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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 org.apache.spark.ml.recommendation
import java.{util => ju}
import scala.collection.mutable
import scala.reflect.ClassTag
import scala.util.Sorting
import com.github.fommil.netlib.BLAS.{getInstance => blas}
import com.github.fommil.netlib.LAPACK.{getInstance => lapack}
import org.netlib.util.intW
import org.apache.spark.{HashPartitioner, Logging, Partitioner}
import org.apache.spark.annotation.DeveloperApi
import org.apache.spark.ml.{Estimator, Model}
import org.apache.spark.ml.param._
import org.apache.spark.rdd.RDD
import org.apache.spark.sql.DataFrame
import org.apache.spark.sql.Dsl._
import org.apache.spark.sql.types.{DoubleType, FloatType, IntegerType, StructField, StructType}
import org.apache.spark.util.Utils
import org.apache.spark.util.collection.{OpenHashMap, OpenHashSet, SortDataFormat, Sorter}
import org.apache.spark.util.random.XORShiftRandom
/**
* Common params for ALS.
*/
private[recommendation] trait ALSParams extends Params with HasMaxIter with HasRegParam
with HasPredictionCol {
/** Param for rank of the matrix factorization. */
val rank = new IntParam(this, "rank", "rank of the factorization", Some(10))
def getRank: Int = get(rank)
/** Param for number of user blocks. */
val numUserBlocks = new IntParam(this, "numUserBlocks", "number of user blocks", Some(10))
def getNumUserBlocks: Int = get(numUserBlocks)
/** Param for number of item blocks. */
val numItemBlocks =
new IntParam(this, "numItemBlocks", "number of item blocks", Some(10))
def getNumItemBlocks: Int = get(numItemBlocks)
/** Param to decide whether to use implicit preference. */
val implicitPrefs =
new BooleanParam(this, "implicitPrefs", "whether to use implicit preference", Some(false))
def getImplicitPrefs: Boolean = get(implicitPrefs)
/** Param for the alpha parameter in the implicit preference formulation. */
val alpha = new DoubleParam(this, "alpha", "alpha for implicit preference", Some(1.0))
def getAlpha: Double = get(alpha)
/** Param for the column name for user ids. */
val userCol = new Param[String](this, "userCol", "column name for user ids", Some("user"))
def getUserCol: String = get(userCol)
/** Param for the column name for item ids. */
val itemCol =
new Param[String](this, "itemCol", "column name for item ids", Some("item"))
def getItemCol: String = get(itemCol)
/** Param for the column name for ratings. */
val ratingCol = new Param[String](this, "ratingCol", "column name for ratings", Some("rating"))
def getRatingCol: String = get(ratingCol)
/**
* Validates and transforms the input schema.
* @param schema input schema
* @param paramMap extra params
* @return output schema
*/
protected def validateAndTransformSchema(schema: StructType, paramMap: ParamMap): StructType = {
val map = this.paramMap ++ paramMap
assert(schema(map(userCol)).dataType == IntegerType)
assert(schema(map(itemCol)).dataType== IntegerType)
val ratingType = schema(map(ratingCol)).dataType
assert(ratingType == FloatType || ratingType == DoubleType)
val predictionColName = map(predictionCol)
assert(!schema.fieldNames.contains(predictionColName),
s"Prediction column $predictionColName already exists.")
val newFields = schema.fields :+ StructField(map(predictionCol), FloatType, nullable = false)
StructType(newFields)
}
}
/**
* Model fitted by ALS.
*/
class ALSModel private[ml] (
override val parent: ALS,
override val fittingParamMap: ParamMap,
k: Int,
userFactors: RDD[(Int, Array[Float])],
itemFactors: RDD[(Int, Array[Float])])
extends Model[ALSModel] with ALSParams {
def setPredictionCol(value: String): this.type = set(predictionCol, value)
override def transform(dataset: DataFrame, paramMap: ParamMap): DataFrame = {
import dataset.sqlContext.createDataFrame
val map = this.paramMap ++ paramMap
val users = userFactors.toDataFrame("id", "features")
val items = itemFactors.toDataFrame("id", "features")
val predict: (Seq[Float], Seq[Float]) => Float = (userFeatures, itemFeatures) => {
if (userFeatures != null && itemFeatures != null) {
blas.sdot(k, userFeatures.toArray, 1, itemFeatures.toArray, 1)
} else {
Float.NaN
}
}
val inputColumns = dataset.schema.fieldNames
val prediction = callUDF(predict, users("features"), items("features")).as(map(predictionCol))
val outputColumns = inputColumns.map(f => dataset(f)) :+ prediction
dataset
.join(users, dataset(map(userCol)) === users("id"), "left")
.join(items, dataset(map(itemCol)) === items("id"), "left")
.select(outputColumns: _*)
// TODO: Just use a dataset("*")
// .select(dataset("*"), prediction)
}
override private[ml] def transformSchema(schema: StructType, paramMap: ParamMap): StructType = {
validateAndTransformSchema(schema, paramMap)
}
}
/**
* Alternating Least Squares (ALS) matrix factorization.
