8 ms·

The $25B eigenvector (2006) [pdf]

342 points by onecooldev24 9y ago

Fej 9y ago
This article is from 2006. It's interesting but I'd hazard a guess that it's hardly relevant to what Google is doing now.
- N_A_T_E 9y ago
  Google has always spoken about adjustments to pagerank and they have been visible but I assume the core concept still applies. Maybe someone with more inside knowledge can comment?
  - saagarjha 9y ago
    Nice try, Bing. But in all seriousness, Google is notoriously tight-lipped about how PageRank works, so I doubt we're going to get any more information than this. I'd love to proven wrong, though!
- dang 9y ago
  Ok, we'll add the year.
dboreham 9y ago
Well...pretty much everything important turns out to be an eigenvector.
- tw1010 9y ago
  That has less to do with some mysterious fact about eigenvectors, and more to do with the fact that linear algebra is incredibly incredibly well studied and understood; with octopus arms sticking into every special case of applied mathematics imaginable. Give it a few decades and "everything" will be some other (today obscure) mathematical idea.
  - tzahola 9y ago
    A category maybe? Wait a sec... everything already is a category.
    - cscurmudgeon 9y ago
      And a set.
      - dboreham 9y ago
        I thought it was known that not everything is a set?
        johncolanduoni 9y ago
        There’s more than one way to define what a set is, and many of these definitions always allow you to postulate there exist further collections that cannot meet that definition of a set ad infinitum. Most importantly ZFC (which is at least in theory the formal basis for the vast majority of mathematics) has this property, and so do many extensions like NBG and TG.
        chestervonwinch 9y ago
        of course - it's the empty set :)
        deleted 9y ago
        [deleted]
  - comicjk 9y ago
    At least one part of the universe really does seem to prefer linear algebra: quantum mechanics. Every quantum state is a linear combination of eigenvectors, and that's unlikely to change within a few decades (it would be a revolution analogous to the discovery of quantum mechanics itself).
    - tw1010 9y ago
amelius 9y ago
Sadly, this seems to be the last thing we've ever heard about the search algorithm of Google. It tells nothing about topics like modern natural language-processing (which defines a different, non-global, ordering of search results, based on the query). How much of the basic algorithm is still in effect?
- endymi0n 9y ago
  From everything that is publically known, assume PageRank to still exist and be one tensor feature on the RankBrain algorithm. https://searchengineland.com/faq-all-about-the-new-google-rankbrain-algorithm-234440 https://searchengineland.com/faq-all-about-the-new-google-ra... Although there haven't been any major announcements, from daily anecdotal evidence I can confirm it's still a major factor to get you into the front pages. I'd say the major changes since deprecating PageRank in practice are 1. Much higher dependence on CTR and bounce rate once you start showing up in the SERPs 2. Much higher influence of a notion of "trust" on links (not just the quantity, but mainly the quality counts now, too much quantity without quality can actually hurt) 3. PageRank much more disconnected from domain level. A few years ago, you could rank with pretty much anything if your DomainPop was high enough. By now, Google got much smarter about different folders that don't have anything to do with what it's ranking your main site for and it's harder to get them ranking. On the bright side, they also got smarter about the negative SEO influence of subdomains or domain changeovers, which won't cost you as dearly. So TL;DR: PageRank still exists, but it's been reduced to an input vector.
  - SamPutnam 9y ago
    For example: "2 or 3 years ago links was 80-90% of what it took to get something ranked, Panda has changed that in an insane way. Here's the test example. Go to Google and search for 'best time to visit Tahiti'. You'll find my little site, VisualItineraries up there, #1 for that, ahead of TripAdvisor, Lonely Planet, USA Today, all these other sites. These other sites have between 10,000 and 250,000 domains linking to them. My site has under 100. I rank #1 for that. Now in case you think it's internal link, anchor text, or page title match. Here's the other proof. Do a google search for 'when should I go to French Polynesia'. The only word in that that matches the page title or any anchor text is the word 'to' - (and it's a) stop word - that's not going to count. VisualItineraries.com is #1 for that too. source: https://www.youtube.com/watch?v=7RvRUt9ejkw https://www.youtube.com/watch?v=7RvRUt9ejkw
