I've searched quite a bit and haven't landed on any useful results.
The problem statement is: Given a set of vectors, I wish to find its approximate k-nearest neighbors. The caveat here is that each of my dimensions resemble a different entity and hence we cannot use the same weight for each dimension while computing the distance. Thus, solutions like kd-tree don't work as is.
Is there any data-structure or any alternate algorithm that I can use to find such approximate weighted k-nearest neighbors.
Note: Multiplying the initial input data with their weights so as to get a uniform weight is not an option.