1、Analysis of Large Graphs: TrustRank and WebSpam,Mining of Massive Datasets Jure Leskovec, Anand Rajaraman, Jeff Ullman Stanford University http:/www.mmds.org,Note to other teachers and users of these slides: We would be delighted if you found this our material useful in giving your own lectures. Fee
2、l free to use these slides verbatim, or to modify them to fit your own needs. If you make use of a significant portion of these slides in your own lecture, please include this message, or a link to our web site: http:/www.mmds.org,Example: PageRank Scores,B 38.4,C 34.3,E 8.1,F 3.9,D 3.9,A 3.3,1.6,1.
3、6,1.6,1.6,1.6,2,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,Random Teleports ( = 0.8),y a = m,1/3 1/3 1/3,0.33 0.20 0.46,0.24 0.20 0.52,0.26 0.18 0.56,7/335/33 21/33,. . .,3,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,
4、1/2 1/2 01/2 0 00 1/2 1,1/3 1/3 1/31/3 1/3 1/31/3 1/3 1/3,y 7/15 7/15 1/15 a 7/15 1/15 1/15 m 1/15 7/15 13/15,0.8,+ 0.2,M,1/NNxN,A,r = A r,Equivalently: = + ,PageRank: The Complete Algorithm,Input: Graph and parameter Directed graph with spider traps and dead ends Parameter Output: PageRank vector S
5、et: 0 = 1 , =1 do: : () = () () = if in-degree of is 0 Now re-insert the leaked PageRank: = + =+ while () (1) ,4,where: = (),If the graph has no dead-ends then the amount of leaked PageRank is 1-. But since we have dead-ends the amount of leaked PageRank may be larger. We have to explicitly account
6、for it by computing S.,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,Some Problems with PageRank,Measures generic popularity of a page Will ignore/miss topic-specific authorities Solution: Topic-Specific PageRank (next) Uses a single measure of importance Other
7、 models of importance Solution: Hubs-and-Authorities Susceptible to Link spam Artificial link topographies created in order to boost page rank Solution: TrustRank,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,5,Topic-Specific PageRank,Topic-Specific PageRank,In
8、stead of generic popularity, can we measure popularity within a topic? Goal: Evaluate Web pages not just according to their popularity, but by how close they are to a particular topic, e.g. “sports” or “history” Allows search queries to be answered based on interests of the user Example: Query “Troj
9、an” wants different pages depending on whether you are interested in sports, history and computer security,7,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,Topic-Specific PageRank,Random walker has a small probability of teleporting at any step Teleport can go t
10、o: Standard PageRank: Any page with equal probability To avoid dead-end and spider-trap problems Topic Specific PageRank: A topic-specific set of “relevant” pages (teleport set) Idea: Bias the random walk When walker teleports, she pick a page from a set S S contains only pages that are relevant to
11、the topic E.g., Open Directory (DMOZ) pages for a given topic/query For each teleport set S, we get a different vector rS,8,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,Matrix Formulation,To make this work all we need is to update the teleportation part of the
12、 PageRank formulation: = +()/| if + otherwise A is stochastic! We weighted all pages in the teleport set S equally Could also assign different weights to pages! Compute as for regular PageRank: Multiply by M, then add a vector Maintains sparseness,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Mass
13、ive Datasets, http:/www.mmds.org,9,Example: Topic-Specific PageRank,1,2,3,4,Suppose S = 1, = 0.8,10,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,S=1,2,3,4, =0.8: r=0.13, 0.10, 0.39, 0.36 S=1,2,3 , =0.8: r=0.17, 0.13, 0.38, 0.30 S=1,2 , =0.8: r=0.26, 0.20, 0.29
14、, 0.23 S=1 , =0.8: r=0.29, 0.11, 0.32, 0.26,S=1, =0.90: r=0.17, 0.07, 0.40, 0.36 S=1 , =0.8: r=0.29, 0.11, 0.32, 0.26 S=1, =0.70: r=0.39, 0.14, 0.27, 0.19,Discovering the Topic Vector S,Create different PageRanks for different topics The 16 DMOZ top-level categories: arts, business, sports, Which to
15、pic ranking to use? User can pick from a menu Classify query into a topic Can use the context of the query E.g., query is launched from a web page talking about a known topic History of queries e.g., “basketball” followed by “Jordan” User context, e.g., users bookmarks, ,11,J. Leskovec, A. Rajaraman
16、, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,Application to Measuring Proximity in Graphs,Random Walk with Restarts: S is a single element,Proximity on Graphs,a.k.a.: Relevance, Closeness, Similarity,Tong-Faloutsos, 06,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets,
