I kind of assumed everyone would know how the underlying page-rank algorithm works.
Put people on pages at random, and have them click on an outgoing link at random. Then, 20% of the time, teleport them to a new, random page. What is their distribution in the long run?
The higher the number, the more likely you are to end up there. This means you have more incoming links, but they are incoming links from pages with higher rankings. Incoming links from lower ranked pages - pages with few incoming links - don't give you much "Google Juice".
I'm curious, do people really not know this? Should I write it up? It's a standard piece of linear algebra to find the eigenvector of the appropriate matrix. I thought pretty much everyone would know it.
For those who are interested, here's a lengthier explanation I wrote that relates PageRank explicitly to solving the eigenvector equation (Mq = q, in the language of the article):
Skip past the opening, and down to "Basic Description of PageRank". The article eventually gets somewhat technical, but hopefully this at least helps explain the basics. Incidentally, I don't use the term "eigenvector" in the article, but when we're analysing an equation like Mq =q, that's an eigenvector equation!
Unfortunately, in the present context, only the early part of the notes will be really accessible to someone who has only just taken an intro class in linear algebra. The later parts, which deal with issues such as how fast the PageRank algorithm converges, really require people to have more mathematical experience.
But it's not the job of such a paper to teach them about these things. This sort of paper serves as context and motivation. The material itself can, and should, be learned from other texts designed to teach it. I think what you have is an excellent piece. Read carefully at first, then skim more and more as you get lost. Inspired, go and read about some of the necessary math, then come back and get further next time.
That is exactly why I took linear algebra in college. I (tried to) read the original Google paper and was like, "eigen-what??" and decided to take the class as an elective.
Linear algebra is stupendously useful material, and I think it really should be standard in any CS curriculum. It wasn't in mine.
> It's a standard piece of linear algebra to find the eigenvector of the appropriate matrix.
Yes please!! I just learned about eigenpairs and the teacher refused to explain their significance. I have no idea what they are beyond their purely abstract definition. I would definitely read your post about this.
Put people on pages at random, and have them click on an outgoing link at random. Then, 20% of the time, teleport them to a new, random page. What is their distribution in the long run?
The higher the number, the more likely you are to end up there. This means you have more incoming links, but they are incoming links from pages with higher rankings. Incoming links from lower ranked pages - pages with few incoming links - don't give you much "Google Juice".
I'm curious, do people really not know this? Should I write it up? It's a standard piece of linear algebra to find the eigenvector of the appropriate matrix. I thought pretty much everyone would know it.