Building Machine Learning Systems with Python - Richert, Coelho

Chapter 2
In the preceding screenshot, the Canadian examples are shown as diamonds, Kama
seeds as circles, and Rosa seeds as triangles. Their respective areas are shown as
white, black, and grey. You might be wondering why the regions are so horizontal,
almost weirdly so. The problem is that the x axis (area) ranges from 10 to 22 while
the y axis (compactness) ranges from 0.75 to 1.0. This means that a small change in x
is actually much larger than a small change in y. So, when we compute the distance
according to the preceding function, we are, for the most part, only taking the x axis
into account.
If you have a physics background, you might have already noticed that we had
been summing up lengths, areas, and dimensionless quantities, mixing up our
units (which is something you never want to do in a physical system). We need to
normalize all of the features to a common scale. There are many solutions to this
problem; a simple one is to normalize to Z-scores. The Z-score of a value is how far
away from the mean it is in terms of units of standard deviation. It comes down to
this simple pair of operations:
# subtract the mean for each feature:
features -= features.mean(axis=0)
# divide each feature by its standard deviation
features /= features.std(axis=0)
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