3 ms·
You can consider mean, mode, and the other centrality measures as points that minimise some sort of average deviation. And depending on which norm you use to me
by FabHK 8y ago
You can consider mean, mode, and the other centrality measures as points that minimise some sort of average deviation. And depending on which norm you use to measure your deviation, you get different centrality measures:
* L_0 -> mode
* L_1 -> median
* L_2 -> mean
* L_infinity -> midrange, I think
where roughly L_p(x) = [ sum_i |x-x_i|^p]^(1/p) ]
- rocqua 8y agoAmong these norms, again the L_2 norm stands out. It being the standard measure of distance. Here, it is important because it is invariant under rotation. We can define rotation without any appeal to length as the "special linear group". This consists of all matrices that have determinant 1. I wonder where exactly the connection between 'rotation invariance' and 'estimate of the expected value' comes from.