在MATLAB中计算给定实例向量的KNN时，如何加权尺寸？

Question

Suppose I have a bunch of instances and I want to find the closest K instances to a particular instance. Moreover, I have some weights showing the strengths of each dimension as we computing the distances. How can I incorporate these weights with the KNN finding process in MATLAB?

Answer 1

There are two methods that can allow you to do this. Looking at the knnsearch documentation, you can either use the seuclidean flag where this performs the standardized Euclidean distance. Each co-ordinate difference between two points is scaled by dividing by a corresponding scale value in S . S by default is the standard deviation for each co-ordinate. You can manually specify each of these scales by specifying the Scale parameter, then specifying a vector where each component will scale each dimension for you instead of the standard deviation in each dimension.

As such, the more contribution a co-ordinate has, the larger the scale should be, as you want to aggregate co-ordinates and will allow distances that are larger to have a smaller Euclidean distance. This is essentially the same thing as weighting the strengths in each dimension.

Alternatively, you can provide your own function that computes the distance between two vectors. You can define what these weights are in your workspace before hand, then create an anonymous function wrapper that accesses these weights when computing whatever distance measure you want yourself. The anonymous function can only take in two vectors, corresponding to two different co-ordinate vectors in KNN. As such, use this anonymous function to access the weights that should be already defined in the workspace then go from there.

Check out: http://www.mathworks.com/help/stats/knnsearch.html