Computing with Mixed Distance Functions

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.

Getting ready

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 ...

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