Python Machine Learning Scaling

When your data has different values, and even different measurement units, it can be difficult to 
compare them. What is kilograms compared to meters? Or altitude compared to time?
The answer to this problem is scaling. We can scale data into new values that are easier to 
compare.
Take a look at the table below, it is the same data set that we used in the 
multiple regression chapter, but this time the volume column 
contains values in liters instead of cm3 (1.0 instead of 1000).
The file is meant for testing purposes only, you can download it here: cars2.csv
It can be difficult to compare the volume 1.0 with the weight 790, but if we 
scale them both into comparable values, we can easily see how much one value 
is compared to the other.
There are different methods for scaling data, in this tutorial we will use a 
method called standardization.
The standardization method  
uses this formula:
z = (x - u) / s
Where z is the new value, 
x is the original value, 
u is the mean and s is the 
standard deviation.
If you take the weight column from the data set above, the first value 
is 790, and the scaled value will be:
If you take the volume column from the data set above, the first value 
is 1.0, and the scaled value 
will be:
(1.0 - 1.61) / 0.38 = -1.59
Now you can compare -2.1 with -1.59 instead of comparing 790 with 1.0.
You do not have to do this manually,
the Python sklearn module has a method called StandardScaler()
which returns a Scaler object with methods for transforming data sets.
Scale all values in the Weight and Volume columns:
Note that the first two values are -2.1 and -1.59, which corresponds to our 
  calculations: 
[[-2.10389253 -1.59336644]
 [-0.55407235 -1.07190106]
 [-1.52166278 -1.59336644]
 [-1.78973979 -1.85409913]
 [-0.63784641 -0.28970299]
 [-1.52166278 -1.59336644]
 [-0.76769621 -0.55043568]
 [ 0.3046118  -0.28970299]
 [-0.7551301  -0.28970299]
 [-0.59595938 -0.0289703 ]
 [-1.30803892 -1.33263375]
 [-1.26615189 -0.81116837]
 [-0.7551301  -1.59336644]
 [-0.16871166 -0.0289703 ]
 [ 0.14125238 -0.0289703 ]
 [ 0.15800719 -0.0289703 ]
 [ 0.3046118  -0.0289703 ]
 [-0.05142797  1.53542584]
 [-0.72580918 -0.0289703 ]
 [ 0.14962979  1.01396046]
 [ 1.2219378  -0.0289703 ]
 [ 0.5685001   1.01396046]
 [ 0.3046118   1.27469315]
 [ 0.51404696 -0.0289703 ]
 [ 0.51404696  1.01396046]
 [ 0.72348212 -0.28970299]
 [ 0.8281997   1.01396046]
 [ 1.81254495  1.01396046]
 [ 0.96642691 -0.0289703 ]
 [ 1.72877089  1.01396046]
 [ 1.30990057  1.27469315]
 [ 1.90050772  1.01396046]
 [-0.23991961 -0.0289703 ]
 [ 0.40932938 -0.0289703 ]
 [ 0.47215993 -0.0289703 ]
 [ 0.4302729   2.31762392]]

Run example »

The task in the Multiple Regression chapter was to predict the CO2 emission from a car 
when you only knew its weight and volume.
When the data set is scaled, you will have to use the scale when you predict values:
Predict the CO2 emission from a 1.3 liter car that weighs 2300 kilograms:
[107.2087328]

Run example »

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