*
* ALS attempts to estimate the ratings matrix `R` as the product of two lower-rank matrices,
* `X` and `Y`, i.e. `X * Yt = 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
* product blocks that need that user's feature vector. This is achieved by pre-computing 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.
*
* For implicit preference data, the algorithm used is based on
* "Collaborative Filtering for Implicit Feedback Datasets", available at
* [[http://dx.doi.org/10.1109/ICDM.2008.22]], 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 extends Estimator[ALSModel] with ALSParams {
import org.apache.spark.ml.recommendation.ALS.Rating
def setRank(value: Int): this.type = set(rank, value)
def setNumUserBlocks(value: Int): this.type = set(numUserBlocks, value)
def setNumItemBlocks(value: Int): this.type = set(numItemBlocks, value)
def setImplicitPrefs(value: Boolean): this.type = set(implicitPrefs, value)
def setAlpha(value: Double): this.type = set(alpha, value)
def setUserCol(value: String): this.type = set(userCol, value)
def setItemCol(value: String): this.type = set(itemCol, value)
def setRatingCol(value: String): this.type = set(ratingCol, value)
def setPredictionCol(value: String): this.type = set(predictionCol, value)
def setMaxIter(value: Int): this.type = set(maxIter, value)
def setRegParam(value: Double): this.type = set(regParam, value)
/** Sets both numUserBlocks and numItemBlocks to the specific value. */
def setNumBlocks(value: Int): this.type = {
setNumUserBlocks(value)
setNumItemBlocks(value)
this
}
setMaxIter(20)
setRegParam(1.0)
override def fit(dataset: DataFrame, paramMap: ParamMap): ALSModel = {
val map = this.paramMap ++ paramMap
val ratings = dataset
.select(col(map(userCol)), col(map(itemCol)), col(map(ratingCol)).cast(FloatType))
.map { row =>
Rating(row.getInt(0), row.getInt(1), row.getFloat(2))
}
val (userFactors, itemFactors) = ALS.train(ratings, rank = map(rank),
numUserBlocks = map(numUserBlocks), numItemBlocks = map(numItemBlocks),
maxIter = map(maxIter), regParam = map(regParam), implicitPrefs = map(implicitPrefs),
alpha = map(alpha))
val model = new ALSModel(this, map, map(rank), userFactors, itemFactors)
Params.inheritValues(map, this, model)
model
}
override private[ml] def transformSchema(schema: StructType, paramMap: ParamMap): StructType = {
validateAndTransformSchema(schema, paramMap)
}
}
/**
* :: DeveloperApi ::
* An implementation of ALS that supports generic ID types, specialized for Int and Long. This is
* exposed as a developer API for users who do need other ID types. But it is not recommended
* because it increases the shuffle size and memory requirement during training. For simplicity,
* users and items must have the same type. The number of distinct users/items should be smaller
* than 2 billion.
*/
@DeveloperApi
object ALS extends Logging {
/** Rating class for better code readability. */
case class Rating[@specialized(Int, Long) ID](user: ID, item: ID, rating: Float)
/** Cholesky solver for least square problems. */
private[recommendation] class CholeskySolver {
private val upper = "U"
private val info = new intW(0)
/**
* Solves a least squares problem with L2 regularization:
*
* min norm(A x - b)^2^ + lambda * n * norm(x)^2^
*
* @param ne a [[NormalEquation]] instance that contains AtA, Atb, and n (number of instances)
* @param lambda regularization constant, which will be scaled by n
* @return the solution x
*/
def solve(ne: NormalEquation, lambda: Double): Array[Float] = {
val k = ne.k
// Add scaled lambda to the diagonals of AtA.
