Spark ML包中的几种归一化方法总结

org.apache.spark.ml.feature包中包含了4种不同的归一化方法：

• Normalizer
• StandardScaler
• MinMaxScaler
• MaxAbsScaler

有时感觉会容易混淆，借助官方文档和实际数据的变换，在这里做一次总结。

原文地址：http://www.neilron.xyz/spark-ml-feature-scaler/

0 数据准备

import org.apache.spark.ml.linalg.Vectorsval dataFrame = spark.createDataFrame(Seq(  (0, Vectors.dense(1.0, 0.5, -1.0)),  (1, Vectors.dense(2.0, 1.0, 1.0)),  (2, Vectors.dense(4.0, 10.0, 2.0)))).toDF("id", "features")dataFrame.show// 原始数据+---+--------------+| id|      features|+---+--------------+|  0|[1.0,0.5,-1.0]||  1| [2.0,1.0,1.0]||  2|[4.0,10.0,2.0]|+---+--------------+

1 Normalizer

Normalizer的作用范围是每一行，使每一个行向量的范数变换为一个单位范数，下面的示例代码都来自spark官方文档加上少量改写和注释。

import org.apache.spark.ml.feature.Normalizer// 正则化每个向量到1阶范数val normalizer = new Normalizer()  .setInputCol("features")  .setOutputCol("normFeatures")  .setP(1.0)val l1NormData = normalizer.transform(dataFrame)println("Normalized using L^1 norm")l1NormData.show()// 将每一行的规整为1阶范数为1的向量，1阶范数即所有值绝对值之和。+---+--------------+------------------+| id|      features|      normFeatures|+---+--------------+------------------+|  0|[1.0,0.5,-1.0]|    [0.4,0.2,-0.4]||  1| [2.0,1.0,1.0]|   [0.5,0.25,0.25]||  2|[4.0,10.0,2.0]|[0.25,0.625,0.125]|+---+--------------+------------------+// 正则化每个向量到无穷阶范数val lInfNormData = normalizer.transform(dataFrame, normalizer.p -> Double.PositiveInfinity)println("Normalized using L^inf norm")lInfNormData.show()// 向量的无穷阶范数即向量中所有值中的最大值+---+--------------+--------------+| id|      features|  normFeatures|+---+--------------+--------------+|  0|[1.0,0.5,-1.0]|[1.0,0.5,-1.0]||  1| [2.0,1.0,1.0]| [1.0,0.5,0.5]||  2|[4.0,10.0,2.0]| [0.4,1.0,0.2]|+---+--------------+--------------+

2 StandardScaler

StandardScaler处理的对象是每一列，也就是每一维特征，将特征标准化为单位标准差或是0均值，或是0均值单位标准差。
主要有两个参数可以设置：
- withStd: 默认为真。将数据标准化到单位标准差。
- withMean: 默认为假。是否变换为0均值。

StandardScaler需要fit数据，获取每一维的均值和标准差，来缩放每一维特征。

import org.apache.spark.ml.feature.StandardScalerval scaler = new StandardScaler()  .setInputCol("features")  .setOutputCol("scaledFeatures")  .setWithStd(true)  .setWithMean(false)// Compute summary statistics by fitting the StandardScaler.val scalerModel = scaler.fit(dataFrame)// Normalize each feature to have unit standard deviation.val scaledData = scalerModel.transform(dataFrame)scaledData.show// 将每一列的标准差缩放到1。+---+--------------+------------------------------------------------------------+|id |features      |scaledFeatures                                              |+---+--------------+------------------------------------------------------------+|0  |[1.0,0.5,-1.0]|[0.6546536707079772,0.09352195295828244,-0.6546536707079771]||1  |[2.0,1.0,1.0] |[1.3093073414159544,0.1870439059165649,0.6546536707079771]  ||2  |[4.0,10.0,2.0]|[2.618614682831909,1.870439059165649,1.3093073414159542]    |+---+--------------+------------------------------------------------------------+

3 MinMaxScaler

MinMaxScaler作用同样是每一列，即每一维特征。将每一维特征线性地映射到指定的区间，通常是[0, 1]。
它也有两个参数可以设置：
- min: 默认为0。指定区间的下限。
- max: 默认为1。指定区间的上限。

import org.apache.spark.ml.feature.MinMaxScalerval scaler = new MinMaxScaler()  .setInputCol("features")  .setOutputCol("scaledFeatures")// Compute summary statistics and generate MinMaxScalerModelval scalerModel = scaler.fit(dataFrame)// rescale each feature to range [min, max].val scaledData = scalerModel.transform(dataFrame)println(s"Features scaled to range: [${scaler.getMin}, ${scaler.getMax}]")scaledData.select("features", "scaledFeatures").show// 每维特征线性地映射，最小值映射到0，最大值映射到1。+--------------+-----------------------------------------------------------+|features      |scaledFeatures                                             |+--------------+-----------------------------------------------------------+|[1.0,0.5,-1.0]|[0.0,0.0,0.0]                                              ||[2.0,1.0,1.0] |[0.3333333333333333,0.05263157894736842,0.6666666666666666]||[4.0,10.0,2.0]|[1.0,1.0,1.0]                                              |+--------------+-----------------------------------------------------------+

4 MaxAbsScaler

MaxAbsScaler将每一维的特征变换到[-1, 1]闭区间上，通过除以每一维特征上的最大的绝对值，它不会平移整个分布，也不会破坏原来每一个特征向量的稀疏性。

import org.apache.spark.ml.feature.MaxAbsScalerval scaler = new MaxAbsScaler()  .setInputCol("features")  .setOutputCol("scaledFeatures")// Compute summary statistics and generate MaxAbsScalerModelval scalerModel = scaler.fit(dataFrame)// rescale each feature to range [-1, 1]val scaledData = scalerModel.transform(dataFrame)scaledData.select("features", "scaledFeatures").show()// 每一维的绝对值的最大值为[4, 10, 2]+--------------+----------------+                                               |      features|  scaledFeatures|+--------------+----------------+|[1.0,0.5,-1.0]|[0.25,0.05,-0.5]|| [2.0,1.0,1.0]|   [0.5,0.1,0.5]||[4.0,10.0,2.0]|   [1.0,1.0,1.0]|+--------------+----------------+

总结

所有4种归一化方法都是线性的变换，当某一维特征上具有非线性的分布时，还需要配合其它的特征预处理方法。