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Scale:

Scale Features

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).

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	1.6	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 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:

(790 - 1292.23) / 238.74 = -2.1

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.

Example

Scale all values in the Weight and Volume columns:

Result:

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 »

Predict CO2 Values

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:

Example

Predict the CO2 emission from a 1.3 liter car that weighs 2300 kilograms:

import pandas
from sklearn import linear_model
from sklearn.preprocessing import StandardScaler
scale = StandardScaler()

df = pandas.read_csv("data.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)

Result:

[107.2087328]

Run example »