val scaledlambda = lambda * ne.n
var i = 0
var j = 2
while (i < ne.triK) {
ne.ata(i) += scaledlambda
i += j
j += 1
}
lapack.dppsv(upper, k, 1, ne.ata, ne.atb, k, info)
val code = info.`val`
assert(code == 0, s"lapack.dppsv returned $code.")
val x = new Array[Float](k)
i = 0
while (i < k) {
x(i) = ne.atb(i).toFloat
i += 1
}
ne.reset()
x
}
}
/** Representing a normal equation (ALS' subproblem). */
private[recommendation] class NormalEquation(val k: Int) extends Serializable {
/** Number of entries in the upper triangular part of a k-by-k matrix. */
val triK = k * (k + 1) / 2
/** A^T^ * A */
val ata = new Array[Double](triK)
/** A^T^ * b */
val atb = new Array[Double](k)
/** Number of observations. */
var n = 0
private val da = new Array[Double](k)
private val upper = "U"
private def copyToDouble(a: Array[Float]): Unit = {
var i = 0
while (i < k) {
da(i) = a(i)
i += 1
}
}
/** Adds an observation. */
def add(a: Array[Float], b: Float): this.type = {
require(a.length == k)
copyToDouble(a)
blas.dspr(upper, k, 1.0, da, 1, ata)
blas.daxpy(k, b.toDouble, da, 1, atb, 1)
n += 1
this
}
/**
* Adds an observation with implicit feedback. Note that this does not increment the counter.
*/
def addImplicit(a: Array[Float], b: Float, alpha: Double): this.type = {
require(a.length == k)
// Extension to the original paper to handle b < 0. confidence is a function of |b| instead
// so that it is never negative.
val confidence = 1.0 + alpha * math.abs(b)
copyToDouble(a)
blas.dspr(upper, k, confidence - 1.0, da, 1, ata)
// For b <= 0, the corresponding preference is 0. So the term below is only added for b > 0.
if (b > 0) {
blas.daxpy(k, confidence, da, 1, atb, 1)
}
this
}
/** Merges another normal equation object. */
def merge(other: NormalEquation): this.type = {
require(other.k == k)
blas.daxpy(ata.length, 1.0, other.ata, 1, ata, 1)
blas.daxpy(atb.length, 1.0, other.atb, 1, atb, 1)
n += other.n
this
}
/** Resets everything to zero, which should be called after each solve. */
def reset(): Unit = {
ju.Arrays.fill(ata, 0.0)
ju.Arrays.fill(atb, 0.0)
n = 0
}
}
/**
* Implementation of the ALS algorithm.
*/
def train[ID: ClassTag](
ratings: RDD[Rating[ID]],
rank: Int = 10,
numUserBlocks: Int = 10,
numItemBlocks: Int = 10,
maxIter: Int = 10,
regParam: Double = 1.0,
implicitPrefs: Boolean = false,
alpha: Double = 1.0)(
implicit ord: Ordering[ID]): (RDD[(ID, Array[Float])], RDD[(ID, Array[Float])]) = {
val userPart = new HashPartitioner(numUserBlocks)
val itemPart = new HashPartitioner(numItemBlocks)
val userLocalIndexEncoder = new LocalIndexEncoder(userPart.numPartitions)
val itemLocalIndexEncoder = new LocalIndexEncoder(itemPart.numPartitions)
val blockRatings = partitionRatings(ratings, userPart, itemPart).cache()
val (userInBlocks, userOutBlocks) = makeBlocks("user", blockRatings, userPart, itemPart)
// materialize blockRatings and user blocks
userOutBlocks.count()
val swappedBlockRatings = blockRatings.map {
case ((userBlockId, itemBlockId), RatingBlock(userIds, itemIds, localRatings)) =>
((itemBlockId, userBlockId), RatingBlock(itemIds, userIds, localRatings))
}
val (itemInBlocks, itemOutBlocks) = makeBlocks("item", swappedBlockRatings, itemPart, userPart)
// materialize item blocks
itemOutBlocks.count()
var userFactors = initialize(userInBlocks, rank)
var itemFactors = initialize(itemInBlocks, rank)
if (implicitPrefs) {
for (iter <- 1 to maxIter) {
userFactors.setName(s"userFactors-$iter").persist()
val previousItemFactors = itemFactors
itemFactors = computeFactors(userFactors, userOutBlocks, itemInBlocks, rank, regParam,
userLocalIndexEncoder, implicitPrefs, alpha)
previousItemFactors.unpersist()
itemFactors.setName(s"itemFactors-$iter").persist()
val previousUserFactors = userFactors
userFactors = computeFactors(itemFactors, itemOutBlocks, userInBlocks, rank, regParam,
itemLocalIndexEncoder, implicitPrefs, alpha)
