Add weighted distance functions between two vectors

[yu-iskw]

I'd like to use weighted distance function with Breeze. However, it is not easy for me to implemet them. If we want to implement like squaredDistance, we need the three parameters version of ZippedValues trait.

• weighted euclidean distance
• weighted cosine distance
• weighted tanimoto distance
  and so on

I tried to implement a sample weighted distance function like below:
A weighted Euclidean distance function implementation
https://gist.github.com/yu-iskw/4e0d3a2f999effbcf640

But it seems that there are things we can't do.

1. Take parameters as the combination of DenseVector and SparseVector
2. Can not use Int, Float and Long type exclude Double in elements of DenseVector and SparseVector.

If anyone have any good idea about implementing them, could you teach me ?
And should we make them in the first place?

[dlwh]

This looks reasonable. We might consider following the VariableUFunc approach used in the polynomial package. Basically, make a class WeightedEuclideanDistance that takes the weight as a ctor param, and have WeightedCosineDistance extend VariableUFunc.

We've talked about (for another issue related to L1 regularization with @dbtsai) adding a map3 to ZipMapValues, which would solve the issues here. Another approach would be to have the implementations be composed from implicits like the other distance ones:

object weightedEuclideanDistance extends UFunc {

  implicit def euclideanDistanceFromZippedValues[T, W, U, WtimesU]
      (implicit mulScalar: OpMulScalar.Impl2[U, W, WtimesU], zipImpl: zipValues.Impl2[T, WtimesU, ZippedValues[Double, Double]]): Impl3[T, U, W, Double] = {

    new Impl2[T, U, Double] {
      def apply(v: T, v2: U, w: W): Double = {
        var distance = 0.0

        zipValues(v, mulScalar(w, v2)).foreach { (a, b) =>
          val score = a - b
          distance += (score * score)
        }
        Math.sqrt(distance)
      }
    }
  }
}

as for Int vs float etc, we can use the expand macro, or require a Field[ScalarType]

[yu-iskw]

Hi @dlwh,

Thank you for your feedback.
I understand that you are currently working to add a map3 to ZipMapValues. I'm looking forward to adding it! If you will merge it, I will try to implement some weighted distance functions.

thanks,