Why Scale Features

Part of the Statistics for ML section of Coddy's Machine Learning journey. Lesson 47 of 64.

Which customer is most like a new one? Many models measure the distance between samples: square each feature's gap, add them up, take the square root.

A 25-year-old earning $52,000 against a 61-year-old earning $53,000:

Two bars of what each feature adds to the distance between the two customers: age, a 36 year gap, adds 1,296, a sliver too thin to see; income, a $1,000 gap, adds 1,000,000, a long bar

For a whole table, axis=1 sums each row's squares and .argmin() finds the nearest row:

a = np.array([25, 52000])  # age, income
X = np.array([[61, 53000],   # the 61-year-old
              [26, 55000]])  # a 26-year-old earning $55,000
dists = np.sqrt(((X - a) ** 2).sum(axis=1))
print(np.round(dists, 2))
print(dists.argmin())

This prints:

[1000.65 3000.  ]
0

The 61-year-old is nearest: dollars come in bigger numbers, so $1,000 outweighs 36 years. Unscaled, the biggest units decide.

This chapter gives every feature a fair say.

Challenge

Medium

A shop compares washing machines by price ($), energy (kWh a year) and water (liters a wash), named in features. The program reads two machine positions, i and j. Print:

Squared gaps: each feature's gap, squared.
Distance: rounded to 2 decimals.
Dominant feature: the name of the feature with the largest squared gap.

For two other machines:

Squared gaps: [2500 6400    1]
Distance: 94.35
Dominant feature: energy

Try it yourself

import numpy as np

features = ["price", "energy", "water"]
# One row per washing machine: price in dollars, energy in kWh per year, water in liters per wash
machines = np.array([[499, 160, 48],
                     [349, 210, 55],
                     [899, 120, 42],
                     [529, 250, 50],
                     [279, 230, 60],
                     [749, 140, 45]])
i = int(input())
j = int(input())

# Write your code below

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Statistics for ML

3Probability by Simulation

Probability as Frequency The Law of Large Numbers Sums of Dice Expected Value Conditional Probability Recap: Dice Stall Odds

6Relationships

Reading Scatter Plots Correlation Correlation Matrix Correlation Heatmaps Correlation Is Not Cause Recap: Ice Cream and Sun

9Feature Scaling

Why Scale FeaturesMin-Max Scaling Standardization StandardScaler Recap: Climbing Partners

12Final Challenges

Train Delays Air Quality Wine Chemistry Clinic Survey

Practice on your own: Online Python compiler