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Spark实现推荐系统中的相似度算法

大数据学习与分享 大数据学习与分享 2022-07-09

在推荐系统中,协同过滤算法是应用较多的,具体又主要划分为基于用户和基于物品的协同过滤算法,核心点就是基于"一个人"或"一件物品",根据这个人或物品所具有的属性,比如对于人就是性别、年龄、工作、收入、喜好等,找出与这个人或物品相似的人或物,当然实际处理中参考的因子会复杂的多。

本篇文章不介绍相关数学概念,主要给出常用的相似度算法代码实现,并且同一算法有多种实现方式。
欧几里得距离
def euclidean2(v1: Vector, v2: Vector): Double = {    require(v1.size == v2.size, s"SimilarityAlgorithms:Vector dimensions do not match: Dim(v1)=${v1.size} and Dim(v2)" + s"=${v2.size}.")
val x = v1.toArray val y = v2.toArray
euclidean(x, y) }
def euclidean(x: Array[Double], y: Array[Double]): Double = {    require(x.length == y.length, s"SimilarityAlgorithms:Array length do not match: Len(x)=${x.length} and Len(y)" + s"=${y.length}.")
math.sqrt(x.zip(y).map(p => p._1 - p._2).map(d => d * d).sum) }   def euclidean(v1: Vector, v2: Vector): Double = {    val sqdist = Vectors.sqdist(v1, v2) math.sqrt(sqdist) }
皮尔逊相关系数
def pearsonCorrelationSimilarity(arr1: Array[Double], arr2: Array[Double]): Double = {    require(arr1.length == arr2.length, s"SimilarityAlgorithms:Array length do not match: Len(x)=${arr1.length} and Len(y)" + s"=${arr2.length}.")
val sum_vec1 = arr1.sum val sum_vec2 = arr2.sum
val square_sum_vec1 = arr1.map(x => x * x).sum val square_sum_vec2 = arr2.map(x => x * x).sum
val zipVec = arr1.zip(arr2)
val product = zipVec.map(x => x._1 * x._2).sum val numerator = product - (sum_vec1 * sum_vec2 / arr1.length)
val dominator = math.pow((square_sum_vec1 - math.pow(sum_vec1, 2) / arr1.length) * (square_sum_vec2 - math.pow(sum_vec2, 2) / arr2.length), 0.5)    if (dominator == 0) Double.NaN else numerator / (dominator * 1.0) }

余弦相似度

  /** jblas实现余弦相似度 */ def cosineSimilarity(v1: DoubleMatrix, v2: DoubleMatrix): Double = { require(x.length == y.length, s"SimilarityAlgorithms:Array length do not match: Len(v1)=${x.length} and Len(v2)" + s"=${y.length}.") v1.dot(v2) / (v1.norm2() * v2.norm2()) } def cosineSimilarity(v1: Vector, v2: Vector): Double = {    require(v1.size == v2.size, s"SimilarityAlgorithms:Vector dimensions do not match: Dim(v1)=${v1.size} and Dim(v2)" + s"=${v2.size}.")
    val x = v1.toArray val y = v2.toArray
cosineSimilarity(x, y) }
def cosineSimilarity(x: Array[Double], y: Array[Double]): Double = {    require(x.length == y.length, s"SimilarityAlgorithms:Array length do not match: Len(x)=${x.length} and Len(y)" + s"=${y.length}.")
    val member = x.zip(y).map(d => d._1 * d._2).sum val temp1 = math.sqrt(x.map(math.pow(_, 2)).sum) val temp2 = math.sqrt(y.map(math.pow(_, 2)).sum)
val denominator = temp1 * temp2    if (denominator == 0) Double.NaN else member / (denominator * 1.0) }

修正余弦相似度

def adjustedCosineSimJblas(x: DoubleMatrix, y: DoubleMatrix): Double = { require(x.length == y.length, s"SimilarityAlgorithms:DoubleMatrix length do not match: Len(x)=${x.length} and Len(y)" + s"=${y.length}.")
val avg = (x.sum() + y.sum()) / (x.length + y.length) val v1 = x.sub(avg) val v2 = y.sub(avg) v1.dot(v2) / (v1.norm2() * v2.norm2()) }
def adjustedCosineSimJblas(x: Array[Double], y: Array[Double]): Double = { require(x.length == y.length, s"SimilarityAlgorithms:Array length do not match: Len(x)=${x.length} and Len(y)" + s"=${y.length}.")
val v1 = new DoubleMatrix(x) val v2 = new DoubleMatrix(y)
adjustedCosineSimJblas(v1, v2) } def adjustedCosineSimilarity(v1: Vector, v2: Vector): Double = { require(v1.size == v2.size, s"SimilarityAlgorithms:Vector dimensions do not match: Dim(v1)=${v1.size} and Dim(v2)" + s"=${v2.size}.") val x = v1.toArray val y = v2.toArray
adjustedCosineSimilarity(x, y) }
def adjustedCosineSimilarity(x: Array[Double], y: Array[Double]): Double = { require(x.length == y.length, s"SimilarityAlgorithms:Array length do not match: Len(x)=${x.length} and Len(y)" + s"=${y.length}.")
val avg = (x.sum + y.sum) / (x.length + y.length)
    val member = x.map(_ - avg).zip(y.map(_ - avg)).map(d => d._1 * d._2).sum
val temp1 = math.sqrt(x.map(num => math.pow(num - avg, 2)).sum) val temp2 = math.sqrt(y.map(num => math.pow(num - avg, 2)).sum)
val denominator = temp1 * temp2 if (denominator == 0) Double.NaN else member / (denominator * 1.0) }

大家如果在实际业务处理中有相关需求,可以根据实际场景对上述代码进行优化或改造,当然很多算法框架提供的一些算法是对这些相似度算法的封装,底层还是依赖于这一套,也能帮助大家做更好的了解。比如Spark MLlib在KMeans算法实现中,底层对欧几里得距离的计算实现。

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