previousUserFactors.unpersist()
}
} else {
for (iter <- 0 until maxIter) {
itemFactors = computeFactors(userFactors, userOutBlocks, itemInBlocks, rank, regParam,
userLocalIndexEncoder)
userFactors = computeFactors(itemFactors, itemOutBlocks, userInBlocks, rank, regParam,
itemLocalIndexEncoder)
}
}
val userIdAndFactors = userInBlocks
.mapValues(_.srcIds)
.join(userFactors)
.values
.setName("userFactors")
.cache()
userIdAndFactors.count()
itemFactors.unpersist()
val itemIdAndFactors = itemInBlocks
.mapValues(_.srcIds)
.join(itemFactors)
.values
.setName("itemFactors")
.cache()
itemIdAndFactors.count()
userInBlocks.unpersist()
userOutBlocks.unpersist()
itemInBlocks.unpersist()
itemOutBlocks.unpersist()
blockRatings.unpersist()
val userOutput = userIdAndFactors.flatMap { case (ids, factors) =>
ids.view.zip(factors)
}
val itemOutput = itemIdAndFactors.flatMap { case (ids, factors) =>
ids.view.zip(factors)
}
(userOutput, itemOutput)
}
/**
* Factor block that stores factors (Array[Float]) in an Array.
*/
private type FactorBlock = Array[Array[Float]]
/**
* Out-link block that stores, for each dst (item/user) block, which src (user/item) factors to
* send. For example, outLinkBlock(0) contains the local indices (not the original src IDs) of the
* src factors in this block to send to dst block 0.
*/
private type OutBlock = Array[Array[Int]]
/**
* In-link block for computing src (user/item) factors. This includes the original src IDs
* of the elements within this block as well as encoded dst (item/user) indices and corresponding
* ratings. The dst indices are in the form of (blockId, localIndex), which are not the original
* dst IDs. To compute src factors, we expect receiving dst factors that match the dst indices.
* For example, if we have an in-link record
*
* {srcId: 0, dstBlockId: 2, dstLocalIndex: 3, rating: 5.0},
*
* and assume that the dst factors are stored as dstFactors: Map[Int, Array[Array[Float]]], which
* is a blockId to dst factors map, the corresponding dst factor of the record is dstFactor(2)(3).
*
* We use a CSC-like (compressed sparse column) format to store the in-link information. So we can
* compute src factors one after another using only one normal equation instance.
*
* @param srcIds src ids (ordered)
* @param dstPtrs dst pointers. Elements in range [dstPtrs(i), dstPtrs(i+1)) of dst indices and
* ratings are associated with srcIds(i).
* @param dstEncodedIndices encoded dst indices
* @param ratings ratings
*
* @see [[LocalIndexEncoder]]
*/
private[recommendation] case class InBlock[@specialized(Int, Long) ID: ClassTag](
srcIds: Array[ID],
dstPtrs: Array[Int],
dstEncodedIndices: Array[Int],
ratings: Array[Float]) {
/** Size of the block. */
def size: Int = ratings.length
require(dstEncodedIndices.length == size)
require(dstPtrs.length == srcIds.length + 1)
}
/**
* Initializes factors randomly given the in-link blocks.
*
* @param inBlocks in-link blocks
* @param rank rank
* @return initialized factor blocks
*/
private def initialize[ID](
inBlocks: RDD[(Int, InBlock[ID])],
rank: Int): 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.map { case (srcBlockId, inBlock) =>
val random = new XORShiftRandom(srcBlockId)
val factors = Array.fill(inBlock.srcIds.length) {
val factor = Array.fill(rank)(random.nextGaussian().toFloat)
val nrm = blas.snrm2(rank, factor, 1)
blas.sscal(rank, 1.0f / nrm, factor, 1)
factor
}
(srcBlockId, factors)
}
}
/**
* A rating block that contains src IDs, dst IDs, and ratings, stored in primitive arrays.
*/
private[recommendation] case class RatingBlock[@specialized(Int, Long) ID: ClassTag](
srcIds: Array[ID],
dstIds: Array[ID],
ratings: Array[Float]) {
/** Size of the block. */
def size: Int = srcIds.length
require(dstIds.length == srcIds.length)
require(ratings.length == srcIds.length)
}
/**
* Builder for [[RatingBlock]]. [[mutable.ArrayBuilder]] is used to avoid boxing/unboxing.
