org.apache.spark.ml.feature包中包含了4種不同的歸一化方法：
- Normalizer
- StandardScaler
- MinMaxScaler
- MaxAbsScaler
有時感覺會容易混淆，藉助官方文檔和實際數據的變換，在這裏做一次總結。
原文地址：http://www.neilron.xyz/spark-ml-feature-scaler/
0 數據準備
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
// 原始數據
+---+--------------+
| 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的作用範圍是每一行，使每一個行向量的範數變換爲一個單位範數，下面的示例代碼都來自spark官方文檔加上少量改寫和註釋。
import org.apache.spark.ml.feature.Normalizer
// 正則化每個向量到1階範數
val normalizer = new Normalizer()
.setInputCol("features")
.setOutputCol("normFeatures")
.setP(1.0)
val l1NormData = normalizer.transform(dataFrame)
println("Normalized using L^1 norm")
l1NormData.show()
// 將每一行的規整爲1階範數爲1的向量，1階範數即所有值絕對值之和。
+---+--------------+------------------+
| 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]|
+---+--------------+------------------+
// 正則化每個向量到無窮階範數
val lInfNormData = normalizer.transform(dataFrame, normalizer.p -> Double.PositiveInfinity)
println("Normalized using L^inf norm")
lInfNormData.show()
// 向量的無窮階範數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處理的對象是每一列，也就是每一維特徵，將特徵標準化爲單位標準差或是0均值，或是0均值單位標準差。
主要有兩個參數可以設置：
- withStd: 默認爲真。將數據標準化到單位標準差。
- withMean: 默認爲假。是否變換爲0均值。
StandardScaler需要fit數據，獲取每一維的均值和標準差，來縮放每一維特徵。
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
// 將每一列的標準差縮放到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作用同樣是每一列，即每一維特徵。將每一維特徵線性地映射到指定的區間，通常是[0, 1]。
它也有兩個參數可以設置：
- min: 默認爲0。指定區間的下限。
- max: 默認爲1。指定區間的上限。
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
// 每維特徵線性地映射，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將每一維的特徵變換到[-1, 1]閉區間上，通過除以每一維特徵上的最大的絕對值，它不會平移整個分佈，也不會破壞原來每一個特徵向量的稀疏性。
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()
// 每一維的絕對值的最大值爲[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]|
+--------------+----------------+總結
所有4種歸一化方法都是線性的變換，當某一維特徵上具有非線性的分佈時，還需要配合其它的特徵預處理方法。