s-c-h 9y ago
I am curious to know what major innovations in search engines happened since the page rank algorithm, or were there only incremental improvements? Also is search considered a solved problem?
- saagarjha 9y ago
  > Also is search considered a solved problem? I certain wouldn't, since I still encounter things that I know are on the internet but Google can't find. It's possible that the next advance won't be actually indexing the web but rather figuring out what the user wants rather than what they requested.
  - ianai 9y ago
    Googles monetization strategy blinds the results. My guess would be either a way to search beyond google or force it to give results that aren’t manipulated somehow.
  - osrec 9y ago
    Google does this to some extent. Recently I've found that Google uses my past queries to make cogent suggestions for my next search (essentially to predict what I want next based on prior info). Eg, if I've just searched for "sully", then a short time after type "t" into Google, the first suggestion is Tom Hanks. I've only noticed this in the last few months.
    - Swizec 9y ago
      I’ve experienced this when learning new programming languages and other domains. When you start, Google results are mostly garbage with a few useful bits. A few months later, it feels like the web is awash in materials to answer your every question and you can always find an answer for your problem in the first 5 results. Part of it is learning which phrases to use when searching, but I’m sure a big part of it is also Google figuring out what you want.
    - leggomylibro 9y ago
      My favorite example of this is the Bullet physics library. Google eventually learned to give me documentation in response to stuff like 'bullet collision', but for awhile it was big on youtube links and gun ranges.
cs702 9y ago
An oldie but a goodie. IMHO, this paper, along with Larry and Sergei's original work[0], should be part of every Linear Algebra course. Few things get students to pay attention like the mention of ungodly amounts of money! [0] http://ilpubs.stanford.edu:8090/422/1/1999-66.pdf http://ilpubs.stanford.edu:8090/422/1/1999-66.pdf
- therein 9y ago
  Can't speak for all linear algebra courses but my linear algebra course in college actually taught that paper for at least two lectures and a discussion section back when I took it.
  - rtpg 9y ago
    I'm also pretty sure a simplified version of this was used for french entrance exams a couple years back. I remember taking a practice exam with this as the topic, at least
- konschubert 9y ago
  Unasked for, arrogant rant: Do you mean in school or in university? Because if somebody is taking linear algebra in university and still didn't understand that this is an extremely important topic, then he should maybe go back to school or take a gap year or something to improve his general education. From a university lecture in linear algebra, I expect that it carries me through as many important topics as possible while giving me the tools to form a good formal and intuitive understanding. The motivation part should be solved by that time.
  - cyberpunk0 9y ago
    You are wrongly assuming most courses aren't taught by overworked professors or TAs who just speed run through problems with no background on the subject and more or less teach you to pass the exams. Not everyone gets ivy league lectures.
    - 9y ago
davesque 9y ago
The resources already linked from this thread are surely superior but, as a shameless plug, I wrote a blog article recently on this very topic as it was presented in my linear algebra course at CU Boulder: https://thought.place/articles/2017/7/22/pagerank/ https://thought.place/articles/2017/7/22/pagerank/
chepeadan 9y ago
Click bait title. You can say the same about sums and multiplication, they are at the basis of most trillion dollar technologies :P
- jamez1 9y ago
  This isn't about eigenvectors in general, it's about a single eigenvector that Google built. The title is accurate, their search product is giving you access to query the eigenvector
- mathgenius 9y ago
  > You can say the same about sums and multiplication Yes indeed. In particular how multiplication distributes over addition. It is powerful technology.
cdibona 9y ago
This post has happened before, it'll happen again: https://news.ycombinator.com/from?site=rose-hulman.edu https://news.ycombinator.com/from?site=rose-hulman.edu

342 points by onecooldev24 9y ago

Fej 9y ago

This article is from 2006. It's interesting but I'd hazard a guess that it's hardly relevant to what Google is doing now.