*/
private[recommendation] class RatingBlockBuilder[@specialized(Int, Long) ID: ClassTag]
extends Serializable {
private val srcIds = mutable.ArrayBuilder.make[ID]
private val dstIds = mutable.ArrayBuilder.make[ID]
private val ratings = mutable.ArrayBuilder.make[Float]
var size = 0
/** Adds a rating. */
def add(r: Rating[ID]): this.type = {
size += 1
srcIds += r.user
dstIds += r.item
ratings += r.rating
this
}
/** Merges another [[RatingBlockBuilder]]. */
def merge(other: RatingBlock[ID]): this.type = {
size += other.srcIds.length
srcIds ++= other.srcIds
dstIds ++= other.dstIds
ratings ++= other.ratings
this
}
/** Builds a [[RatingBlock]]. */
def build(): RatingBlock[ID] = {
RatingBlock[ID](srcIds.result(), dstIds.result(), ratings.result())
}
}
/**
* Partitions raw ratings into blocks.
*
* @param ratings raw ratings
* @param srcPart partitioner for src IDs
* @param dstPart partitioner for dst IDs
*
* @return an RDD of rating blocks in the form of ((srcBlockId, dstBlockId), ratingBlock)
*/
private def partitionRatings[ID: ClassTag](
ratings: RDD[Rating[ID]],
srcPart: Partitioner,
dstPart: Partitioner): RDD[((Int, Int), RatingBlock[ID])] = {
/* The implementation produces the same result as the following but generates less objects.
ratings.map { r =>
((srcPart.getPartition(r.user), dstPart.getPartition(r.item)), r)
}.aggregateByKey(new RatingBlockBuilder)(
seqOp = (b, r) => b.add(r),
combOp = (b0, b1) => b0.merge(b1.build()))
.mapValues(_.build())
*/
val numPartitions = srcPart.numPartitions * dstPart.numPartitions
ratings.mapPartitions { iter =>
val builders = Array.fill(numPartitions)(new RatingBlockBuilder[ID])
iter.flatMap { r =>
val srcBlockId = srcPart.getPartition(r.user)
val dstBlockId = dstPart.getPartition(r.item)
val idx = srcBlockId + srcPart.numPartitions * dstBlockId
val builder = builders(idx)
builder.add(r)
if (builder.size >= 2048) { // 2048 * (3 * 4) = 24k
builders(idx) = new RatingBlockBuilder
Iterator.single(((srcBlockId, dstBlockId), builder.build()))
} else {
Iterator.empty
}
} ++ {
builders.view.zipWithIndex.filter(_._1.size > 0).map { case (block, idx) =>
val srcBlockId = idx % srcPart.numPartitions
val dstBlockId = idx / srcPart.numPartitions
((srcBlockId, dstBlockId), block.build())
}
}
}.groupByKey().mapValues { blocks =>
val builder = new RatingBlockBuilder[ID]
blocks.foreach(builder.merge)
builder.build()
}.setName("ratingBlocks")
}
/**
* Builder for uncompressed in-blocks of (srcId, dstEncodedIndex, rating) tuples.
* @param encoder encoder for dst indices
*/
private[recommendation] class UncompressedInBlockBuilder[@specialized(Int, Long) ID: ClassTag](
encoder: LocalIndexEncoder)(
implicit ord: Ordering[ID]) {
private val srcIds = mutable.ArrayBuilder.make[ID]
private val dstEncodedIndices = mutable.ArrayBuilder.make[Int]
private val ratings = mutable.ArrayBuilder.make[Float]
/**
* Adds a dst block of (srcId, dstLocalIndex, rating) tuples.
*
* @param dstBlockId dst block ID
* @param srcIds original src IDs
* @param dstLocalIndices dst local indices
* @param ratings ratings
*/
def add(
dstBlockId: Int,
srcIds: Array[ID],
dstLocalIndices: Array[Int],
ratings: Array[Float]): this.type = {
val sz = srcIds.length
require(dstLocalIndices.length == sz)
require(ratings.length == sz)
this.srcIds ++= srcIds
this.ratings ++= ratings
var j = 0
while (j < sz) {
this.dstEncodedIndices += encoder.encode(dstBlockId, dstLocalIndices(j))
j += 1
}
this
}
/** Builds a [[UncompressedInBlock]]. */
def build(): UncompressedInBlock[ID] = {
new UncompressedInBlock(srcIds.result(), dstEncodedIndices.result(), ratings.result())
}
}
/**
* A block of (srcId, dstEncodedIndex, rating) tuples stored in primitive arrays.
