Spark ML: Data de-normalization

问题:

I need to de-normalize data that was normalized using the MinMaxScaler method of ML in Spark.

I was able to normalize my data following these steps: Spark: convert an RDD[LabeledPoint] to a Dataframe to apply MinMaxScaler, and after scaling get the normalized RDD[LabeledPoint] that I've posted earlier.

For example, the original df had the two first columns and, after scaling, the result was:

+------+--------------------+--------------------+
|labels|            features|      featuresScaled|
+------+--------------------+--------------------+
|   1.0|[6.0,7.0,42.0,1.1...|[1.0,0.2142857142...|
|   1.0|[6.0,18.0,108.0,3...|[1.0,1.0,1.0,1.0,...|
|   1.0|[5.0,7.0,35.0,1.4...|[0.0,0.2142857142...|
|   1.0|[5.0,8.0,40.0,1.6...|[0.0,0.2857142857...|
|   1.0|[6.0,4.0,24.0,0.6...|[1.0,0.0,0.0,0.0,...|
+------+--------------------+--------------------+

The problem is, now I need to do the opposite process: de-normalize.

To do so, I need the min and max values for each feature column inside the features vector, and the values to be denormalized.

To get min and max, I ask to the MinMaxScaler as follows:

val df_fitted = scaler.fit(df_all)
val df_fitted_original_min = df_fited.originalMin   // Vector
val df_fitted_original_max = df_fited.originalMax   // Vector

df_fited_original_min[1.0,1.0,7.0,0.007,0.052,0.062,1.0,1.0,7.0,1.0]
df_fited_original_max[804.0,553.0,143993.0,537.0,1.0,1.0,4955.0,28093.0,42821.0,3212.0]

And, on the other hand, I have the DataFrame as this:

+--------------------+-----+--------------------+--------------------+-----+-----+--------------------+--------------------+--------------------+-----+
|               col_0|col_1|               col_2|               col_3|col_4|col_5|               col_6|               col_7|               col_8|col_9|
+--------------------+-----+--------------------+--------------------+-----+-----+--------------------+--------------------+--------------------+-----+
|0.009069428120139292|  0.0|9.015488712438252E-6|2.150418860440459E-4|  1.0|  1.0|0.001470074844665...|2.205824685144127...|2.780971210319238...|  0.0|
|0.008070826019024355|  0.0|3.379696051366339...|2.389342641479033...|  1.0|  1.0|0.001308210192425627|1.962949264985630...|1.042521123176856...|  0.0|
|0.009774715414895803|  0.0|1.299590589291292...|1.981673063697640...|  1.0|  1.0|0.001584395736407...|2.377361424206848...| 4.00879434193585E-5|  0.0|
|0.009631155146285946|  0.0|1.218569739510422...|2.016021040879828E-4|  1.0|  1.0|0.001561125874539...|2.342445354515269...|3.758872615157643E-5|  0.0|

Now, I need to apply the following equation to get the new values, but I do not how can I make it.

X_original = ( X_scaled * (max - min) ) + min

For each position in the DF, I have to apply this equation with the corresponding max and min value into the vector.

For example: In the first row and column of the DF is 0.009069428120139292. In the same column, the corresponding min and max values are: 1.0 and 804.0. So, the denormalized value is:

X_den = ( 0.009069428120139292 * (804.0 - 1.0) ) + 1.0

It is necessary to clarify that the DF that was normalized in first place, during the program was modified. Due to that I need apply the de-normalization (if not, the easiest way is to a keep a copy of the original DF).

回答1:

You "simply" apply the inverse operations in the opposite order. The equation is in the documentation here. The code of interest is:

X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0))
X_scaled = X_std * (max - min) + min

You now have the data set of X_saled values, and you want to recover the original X values. Your immedicate problem is that you lose some basic information in the transformation. X_scaled is a set of data on the range [0, 1]; you have no way of knowing what the original range was.

To make this work, find and keep the original min and `max values. Now, it's easy to reverse the linear transformation for each element:

X_original = X_scaled * (max - min) + min

Can you take it from there?

回答2:

I've got the answer from the following one https://stackoverflow.com/a/50314767/9759150, plus a slightly adaptation to my problem I've completed the de-normalization process.

Let's consider normalized_df as the dataframe with 10 columns (showd in my question):

import org.apache.spark.sql.Column
import org.apache.spark.sql.functions._

val updateFunction = (columnValue: Column, minValue: Int, maxValue: Int) =>
    (columnValue * ( lit(maxValue) - lit(minValue))) + lit(minValue)

val updateColumns = (df: DataFrame, minVector: Vector, maxVector: Vector, updateFunction: (Column, Int, Int) => Column) => {
    val columns = df.columns
    minVector.toArray.zipWithIndex.map{
      case (updateValue, index) =>
        updateFunction( col(columns(index.toInt)), minVector(index).toInt, maxVector(index).toInt ).as(columns(index.toInt))
    }
}

var dfUpdated = normalized_df.select(
  updateColumns(normalized_df, df_fitted_original_min, df_fitted_original_max, updateFunction) :_*
)