N_A_T_E 9y ago
Google has always spoken about adjustments to pagerank and they have been visible but I assume the core concept still applies. Maybe someone with more inside knowledge can comment?
- saagarjha 9y ago
  Nice try, Bing. But in all seriousness, Google is notoriously tight-lipped about how PageRank works, so I doubt we're going to get any more information than this. I'd love to proven wrong, though!
dang 9y ago
Ok, we'll add the year.

dboreham 9y ago

Well...pretty much everything important turns out to be an eigenvector.

tw1010 9y ago
That has less to do with some mysterious fact about eigenvectors, and more to do with the fact that linear algebra is incredibly incredibly well studied and understood; with octopus arms sticking into every special case of applied mathematics imaginable. Give it a few decades and "everything" will be some other (today obscure) mathematical idea.
- tzahola 9y ago
  A category maybe? Wait a sec... everything already is a category.
  - cscurmudgeon 9y ago
    And a set.
    - dboreham 9y ago
      I thought it was known that not everything is a set?
      - johncolanduoni 9y ago
        There’s more than one way to define what a set is, and many of these definitions always allow you to postulate there exist further collections that cannot meet that definition of a set ad infinitum. Most importantly ZFC (which is at least in theory the formal basis for the vast majority of mathematics) has this property, and so do many extensions like NBG and TG.
      - chestervonwinch 9y ago
        of course - it's the empty set :)
      - deleted 9y ago
        [deleted]
- comicjk 9y ago
  At least one part of the universe really does seem to prefer linear algebra: quantum mechanics. Every quantum state is a linear combination of eigenvectors, and that's unlikely to change within a few decades (it would be a revolution analogous to the discovery of quantum mechanics itself).
  - tw1010 9y ago

amelius 9y ago

Sadly, this seems to be the last thing we've ever heard about the search algorithm of Google. It tells nothing about topics like modern natural language-processing (which defines a different, non-global, ordering of search results, based on the query). How much of the basic algorithm is still in effect?

endymi0n 9y ago
From everything that is publically known, assume PageRank to still exist and be one tensor feature on the RankBrain algorithm. https://searchengineland.com/faq-all-about-the-new-google-rankbrain-algorithm-234440 https://searchengineland.com/faq-all-about-the-new-google-ra... Although there haven't been any major announcements, from daily anecdotal evidence I can confirm it's still a major factor to get you into the front pages. I'd say the major changes since deprecating PageRank in practice are 1. Much higher dependence on CTR and bounce rate once you start showing up in the SERPs 2. Much higher influence of a notion of "trust" on links (not just the quantity, but mainly the quality counts now, too much quantity without quality can actually hurt) 3. PageRank much more disconnected from domain level. A few years ago, you could rank with pretty much anything if your DomainPop was high enough. By now, Google got much smarter about different folders that don't have anything to do with what it's ranking your main site for and it's harder to get them ranking. On the bright side, they also got smarter about the negative SEO influence of subdomains or domain changeovers, which won't cost you as dearly. So TL;DR: PageRank still exists, but it's been reduced to an input vector.
- SamPutnam 9y ago
  For example: "2 or 3 years ago links was 80-90% of what it took to get something ranked, Panda has changed that in an insane way. Here's the test example. Go to Google and search for 'best time to visit Tahiti'. You'll find my little site, VisualItineraries up there, #1 for that, ahead of TripAdvisor, Lonely Planet, USA Today, all these other sites. These other sites have between 10,000 and 250,000 domains linking to them. My site has under 100. I rank #1 for that. Now in case you think it's internal link, anchor text, or page title match. Here's the other proof. Do a google search for 'when should I go to French Polynesia'. The only word in that that matches the page title or any anchor text is the word 'to' - (and it's a) stop word - that's not going to count. VisualItineraries.com is #1 for that too. source: https://www.youtube.com/watch?v=7RvRUt9ejkw https://www.youtube.com/watch?v=7RvRUt9ejkw

s-c-h 9y ago

I am curious to know what major innovations in search engines happened since the page rank algorithm, or were there only incremental improvements? Also is search considered a solved problem?

