One question to consider when constructing classifiers is whether or not the method is location-scale invariant. This property holds if subjecting any subset of features in the training data to a linear trans- formation cannot change the prediction. For example, a classifier is location-scale invariant if changing the units of a feature from feet to inches, or from degrees fahrenheit to celsius, does not change the predictions (as long as the transformation is consistently applied to all classes and test data).
This is a crucial question, since if a classifier is not location-scale invariant, we need to decide how to make the units of each feature comparable. One way of doing this is to standardize quantitative features, typically by subtracting the mean then dividing by the standard deviation, so that each feature has mean zero and standard deviation 1. Doing this makes them essentially unitless. However, for some applications this may not be a suitable approach to this problem.
my quesstion is that KNN classifier, assuming Euclidean distance is used, location-scale invariant? Why or why not?