In locally weighted regression how determine distance from query point with more than one dimension

Question

If the query point in a locally weighted regression is multidimensional (for different features), how do we determine if there are points close-by the query point? This is especially true if the features have different units.

Answer 1

If x is a vector of individual differences for each attribute, the "size" of x can be measured using a variety of norms (and the distance between any two points). The L2 norm is the most widely used norm. Different normalization procedures can be employed, but you should be fine if you scale each feature so that 80% of the points have a value between -10 and 10

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