Questions to weighting formulae and matrix factorisation

[mmlynarik]

Hi,

I just wanted to ask three questions:

1. Why is the tf measure calculated here using sqrt and not the classic relative frequency?

2. Why are you using here the K1=100 when literature recommends using values around 1?

3. Why are you here not incorporating singular value matrix (i.e. sqrt(sigma_i) for each artist_factor coordinate) when calculating cosine distances of artists? In fact the image displaying matrix factorisation should contain apart from two thin matrices also the square singular value matrix in order for the picture to be complete. Anyway, I know that the singular values are evenly applied to each two vectors being compared, but nevertheless it modifies the resulting cosine distance and therefore it's not trivially clear whether they should or should not not be used in the calculations. Here's the visual representation of what I'm thinking:

What it actually means is whether we should (in case of K=2) compare x_1*y_1 + x_2*y_2 or \sigma_1*x_1*y_1 + \sigma_2*x_2*y_2.

Thanks!