When dealing with data observations that have multiple features, we should be aware that features can be scaled differently on different scales. In this recipe, we account for that to improve our housing value predictions.
It is important to extend the nearest neighbor algorithm to take into account variables that are scaled differently. In this example, we will show how to scale the
distance function for different variables. Specifically, we will scale the
distance function as a function of the feature variance.
The key to weighting the
distance function is to use a weight matrix. The
distance function written with matrix operations becomes the following formula:
Here, A is a diagonal weight matrix ...