SS23_IR: HITS Example (Lecture 12 Slides)

Hello, while studying for the second exam, i tried to understand the HITS example given in the slides. However, if i try to calculate the first step (x0->x1 and y0 ->y1), i get completly different results. I was using the non-matrix version (looking at the graph and taking the scores as seen under x0 and y0). I also tried two different types of normalization. Firstly just dividing by sum of the corresponding scores, like i've seen in different video/articles of the HITS algorithm and secondly dividing by the square root of the sum of the squares, like it's written in the wikipedia article. Both versions did not produce the right results. Here are my results:

What did i do wrong? Or what kind of normalization is used in the example?

Also, why is the authority score of P1 not 0 after the first step? Only P3 points to it and P3 has a hub score of 0, so shouldn't it be 0 as well?

Thanks in advance!

Philipp

Re: HITS Example (Lecture 12 Slides)

per Benedikt Ebing - dilluns, 9 d’octubre 2023, 10:54

Hi Philipp,

in the example on the slides the formula x^(k+1) = L^TLx^(k-1) is used (and the equivalent for the hub scores). So basically the example computes two iterations at once. If you compute another iteration on your results, you should get what is stated under x(1) and y(1) on the slides. Normalization is done by the sum of scores.

Best,
Benedikt

Re: HITS Example (Lecture 12 Slides)

per Philipp Treutlein - dilluns, 9 d’octubre 2023, 16:20

Hi Benedikt,
i calculated another step and got the right results now, thank you! Seems like i didn't look at the matrix formula enough, didn't notice the (k+1) and (k-1) parts meaning two steps at once, but makes sense.

Thanks again!
Philipp