spark-shell：对包含user_id、sku_id1~sku_id16的数据集DataFrame进行SVD分解，对数据进行降维保留前5个奇异值信息，根据该用户已购买的商品分别与未购买的商品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，这是一个关于使用Spark进行SVD分解和商品推荐的问题，下面是解决方案：

首先，我们需要加载数据集DataFrame，并对其进行SVD分解，保留前5个奇异值信息。可以使用Spark的ml库中的SVD算法实现，代码如下：

import org.apache.spark.ml.feature.VectorAssembler
import org.apache.spark.ml.linalg.Vectors
import org.apache.spark.ml.recommendation.ALS
import org.apache.spark.ml.recommendation.ALS.Rating

// 加载数据集DataFrame
val df = spark.read.format("csv").option("header", "true").load("data.csv")

// 将数据集转化为Rating类型
val assembler = new VectorAssembler().setInputCols(Array("sku_id1", "sku_id2", "sku_id3", "sku_id4", "sku_id5", "sku_id6", "sku_id7", "sku_id8", "sku_id9", "sku_id10", "sku_id11", "sku_id12", "sku_id13", "sku_id14", "sku_id15", "sku_id16")).setOutputCol("features")
val ratings = assembler.transform(df).rdd.map(row => Rating(row.getInt(0), row.getInt(1), 1.0))

// 训练ALS模型并进行SVD分解，保留前5个奇异值信息
val rank = 5
val numIterations = 10
val als = new ALS().setRank(rank).setMaxIter(numIterations).setImplicitPrefs(true).setUserCol("user_id").setItemCol("sku_id").setRatingCol("rating")
val model = als.fit(ratings)
val userFactors = model.userFactors.select("id", "features").withColumnRenamed("id", "user_id")
val itemFactors = model.itemFactors.select("id", "features").withColumnRenamed("id", "sku_id")

接下来，我们需要计算用户已购买商品和未购买商品之间的余弦相似度，并求均值。代码如下：

import org.apache.spark.ml.feature.Normalizer
import org.apache.spark.sql.functions._

// 获取用户已购买的商品
val userPurchasedItems = df.select("user_id", "sku_id1", "sku_id2", "sku_id3", "sku_id4", "sku_id5", "sku_id6", "sku_id7", "sku_id8", "sku_id9", "sku_id10", "sku_id11", "sku_id12", "sku_id13", "sku_id14", "sku_id15", "sku_id16").where(col("user_id") === 1).collect()(0).toSeq.drop(1).map(_.asInstanceOf[Int])

// 获取用户未购买的商品
val userNotPurchasedItems = df.select("sku_id").distinct().as("a").join(df.select("user_id").where(col("user_id") === 1).as("b"), col("a.sku_id") === col("b.sku_id"), "leftanti").select("sku_id").rdd.map(row => row.getInt(0))

// 将用户已购买的商品和未购买的商品分别与商品向量进行内积计算余弦相似度
val userPurchasedItemsVector = itemFactors.where(col("sku_id").isin(userPurchasedItems: _*)).select("sku_id", "features").cache()
val userNotPurchasedItemsVector = itemFactors.where(col("sku_id").isin(userNotPurchasedItems: _*)).select("sku_id", "features").cache()
val norm = new Normalizer().setInputCol("features").setOutputCol("normFeatures")
val userPurchasedItemsNormVector = norm.transform(userPurchasedItemsVector).select("sku_id", "normFeatures").cache()
val userNotPurchasedItemsNormVector = norm.transform(userNotPurchasedItemsVector).select("sku_id", "normFeatures").cache()
val sim = userNotPurchasedItemsNormVector.crossJoin(userPurchasedItemsNormVector).withColumn("similarity", dot(col("normFeatures"), col("normFeatures_1"))).groupBy("sku_id").agg(avg("similarity").alias("similarity")).sort(desc("similarity"))

// 输出相似度最大的5件商品id
val recommendItems = sim.select("sku_id").limit(5).collect().map(row => row.getInt(0)).toSeq
println(recommendItems)

最后，我们将相似度最大的5件商品id输出作为推荐使用。代码如下：

// 输出相似度最大的5件商品id
val recommendItems = sim.select("sku_id").limit(5).collect().map(row => row.getInt(0)).toSeq
println(recommendItems)

这样，我们就完成了使用Spark进行SVD分解和商品推荐的任务。