spark-shell： 对DataFrame进行SVD分解，对数据进行降维保留前5个奇异值信息，计算用户已购买的商品分别与未购买的商品，根据计算结果计算余弦相似度再进行累加求均值，将均值最大的5件商品id进行输出作为推荐使用

好的，您的问题是关于Spark的DataFrame进行SVD分解和商品推荐的问题。首先，您需要导入Spark SQL和ML库：

import org.apache.spark.ml.linalg.{Matrix, SingularValueDecomposition, Vector, Vectors}
import org.apache.spark.ml.recommendation.ALS
import org.apache.spark.sql.functions.{col, expr}

接下来，您需要准备好您的数据，假设您有一个名为“purchaseHistory”的DataFrame，它包含用户ID、商品ID和购买数量：

val purchaseHistory = Seq((1, 101, 2), (1, 102, 1), (2, 101, 1), (2, 103, 3), (3, 102, 2), (3, 103, 1), (4, 101, 1), (4, 104, 4)).toDF("userId", "itemId", "purchaseCount")

然后，您可以使用ALS算法对数据进行训练，并生成一个名为“model”的模型：

val als = new ALS().setMaxIter(5).setRegParam(0.01).setUserCol("userId").setItemCol("itemId").setRatingCol("purchaseCount")
val model = als.fit(purchaseHistory)

接下来，您可以使用模型中的SVD分解来获取用户和商品的低维度表示：

val userFactors = model.userFactors
val itemFactors = model.itemFactors
val userMatrix = userFactors.select("features").rdd.map { case Row(v: Vector) => Vectors.dense(v.toArray) }.cache()
val itemMatrix = itemFactors.select("features").rdd.map { case Row(v: Vector) => Vectors.dense(v.toArray) }.cache()
val mat = new RowMatrix(itemMatrix)
val svd = mat.computeSVD(5, computeU = false)
val v = svd.V
val itemSingularValues = svd.s

现在，您可以计算每个用户和已购买商品之间的余弦相似度，并将它们加起来并求平均值：

val userItem = purchaseHistory.select("userId", "itemId")
val itemVectors = model.itemFactors.select("itemId", "features").as[(Int, Vector)].rdd.map { case (id, vec) => (id, vec) }.cache()
val userVectors = model.userFactors.select("userId", "features").as[(Int, Vector)].rdd.map { case (id, vec) => (id, vec) }.cache()

val joined = userItem.join(itemVectors).rdd.map { case (uid, iid, vec) => (uid, (iid, vec)) }
val userVecs = joined.join(userVectors).map { case (uid, ((iid, iVec), uVec)) => (uid, iVec, uVec) }

val cosineSim = userVecs.map { case (uid, iVec, uVec) =>
  val cosSim = Vectors.dot(iVec, uVec) / (Vectors.norm(iVec, 2) * Vectors.norm(uVec, 2))
  (uid, cosSim)
}.toDF("userId", "cosineSim")

val avgCosSim = cosineSim.groupBy("userId").agg(expr("avg(cosineSim) as avgCosineSim"))

最后，您可以找到每个用户购买过的商品，并计算它们与未购买商品的平均余弦相似度，然后找到均值最大的5件商品：

val userItems = purchaseHistory.select("userId", "itemId")
val allItems = model.itemFactors.select("itemId")
val itemsToRecommend = allItems.except(userItems.select("itemId"))
val userAndItemsToRecommend = itemsToRecommend.crossJoin(avgCosSim)

val itemVecs = itemVectors.collectAsMap()
val userVecs = userVectors.collectAsMap()

val recommended = userAndItemsToRecommend.rdd.map { case Row(iid: Int, uid: Int, avgCosineSim: Double) =>
  val iVec = itemVecs(iid)
  val uVec = userVecs(uid)
  val cosSim = Vectors.dot(iVec, uVec) / (Vectors.norm(iVec, 2) * Vectors.norm(uVec, 2))
  (iid, cosSim * avgCosineSim)
}.reduceByKey(_ + _).map { case (iid, score) => (score, iid) }.sortByKey(false).take(5).map { case (score, iid) => iid }

recommended.foreach(println)

以上代码将输出5个商品的ID，这些商品最有可能被用户购买并作为推荐商品。