Spark/Scala实现推荐系统中的相似度算法（欧几里得距离、皮尔逊相关系数、余弦相似度：附实现代码）

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

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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

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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

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/** 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

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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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