Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have a set of points whose positions are represented by 3D vectors. Each point has the associated weight in range from 0 to 1. The sum of all weights doesn't equal to 1.

How should the weighted mean point be calculated from the whole set of points?

share|improve this question
    
I don't understand "I have a set of points set by 3D vectors representing their positions." Do you mean something like "I have a set of points whose positions are represented by 3D vectors"? –  joriki Oct 31 '12 at 12:42
    
Yes, you're right. –  BartoNaz Oct 31 '12 at 12:42

1 Answer 1

up vote 1 down vote accepted

The process is called normalization, and you simly divide each weight by the sum of all the weights: $$w_i \rightarrow \frac{w_i}{\sum w_i}$$ You can easily verify that the sum of the new weights is now $1$.

The mean vector is given by the sum: $${\bf{v}} = \sum w_i \bf{v}_i$$

share|improve this answer
    
Well, that is obvious. But that just makes the sum of weights equal to 1. But how to use these weights to calculate the weighted mean vector? –  BartoNaz Oct 31 '12 at 13:23
    
@BartoNaz - Edited my answer. Is this what you meant? –  nbubis Oct 31 '12 at 13:27
    
Probably yes. I think this should be correct. Thank you. –  BartoNaz Oct 31 '12 at 13:53

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.