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,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],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],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,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],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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