Normlize norms on board words

[simonlindholm]

Some words on the board are quite vague and far from other words. Can we increase their norms, to give equal consideration to all words on the board?

[HalfVoxel]

The normalization could for example happen by setting Σ_w distance(current_word,w) = number_of_words. I.e the distance to other words is 1 on average. Might have to modify the distance metric though as right now it ranges from -1 to 1 which makes the normalization unstable (as the sum is probably close to zero).

This could have the effect of making the distance non-symmetric though (so distance(a,b) != distance(b,a)). Maybe we would use the average of the normalization constants for 2 words when we check the distances between them.

[simonlindholm]

Distance is already a bit asymmetric, ever since I added norms - we want to care about norms for the dictionary word, but not the word on the board. Codewise this is done by making the signature "distance(fixedWord, dynamicWord)", where only dynamicWord cares about its norm. Or something like that.

Aren't most words positively correlated right now? Or maybe that's selection bias. But yeah, we should make sure that these sums don't have outrageous values (e.g. negative).