Machine Learning - Scaling

Feature Scaling (Scale Features)

When your data has different values, even with different units of measurement, it may be difficult to compare them. How many kilograms is a meter compared to a kilogram? Or altitude compared to time?

The answer to this question is scaling. We can scale the data to new values that are easy to compare.

Please see the table below, which is in line with what we haveMultiple RegressionThe dataset used in Chapter 1 is the same, but this time, the Volume column contains units in liters instead of ccm (1.0 instead of 1000).

Car Model Volume Weight CO2
Toyota Aygo 1.0 790 99
Mitsubishi Space Star 1.2 1160 95
Skoda Citigo 1.0 929 95
Fiat 500 0.9 865 90
Mini Cooper 1.5 1140 105
VW Up! 1.0 929 105
Skoda Fabia 1.4 1109 90
Mercedes A-Class 1.5 1365 92
Ford Fiesta 1.5 1112 98
Audi A1 1.6 1150 99
Hyundai I20 1.1 980 99
Suzuki Swift 1.3 990 101
Ford Fiesta 1.0 1112 99
Honda Civic 1.6 1252 94
Hundai I30 1.6 1326 97
Opel Astra 1.6 1330 97
BMW 1 1.6 1365 99
Mazda 3 2.2 1280 104
Skoda Rapid 1.6 1119 104
Ford Focus 2.0 1328 105
Ford Mondeo 1.6 1584 94
Opel Insignia 2.0 1428 99
Mercedes C-Class 2.1 1365 99
Skoda Octavia 1.6 1415 99
Volvo S60 2.0 1415 99
Mercedes CLA 1.5 1465 102
Audi A4 2.0 1490 104
Audi A6 2.0 1725 114
Volvo V70 1.7 1523 109
BMW 5 2.0 1705 114
Mercedes E-Class 2.1 1605 115
Volvo XC70 2.0 1746 117
Ford B-Max 1.6 1235 104
BMW 2 1.6 1390 108
Opel Zafira 1.6 1405 109
Mercedes SLK 2.5 1395 120

It is difficult to compare displacement 1.0 with weight 790, but if we scale them to comparable values, we can easily see how much one value is compared to another.

There are many methods to scale data, in this tutorial, we will use a method called standardization (standardization).

The standardization method uses the following 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 obtain weight Column, the first value is 790, and the scaled value is:

(790 - 1292.23) / 238.74 = -2.1

If you obtain volume Column, the first value is 1.0, and the scaled value is:

(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 need to perform this operation manually, the Python sklearn module has a function named StandardScaler() method, which returns a Scaler object with the transformed dataset method.

Example

Scale all values in the Weight and Volume columns:

import pandas
from sklearn import linear_model
from sklearn.preprocessing import StandardScaler
scale = StandardScaler()
df = pandas.read_csv("cars2.csv")
X = df[['Weight', 'Volume']]
scaledX = scale.fit_transform(X)
print(scaledX)

Results:

Please note, the first two values are -2.1 and -1.59, corresponding 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 Instance

Predict CO2 Value

Multiple RegressionThe task of this chapter is to predict the carbon dioxide emissions of a car from its weight and displacement without knowing any other information.

After scaling the dataset, the scaling factor must be used when predicting the values:

Example

Predict the carbon dioxide emissions of a 1.3-liter car weighing 2300 kilograms:

import pandas
from sklearn import linear_model
from sklearn.preprocessing import StandardScaler
scale = StandardScaler()
df = pandas.read_csv("cars2.csv")
X = df[['Weight', 'Volume']]
y = df['CO2']
scaledX = scale.fit_transform(X)
regr = linear_model.LinearRegression()
regr.fit(scaledX, y)
scaled = scale.transform([[2300, 1.3]])
predictedCO2 = regr.predict([scaled[0]])
print(predictedCO2)

Results:

[107.2087328]

Run Instance