17、http:/www.mmds.org,13,Good proximity measure?,Shortest path is not good:No effect of degree-1 nodes (E, F, G)! Multi-faceted relationships,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,14,Good proximity measure?,Network flow is not good:Does not punish long pat
18、hs,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,15,What is good notion of proximity?,Multiple connectionsQuality of connectionDirect & Indirect connectionsLength, Degree, Weight,Tong-Faloutsos, 06,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Dataset
19、s, http:/www.mmds.org,16,SimRank: Idea,SimRank: Random walks from a fixed node on k-partite graphs Setting: k-partite graph with k types of nodes E.g.: Authors, Conferences, Tags Topic Specific PageRank from node u: teleport set S = u Resulting scores measures similarity to node u Problem: Must be d
20、one once for each node u Suitable for sub-Web-scale applications,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,17,Authors,Conferences,Tags,18,SimRank: Example,Conference,Author,Q: What is most relatedconference to ICDM?,J. Leskovec, A. Rajaraman, J. Ullman: Min
21、ing of Massive Datasets, http:/www.mmds.org,A: Topic-Specific PageRank with teleport set S=ICDM,SimRank: Example,19,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,PageRank: Summary,“Normal” PageRank: Teleports uniformly at random to any node All nodes have the s
22、ame probability of surfer landing there: S = 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1 Topic-Specific PageRank also known as Personalized PageRank: Teleports to a topic specific set of pages Nodes can have different probabilities of surfer landing there: S = 0.1, 0, 0, 0.2, 0, 0, 0.5, 0, 0, 0
23、.2 Random Walk with Restarts: Topic-Specific PageRank where teleport is always to the same node. S=0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,20,TrustRank: Combating the Web Spam,What is Web Spam?,Spamming: Any deliberate acti
24、on to boost a web pages position in search engine results, incommensurate with pages real value Spam: Web pages that are the result of spamming This is a very broad definition SEO industry might disagree! SEO = search engine optimizationApproximately 10-15% of web pages are spam,22,J. Leskovec, A. R
25、ajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,Web Search,Early search engines: Crawl the Web Index pages by the words they contained Respond to search queries (lists of words) with the pages containing those words Early page ranking: Attempt to order pages matching a search que
26、ry by “importance” First search engines considered: (1) Number of times query words appeared (2) Prominence of word position, e.g. title, header,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,23,First Spammers,As people began to use search engines to find things
27、 on the Web, those with commercial interests tried to exploit search engines to bring people to their own site whether they wanted to be there or not Example: Shirt-seller might pretend to be about “movies” Techniques for achieving high relevance/importance for a web page,J. Leskovec, A. Rajaraman,
28、J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,24,First Spammers: Term Spam,How do you make your page appear to be about movies? (1) Add the word movie 1,000 times to your page Set text color to the background color, so only search engines would see it (2) Or, run the query “movie” on you
29、r target search engine See what page came first in the listings Copy it into your page, make it “invisible” These and similar techniques are term spam,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,25,Googles Solution to Term Spam,Believe what people say about y
30、ou, rather than what you say about yourself Use words in the anchor text (words that appear underlined to represent the link) and its surrounding textPageRank as a tool to measure the “importance” of Web pages,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,26,Wh
31、y It Works?,Our hypothetical shirt-seller looses Saying he is about movies doesnt help, because others dont say he is about movies His page isnt very important, so it wont be ranked high for shirts or movies Example: Shirt-seller creates 1,000 pages, each links to his with “movie” in the anchor text
32、 These pages have no links in, so they get little PageRank So the shirt-seller cant beat truly important movie pages, like IMDB,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,27,Why it does not work?,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datase
