterations: Int,
samplingRate: Double, matchThreshold: Double)
samplingRate: Double, matchThreshold: Double, implicitPrefs: Boolean = false)
{
val (sampledRatings, trueRatings) = ALSSuite.generateRatings(users, products,
features, samplingRate)
val model = ALS.train(sc.parallelize(sampledRatings), features, iterations)
val (sampledRatings, trueRatings, truePrefs) = ALSSuite.generateRatings(users, products,
features, samplingRate, implicitPrefs)
val model = implicitPrefs match {
case false => ALS.train(sc.parallelize(sampledRatings), features, iterations)
case true => ALS.trainImplicit(sc.parallelize(sampledRatings), features, iterations)
}
val predictedU = new DoubleMatrix(users, features)
for ((u, vec) <- model.userFeatures.collect(); i <- 0 until features) {
@ -112,12 +132,31 @@ class ALSSuite extends FunSuite with BeforeAndAfterAll {
}
val predictedRatings = predictedU.mmul(predictedP.transpose)
for (u <- 0 until users; p <- 0 until products) {
val prediction = predictedRatings.get(u, p)
val correct = trueRatings.get(u, p)
if (math.abs(prediction - correct) > matchThreshold) {
fail("Model failed to predict (%d, %d): %f vs %f\ncorr: %s\npred: %s\nU: %s\n P: %s".format(
u, p, correct, prediction, trueRatings, predictedRatings, predictedU, predictedP))
if (!implicitPrefs) {
for (u <- 0 until users; p <- 0 until products) {
val prediction = predictedRatings.get(u, p)
val correct = trueRatings.get(u, p)
if (math.abs(prediction - correct) > matchThreshold) {
fail("Model failed to predict (%d, %d): %f vs %f\ncorr: %s\npred: %s\nU: %s\n P: %s".format(
u, p, correct, prediction, trueRatings, predictedRatings, predictedU, predictedP))
}
}
} else {
// For implicit prefs we use the confidence-weighted RMSE to test (ref Mahout's tests)
var sqErr = 0.0
var denom = 0.0
for (u <- 0 until users; p <- 0 until products) {
val prediction = predictedRatings.get(u, p)
val truePref = truePrefs.get(u, p)
val confidence = 1 + 1.0 * trueRatings.get(u, p)
val err = confidence * (truePref - prediction) * (truePref - prediction)
sqErr += err
denom += 1
}
val rmse = math.sqrt(sqErr / denom)
if (math.abs(rmse) > matchThreshold) {
fail("Model failed to predict RMSE: %f\ncorr: %s\npred: %s\nU: %s\n P: %s".format(
rmse, truePrefs, predictedRatings, predictedU, predictedP))
}
}
}