saagarjha 9y ago
> Also is search considered a solved problem? I certain wouldn't, since I still encounter things that I know are on the internet but Google can't find. It's possible that the next advance won't be actually indexing the web but rather figuring out what the user wants rather than what they requested.
- ianai 9y ago
  Googles monetization strategy blinds the results. My guess would be either a way to search beyond google or force it to give results that aren’t manipulated somehow.
- osrec 9y ago
  Google does this to some extent. Recently I've found that Google uses my past queries to make cogent suggestions for my next search (essentially to predict what I want next based on prior info). Eg, if I've just searched for "sully", then a short time after type "t" into Google, the first suggestion is Tom Hanks. I've only noticed this in the last few months.
  - Swizec 9y ago
    I’ve experienced this when learning new programming languages and other domains. When you start, Google results are mostly garbage with a few useful bits. A few months later, it feels like the web is awash in materials to answer your every question and you can always find an answer for your problem in the first 5 results. Part of it is learning which phrases to use when searching, but I’m sure a big part of it is also Google figuring out what you want.
  - leggomylibro 9y ago
    My favorite example of this is the Bullet physics library. Google eventually learned to give me documentation in response to stuff like 'bullet collision', but for awhile it was big on youtube links and gun ranges.

cs702 9y ago

An oldie but a goodie. IMHO, this paper, along with Larry and Sergei's original work[0], should be part of every Linear Algebra course. Few things get students to pay attention like the mention of ungodly amounts of money! [0] http://ilpubs.stanford.edu:8090/422/1/1999-66.pdf http://ilpubs.stanford.edu:8090/422/1/1999-66.pdf

therein 9y ago
Can't speak for all linear algebra courses but my linear algebra course in college actually taught that paper for at least two lectures and a discussion section back when I took it.
- rtpg 9y ago
  I'm also pretty sure a simplified version of this was used for french entrance exams a couple years back. I remember taking a practice exam with this as the topic, at least
konschubert 9y ago
Unasked for, arrogant rant: Do you mean in school or in university? Because if somebody is taking linear algebra in university and still didn't understand that this is an extremely important topic, then he should maybe go back to school or take a gap year or something to improve his general education. From a university lecture in linear algebra, I expect that it carries me through as many important topics as possible while giving me the tools to form a good formal and intuitive understanding. The motivation part should be solved by that time.
- cyberpunk0 9y ago
  You are wrongly assuming most courses aren't taught by overworked professors or TAs who just speed run through problems with no background on the subject and more or less teach you to pass the exams. Not everyone gets ivy league lectures.
  - 9y ago

davesque 9y ago

The resources already linked from this thread are surely superior but, as a shameless plug, I wrote a blog article recently on this very topic as it was presented in my linear algebra course at CU Boulder: https://thought.place/articles/2017/7/22/pagerank/ https://thought.place/articles/2017/7/22/pagerank/

chepeadan 9y ago

Click bait title. You can say the same about sums and multiplication, they are at the basis of most trillion dollar technologies :P

jamez1 9y ago
This isn't about eigenvectors in general, it's about a single eigenvector that Google built. The title is accurate, their search product is giving you access to query the eigenvector
mathgenius 9y ago
> You can say the same about sums and multiplication Yes indeed. In particular how multiplication distributes over addition. It is powerful technology.

cdibona 9y ago

This post has happened before, it'll happen again: https://news.ycombinator.com/from?site=rose-hulman.edu https://news.ycombinator.com/from?site=rose-hulman.edu