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Last update: February 19, 2014
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Data Normalization
GeneXproTools supports different kinds of data normalization (Standardization,
0/1 Normalization and Min/Max Normalization), normalizing all numeric input variables
using data statistics derived from the training dataset. This means that the validation/test dataset
is also normalized using the training data statistics such as averages, standard deviations,
and min and max values evaluated for all numeric variables.
Data normalization can be very useful for datasets with variables in very different
scales or ranges. Note, however, that data normalization is not a requirement even
in these cases, as the learning algorithms of GeneXproTools can handle
unscaled data
quite well. Notwithstanding, GeneXproTools allows you to
check very quickly and
easily if normalizing your data improves modeling: if not, also as quickly,
you can revert to the original raw data.
It’s worth pointing out that GeneXproTools offers not just a convenient way of trying out
different normalization schemes. As is the case for
categorical variables and
missing values,
GeneXproTools generates code that also supports data scaling, allowing you to deploy
your models confidently knowing that you can use exactly the same data format that
was used to load the data into GeneXproTools. Below is a sample code in
R of a
regression model created using data standardized in the GeneXproTools environment.
#------------------------------------------------------------------------
# Regression model generated by GeneXproTools 5.0
# GEP File: D:\GeneXproTools\V5.0\OnlineGuide\ConcreteStrength-Std_01.gep
# Training Records: 687
# Validation Records: 343
# Fitness Function: Positive Correl
# Training Fitness: 902.425484649759
# Training R-square: 0.814371755345348
# Validation Fitness: 910.563337228454
# Validation R-square: 0.829125591104619
#------------------------------------------------------------------------
gepModel <- function(d)
{
G1C5 <- -9.56011932737205
G1C8 <- -8.63162785729545
G2C3 <- 1.49617681508835
G3C1 <- 2.18332468642232
G3C6 <- -2.90885921811579
G3C7 <- 1.75264748069704
G4C8 <- 1.12216559343242
G6C5 <- -3.60847804193243
d <- Standardize(d)
y <- 0.0
y <- exp(((min(((G1C8+G1C8)/2.0),(d[4]+d[7]))-(d[8]*d[8]))-G1C5))
y <- y + (d[8]/((G2C3+d[8])/2.0))
y <- y + ((G3C1+(tanh(G3C7)*d[1]))+((tanh(d[8])+(G3C6-d[5]))/2.0))
y <- y + (d[2]-(1.0-((((min(d[5],d[6])+(d[7]*G4C8))/2.0)+((d[6]+d[1])/2.0))/2.0)))
y <- y + atan(d[5])
y <- y + ((gep3Rt(d[8])+max(((d[6] ^ 2)-(1.0-G6C5)),(d[1]+d[3])))/2.0)
y <- Reverse_Standardization(y)
return (y)
}
gep3Rt <- function(x)
{
return (if (x < 0.0) (-((-x) ^ (1.0/3.0))) else (x ^ (1.0/3.0)))
}
Standardize <- function (input)
{
AVERAGE_1 <- 280.949490538574
STDEV_1 <- 102.976876719742
input[1] <- (input[1] - AVERAGE_1) / STDEV_1
AVERAGE_2 <- 73.3764192139738
STDEV_2 <- 85.4464915167598
input[2] <- (input[2] - AVERAGE_2) / STDEV_2
AVERAGE_3 <- 55.0788937409025
STDEV_3 <- 64.0807915707749
input[3] <- (input[3] - AVERAGE_3) / STDEV_3
AVERAGE_4 <- 181.878602620087
STDEV_4 <- 21.7339765533138
input[4] <- (input[4] - AVERAGE_4) / STDEV_4
AVERAGE_5 <- 6.12983988355168
STDEV_5 <- 5.93069279508886
input[5] <- (input[5] - AVERAGE_5) / STDEV_5
AVERAGE_6 <- 973.916593886463
STDEV_6 <- 76.777259058253
input[6] <- (input[6] - AVERAGE_6) / STDEV_6
AVERAGE_7 <- 771.181804949053
STDEV_7 <- 79.7070075911026
input[7] <- (input[7] - AVERAGE_7) / STDEV_7
AVERAGE_8 <- 45.2823871906841
STDEV_8 <- 64.9243023773916
input[8] <- (input[8] - AVERAGE_8) / STDEV_8
return (input)
}
Reverse_Standardization <- function(modelOutput)
{
# Model standardization
MODEL_AVERAGE <- 0.836965914165358
MODEL_STDEV <- 1.73854230290885
modelOutput <- (modelOutput - MODEL_AVERAGE)/MODEL_STDEV
# Reverse standardization
TARGET_AVERAGE <- 35.49461426492
TARGET_STDEV <- 16.3004798384353
return (modelOutput * TARGET_STDEV + TARGET_AVERAGE)
}
It’s also worth pointing out that for regression problems with a continuous response variable,
the response variable is also normalized. For model deployment this also requires the
reverse-normalization of the model output of the generated models, which GeneXproTools
implements in all the code generated for model scoring. Note, however, that on the
charts and tables for model visualization and selection within GeneXproTools, the
raw “normalized” model output (not really normalized, but
generated to match
normalized actual values) is shown, as it is usually compared with the normalized response variable.
An interesting and useful application of this normalization/reverse-normalization technique
in regression problems is that, with normalized
data, the fitness functions strictly based on correlations
between predicted and actual values (R-square,
Bounded R-square,
Positive Correl and
Bounded Positive Correl), work just like any other fitness function in the sense that
the model output is brought back to scale by the reverse-normalization function.
This might prove advantageous for problems where higher R-square values are easier
and faster to achieve with an R-square-like fitness function than with any other
function. The reason for this lies in the fact that R-square-like fitness functions
measure only correlation, allowing evolution to take place over a richer
unconstrained fitness landscape.
See Also:
Related Tutorials:
Related Videos:
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