*/
private[recommendation] class UncompressedInBlock[@specialized(Int, Long) ID: ClassTag](
val srcIds: Array[ID],
val dstEncodedIndices: Array[Int],
val ratings: Array[Float])(
implicit ord: Ordering[ID]) {
/** Size the of block. */
def length: Int = srcIds.length
/**
* Compresses the block into an [[InBlock]]. The algorithm is the same as converting a
* sparse matrix from coordinate list (COO) format into compressed sparse column (CSC) format.
* Sorting is done using Spark's built-in Timsort to avoid generating too many objects.
*/
def compress(): InBlock[ID] = {
val sz = length
assert(sz > 0, "Empty in-link block should not exist.")
sort()
val uniqueSrcIdsBuilder = mutable.ArrayBuilder.make[ID]
val dstCountsBuilder = mutable.ArrayBuilder.make[Int]
var preSrcId = srcIds(0)
uniqueSrcIdsBuilder += preSrcId
var curCount = 1
var i = 1
var j = 0
while (i < sz) {
val srcId = srcIds(i)
if (srcId != preSrcId) {
uniqueSrcIdsBuilder += srcId
dstCountsBuilder += curCount
preSrcId = srcId
j += 1
curCount = 0
}
curCount += 1
i += 1
}
dstCountsBuilder += curCount
val uniqueSrcIds = uniqueSrcIdsBuilder.result()
val numUniqueSrdIds = uniqueSrcIds.length
val dstCounts = dstCountsBuilder.result()
val dstPtrs = new Array[Int](numUniqueSrdIds + 1)
var sum = 0
i = 0
while (i < numUniqueSrdIds) {
sum += dstCounts(i)
i += 1
dstPtrs(i) = sum
}
InBlock(uniqueSrcIds, dstPtrs, dstEncodedIndices, ratings)
}
private def sort(): Unit = {
val sz = length
// Since there might be interleaved log messages, we insert a unique id for easy pairing.
val sortId = Utils.random.nextInt()
logDebug(s"Start sorting an uncompressed in-block of size $sz. (sortId = $sortId)")
val start = System.nanoTime()
val sorter = new Sorter(new UncompressedInBlockSort[ID])
sorter.sort(this, 0, length, Ordering[KeyWrapper[ID]])
val duration = (System.nanoTime() - start) / 1e9
logDebug(s"Sorting took $duration seconds. (sortId = $sortId)")
}
}
/**
* A wrapper that holds a primitive key.
*
* @see [[UncompressedInBlockSort]]
*/
private class KeyWrapper[@specialized(Int, Long) ID: ClassTag](
implicit ord: Ordering[ID]) extends Ordered[KeyWrapper[ID]] {
var key: ID = _
override def compare(that: KeyWrapper[ID]): Int = {
ord.compare(key, that.key)
}
def setKey(key: ID): this.type = {
this.key = key
this
}
}
/**
* [[SortDataFormat]] of [[UncompressedInBlock]] used by [[Sorter]].
*/
private class UncompressedInBlockSort[@specialized(Int, Long) ID: ClassTag](
implicit ord: Ordering[ID])
extends SortDataFormat[KeyWrapper[ID], UncompressedInBlock[ID]] {
override def newKey(): KeyWrapper[ID] = new KeyWrapper()
override def getKey(
data: UncompressedInBlock[ID],
pos: Int,
reuse: KeyWrapper[ID]): KeyWrapper[ID] = {
if (reuse == null) {
new KeyWrapper().setKey(data.srcIds(pos))
} else {
reuse.setKey(data.srcIds(pos))
}
}
override def getKey(
data: UncompressedInBlock[ID],
pos: Int): KeyWrapper[ID] = {
getKey(data, pos, null)
}
private def swapElements[@specialized(Int, Float) T](
data: Array[T],
pos0: Int,
pos1: Int): Unit = {
val tmp = data(pos0)
data(pos0) = data(pos1)
data(pos1) = tmp
}
override def swap(data: UncompressedInBlock[ID], pos0: Int, pos1: Int): Unit = {
swapElements(data.srcIds, pos0, pos1)
swapElements(data.dstEncodedIndices, pos0, pos1)
swapElements(data.ratings, pos0, pos1)
}
override def copyRange(
src: UncompressedInBlock[ID],
srcPos: Int,
dst: UncompressedInBlock[ID],
dstPos: Int,
length: Int): Unit = {
System.arraycopy(src.srcIds, srcPos, dst.srcIds, dstPos, length)
System.arraycopy(src.dstEncodedIndices, srcPos, dst.dstEncodedIndices, dstPos, length)
System.arraycopy(src.ratings, srcPos, dst.ratings, dstPos, length)
}
override def allocate(length: Int): UncompressedInBlock[ID] = {
new UncompressedInBlock(
new Array[ID](length), new Array[Int](length), new Array[Float](length))
}
override def copyElement(
src: UncompressedInBlock[ID],
srcPos: Int,
dst: UncompressedInBlock[ID],
dstPos: Int): Unit = {
dst.srcIds(dstPos) = src.srcIds(srcPos)
dst.dstEncodedIndices(dstPos) = src.dstEncodedIndices(srcPos)
dst.ratings(dstPos) = src.ratings(srcPos)
}
}
/**
* Creates in-blocks and out-blocks from rating blocks.
