I'm just curious on how to average a high dimensional vector?
I have several vectors that hold the frequency of words, and my supervisor wants me to: Average the high dimensional vectors. (Aardvark to Zebra) Not the 2D coordinates of the points.
However, I'm not entirely sure what he means by this and I've checked online for resources, but I can't find any that resonate with me - I'm a music student by discipline, so any help would be appreciated.
Problem:
I have 6 vectors that represent the frequencies of words in a collection - which I have these vectors stored in separate documents. I then want to be able to find the top 20 of words of selection. To do this, i would need to take the average vector (centroid) of the selection and list the top 20. How do i average these vectors (see google drive link below) and return the top 20 of that selection.
What does it mean to average? It means to sum up the vectors and divide by a scalar. Both operations are available for vector spaces (over $\mathbb{R}$, $\mathbb{C}$ and other related fields).
For instance you can define the average between $v_1,v_2\in\mathbb{R}^n$ to be $\frac{1}{2}\cdot (v_1+v_2)$ where the addition is in the vector space (i.e. pointwise addition) and $\frac{1}{2}$ is a scaler in $\mathbb{R}$. This is equivalent to average coordinate-wise.