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.Vectors
val 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.StandardScaler
val 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.MinMaxScaler
val scaler = new MinMaxScaler()
.setInputCol("features")
.setOutputCol("scaledFeatures")
// Compute summary statistics and generate MinMaxScalerModel
val 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.MaxAbsScaler
val scaler = new MaxAbsScaler()
.setInputCol("features")
.setOutputCol("scaledFeatures")
// Compute summary statistics and generate MaxAbsScalerModel
val 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。