* @param prefix prefix for in/out-block names
* @param ratingBlocks rating blocks
* @param srcPart partitioner for src IDs
* @param dstPart partitioner for dst IDs
* @return (in-blocks, out-blocks)
*/
private def makeBlocks[ID: ClassTag](
prefix: String,
ratingBlocks: RDD[((Int, Int), RatingBlock[ID])],
srcPart: Partitioner,
dstPart: Partitioner)(
implicit srcOrd: Ordering[ID]): (RDD[(Int, InBlock[ID])], RDD[(Int, OutBlock)]) = {
val inBlocks = ratingBlocks.map {
case ((srcBlockId, dstBlockId), RatingBlock(srcIds, dstIds, ratings)) =>
// The implementation is a faster version of
// val dstIdToLocalIndex = dstIds.toSet.toSeq.sorted.zipWithIndex.toMap
val start = System.nanoTime()
val dstIdSet = new OpenHashSet[ID](1 << 20)
dstIds.foreach(dstIdSet.add)
val sortedDstIds = new Array[ID](dstIdSet.size)
var i = 0
var pos = dstIdSet.nextPos(0)
while (pos != -1) {
sortedDstIds(i) = dstIdSet.getValue(pos)
pos = dstIdSet.nextPos(pos + 1)
i += 1
}
assert(i == dstIdSet.size)
Sorting.quickSort(sortedDstIds)
val dstIdToLocalIndex = new OpenHashMap[ID, Int](sortedDstIds.length)
i = 0
while (i < sortedDstIds.length) {
dstIdToLocalIndex.update(sortedDstIds(i), i)
i += 1
}
logDebug(
"Converting to local indices took " + (System.nanoTime() - start) / 1e9 + " seconds.")
val dstLocalIndices = dstIds.map(dstIdToLocalIndex.apply)
(srcBlockId, (dstBlockId, srcIds, dstLocalIndices, ratings))
}.groupByKey(new HashPartitioner(srcPart.numPartitions))
.mapValues { iter =>
val builder =
new UncompressedInBlockBuilder[ID](new LocalIndexEncoder(dstPart.numPartitions))
iter.foreach { case (dstBlockId, srcIds, dstLocalIndices, ratings) =>
builder.add(dstBlockId, srcIds, dstLocalIndices, ratings)
}
builder.build().compress()
}.setName(prefix + "InBlocks").cache()
val outBlocks = inBlocks.mapValues { case InBlock(srcIds, dstPtrs, dstEncodedIndices, _) =>
val encoder = new LocalIndexEncoder(dstPart.numPartitions)
val activeIds = Array.fill(dstPart.numPartitions)(mutable.ArrayBuilder.make[Int])
var i = 0
val seen = new Array[Boolean](dstPart.numPartitions)
while (i < srcIds.length) {
var j = dstPtrs(i)
ju.Arrays.fill(seen, false)
while (j < dstPtrs(i + 1)) {
val dstBlockId = encoder.blockId(dstEncodedIndices(j))
if (!seen(dstBlockId)) {
activeIds(dstBlockId) += i // add the local index in this out-block
seen(dstBlockId) = true
}
j += 1
}
i += 1
}
activeIds.map { x =>
x.result()
}
}.setName(prefix + "OutBlocks").cache()
(inBlocks, outBlocks)
}
/**
* Compute dst factors by constructing and solving least square problems.
