Question

Lets say I have a reference node R and several test nodes T₁, T₂…. T_n.
Any particular node has a set of properties Rp₁, Rp₂, … Rp_n and T₁p₁, T₁p₂, T₁p₃, … T₁p_n, and T₂p₁, T₂p₂, T₂p₃, … T₂p_n, and so on. So, any node can have n properties, each of a particular type.

I have my own method of defining the distance between any two properties of the same kind between any two nodes. Furthermore, I would weigh the distances between properties and then sum them up. Thus, the distance between R and T₁ would be:

dRT₁ = w₁*dRT₁p₁ + w₂*dRT₁p₂ + w₃*dRT₁p₃ + w₄*dRT₁p₄ + … w_n*dRT₁p_n.

Now, given the reference node R, and the test nodes T₁, T₂ …. T_n, and given that I know the distance is the least between R and a particular node T_m (1<m<n), and if the weights are actually variables and the distances are actually constants, how do I calculate the weights such that dRTm is the minimal among all the distances between R and every other test nodes.

We have the distances dRT₁, dRT₂, dRT₃, dRT₄, … dRT_n and we know that dRT_m is minimum. What algorithm should we use to determine the weights?

Answer 1

This looks like http://en.wikipedia.org/wiki/Linear_regression, where after the article says “Thus the model takes the form” y is dRt1, the x variables are e.g. dRT1p1, and the beta variables they are trying to work out – their parameter vector – is your w1, w2…