33、ts, http:/www.mmds.org,28,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,29,SPAM FARMING,Google vs. Spammers: Round 2!,Once Google became the dominant search engine, spammers began to work out ways to fool GoogleSpam farms were developed to concentrate PageRank
34、on a single pageLink spam: Creating link structures that boost PageRank of a particular page,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,30,Link Spamming,Three kinds of web pages from a spammers point of view Inaccessible pages Accessible pages e.g., blog com
35、ments pages spammer can post links to his pages Owned pages Completely controlled by spammer May span multiple domain names,31,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,Link Farms,Spammers goal: Maximize the PageRank of target page tTechnique: Get as many l
36、inks from accessible pages as possible to target page t Construct “link farm” to get PageRank multiplier effect,32,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,Link Farms,One of the most common and effective organizations for a link farm,33,J. Leskovec, A. Raj
37、araman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,Millions of farm pages,Analysis,x: PageRank contributed by accessible pages y: PageRank of target page t Rank of each “farm” page = + 1 =+ + 1 + 1 =+ 2 + 1 + 1 = + where = 1+,34,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive
38、Datasets, http:/www.mmds.org,N# pages on the web M# of pages spammer owns,Analysis,= + where = 1+ For b = 0.85, 1/(1-b2)= 3.6Multiplier effect for acquired PageRank By making M large, we can make y as large as we want,35,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmd
39、s.org,N# pages on the web M# of pages spammer owns,TrustRank: Combating the Web Spam,Combating Spam,Combating term spam Analyze text using statistical methods Similar to email spam filtering Also useful: Detecting approximate duplicate pages Combating link spam Detection and blacklisting of structur
40、es that look like spam farms Leads to another war hiding and detecting spam farms TrustRank = topic-specific PageRank with a teleport set of trusted pages Example: .edu domains, similar domains for non-US schools,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,37
41、,TrustRank: Idea,Basic principle: Approximate isolation It is rare for a “good” page to point to a “bad” (spam) pageSample a set of seed pages from the webHave an oracle (human) to identify the good pages and the spam pages in the seed set Expensive task, so we must make seed set as small as possibl
42、e,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,38,Trust Propagation,Call the subset of seed pages that are identified as good the trusted pagesPerform a topic-sensitive PageRank with teleport set = trusted pages Propagate trust through links: Each page gets a
43、trust value between 0 and 1Solution 1: Use a threshold value and mark all pages below the trust threshold as spam,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,39,Simple Model: Trust Propagation,Set trust of each trusted page to 1 Suppose trust of page p is tp
44、Page p has a set of out-links op For each qop, p confers the trust to qb tp /|op| for 0 b 1 Trust is additive Trust of p is the sum of the trust conferred on p by all its in-linked pages Note similarity to Topic-Specific PageRank Within a scaling factor, TrustRank = PageRank with trusted pages as te
45、leport set,40,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,Why is it a good idea?,Trust attenuation: The degree of trust conferred by a trusted page decreases with the distance in the graphTrust splitting: The larger the number of out-links from a page, the le
46、ss scrutiny the page author gives each out-link Trust is split across out-links,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,41,Picking the Seed Set,Two conflicting considerations: Human has to inspect each seed page, so seed set must be as small as possibleMu
47、st ensure every good page gets adequate trust rank, so need make all good pages reachable from seed set by short paths,42,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,Approaches to Picking Seed Set,Suppose we want to pick a seed set of k pages How to do that?
48、(1) PageRank: Pick the top k pages by PageRank Theory is that you cant get a bad pages rank really high (2) Use trusted domains whose membership is controlled, like .edu, .mil, .gov,J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http:/www.mmds.org,43,Spam Mass,In the TrustRank model, we start with good pages and propagate trustComplementary view: What fraction of a pages PageRank comes from spam pages?In practice, we dont know all the spam pages, so we need to estimate,