*
* @param srcFactorBlocks src factors
* @param srcOutBlocks src out-blocks
* @param dstInBlocks dst in-blocks
* @param rank rank
* @param regParam regularization constant
* @param srcEncoder encoder for src local indices
* @param implicitPrefs whether to use implicit preference
* @param alpha the alpha constant in the implicit preference formulation
*
* @return dst factors
*/
private def computeFactors[ID](
srcFactorBlocks: RDD[(Int, FactorBlock)],
srcOutBlocks: RDD[(Int, OutBlock)],
dstInBlocks: RDD[(Int, InBlock[ID])],
rank: Int,
regParam: Double,
srcEncoder: LocalIndexEncoder,
implicitPrefs: Boolean = false,
alpha: Double = 1.0): RDD[(Int, FactorBlock)] = {
val numSrcBlocks = srcFactorBlocks.partitions.length
val YtY = if (implicitPrefs) Some(computeYtY(srcFactorBlocks, rank)) else None
val srcOut = srcOutBlocks.join(srcFactorBlocks).flatMap {
case (srcBlockId, (srcOutBlock, srcFactors)) =>
srcOutBlock.view.zipWithIndex.map { case (activeIndices, dstBlockId) =>
(dstBlockId, (srcBlockId, activeIndices.map(idx => srcFactors(idx))))
}
}
val merged = srcOut.groupByKey(new HashPartitioner(dstInBlocks.partitions.length))
dstInBlocks.join(merged).mapValues {
case (InBlock(dstIds, srcPtrs, srcEncodedIndices, ratings), srcFactors) =>
val sortedSrcFactors = new Array[FactorBlock](numSrcBlocks)
srcFactors.foreach { case (srcBlockId, factors) =>
sortedSrcFactors(srcBlockId) = factors
}
val dstFactors = new Array[Array[Float]](dstIds.length)
var j = 0
val ls = new NormalEquation(rank)
val solver = new CholeskySolver // TODO: add NNLS solver
while (j < dstIds.length) {
ls.reset()
if (implicitPrefs) {
ls.merge(YtY.get)
}
var i = srcPtrs(j)
while (i < srcPtrs(j + 1)) {
val encoded = srcEncodedIndices(i)
val blockId = srcEncoder.blockId(encoded)
val localIndex = srcEncoder.localIndex(encoded)
val srcFactor = sortedSrcFactors(blockId)(localIndex)
val rating = ratings(i)
if (implicitPrefs) {
ls.addImplicit(srcFactor, rating, alpha)
} else {
ls.add(srcFactor, rating)
}
i += 1
}
dstFactors(j) = solver.solve(ls, regParam)
j += 1
}
dstFactors
}
}
/**
* Computes the Gramian matrix of user or item factors, which is only used in implicit preference.
* Caching of the input factors is handled in [[ALS#train]].
*/
private def computeYtY(factorBlocks: RDD[(Int, FactorBlock)], rank: Int): NormalEquation = {
factorBlocks.values.aggregate(new NormalEquation(rank))(
seqOp = (ne, factors) => {
factors.foreach(ne.add(_, 0.0f))
ne
},
combOp = (ne1, ne2) => ne1.merge(ne2))
}
/**
* Encoder for storing (blockId, localIndex) into a single integer.
*
* We use the leading bits (including the sign bit) to store the block id and the rest to store
* the local index. This is based on the assumption that users/items are approximately evenly
* partitioned. With this assumption, we should be able to encode two billion distinct values.
*
* @param numBlocks number of blocks
*/
private[recommendation] class LocalIndexEncoder(numBlocks: Int) extends Serializable {
require(numBlocks > 0, s"numBlocks must be positive but found $numBlocks.")
private[this] final val numLocalIndexBits =
math.min(java.lang.Integer.numberOfLeadingZeros(numBlocks - 1), 31)
private[this] final val localIndexMask = (1 << numLocalIndexBits) - 1
/** Encodes a (blockId, localIndex) into a single integer. */
def encode(blockId: Int, localIndex: Int): Int = {
require(blockId < numBlocks)
require((localIndex & ~localIndexMask) == 0)
(blockId << numLocalIndexBits) | localIndex
}
/** Gets the block id from an encoded index. */
@inline
def blockId(encoded: Int): Int = {
encoded >>> numLocalIndexBits
}
/** Gets the local index from an encoded index. */
@inline
def localIndex(encoded: Int): Int = {
encoded & localIndexMask
}
}
}
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