I am studying for a paper, and would like to understand if the following operation represent a normalisation.

I have two vectors A, B of same length. I multiply their items, element-wise, sum the resulting vector, and divide by the sum of A.

(Hope the notation of element wise is correct, I looked at: Symbol for elementwise multiplication of vectors)

Is it the following a type of normalisation ? Does it have a meaning in physics to help me understand the scope of this operation?

$$\frac{\sum_{i=1}^n(\mathbf a \circ \mathbf b )} {\sum_{i=1}^n \mathbf ai}$$

E.g. given a = [2,5], b = [3,7] => [6,35].sum() / [2,5].sum() => $\frac{41}{7}$

  • $\begingroup$ In the denominator, you seem to be saying $2+5=10$ $\endgroup$
    – saulspatz
    Apr 23, 2019 at 23:14
  • $\begingroup$ What is the paper? Can you provide a link for context? $\endgroup$
    – Spencer
    Apr 24, 2019 at 0:01
  • $\begingroup$ tks saul, corrected. Spencer, corrected text - sorry guys, yesterday night been a long day for me! The context is related to topological analysis, the objective is to extract properties of a network for training purpose. In the example above, a, b are two arrays of different types of quantities which are exchanged along edges of a network, say prices and quantities. So the final result measure would be in prices units (€ * Kg / Kg ). $\endgroup$
    – user305883
    Apr 24, 2019 at 6:33


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