Why is SVM sensitive to feature scales?

Question

Support vector machine

Hey!
I am reading a machine learning book - "Applied Machine Learning with Scikit-learn and Tensorflow". I came across the following sidebar:



Question: why in the case shown in the left picture is the widest strip close to the horizontal, if we can draw exactly the same strip as in the right picture and it will be wider than the horizontal one? How does this even work in the context of feature scaling? And shouldn’t it go through like this, if it’s a large margin classification, then in theory on both images the border should be like on the right

Answer 1

You can say for a long time that scaling is a non-linear transformation, explain - but everything is already written in the book. Therefore, it is better to try writing a scaling function with pens and see how it transforms your points (at least those on the graph), and how it transforms the points of the dividing line.
Draw a graph, and then all questions will disappear by themselves, without abstruse explanations.