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The Anatomy of a Large-Scale Hypertextual Web Search Engine Sergey Brin, Lawrence Page Presented By: Paolo Lim April 10, 2007 CS 331 - Data Mining 1 AKA: The Original Google Paper Larry Page and Sergey Brin CS 331 - Data Mining 2 Presentation Outline Design goals of Google search engine Link Analysis and other features System architecture and major structures Crawling, indexing, and searching the web Performance and results Conclusions Final exam questions CS 331 - Data Mining 3 Linear Algebra Background PageRank involves knowledge of: Matrix addition/multiplication Eigenvectors and Eigenvalues Power iteration Dot product Not discussed in detail in presentation For reference: http://cs.wellesley.edu/~cs249B/math/Linear%20Alg ebra/CS298LinAlgpart1.pdf http://www.cse.buffalo.edu/~hungngo/classes/2005/ Expanders/notes/LA-intro.pdf CS 331 - Data Mining 4 Google Design Goals Scaling with the web’s growth Improved search quality Number of documents increasing rapidly, but user’s ability to look at documents lags Lots of “junk” results, little relevance Academic search engine research Development and understanding in academic realm System that reasonable number of people can actually use Support novel research activities of large-scale web data by other researchers and students CS 331 - Data Mining 5 Link Analysis Basics PageRank Algorithm A Top 10 IEEE ICDM data mining algorithm Large basis for ranking system (discussed later) Tries to incorporate ideas from academic community (publishing and citations) Anchor Text Analysis <a href=http://www.com> ANCHOR TEXT </a> CS 331 - Data Mining 6 Intuition: Why Links, Anyway? Links represent citations Quantity of links to a website makes the website more popular Quality of links to a website also helps in computing rank Link structure largely unused before Larry Page proposed it to thesis advisor CS 331 - Data Mining 7 Naïve PageRank Each link’s vote is proportional to the importance of its’ source page If page P with important I has N outlinks, then each link gets I / N votes Simple recursive formulation: PR(A) = PR(p1)/C(p1) + … + PR(pn)/C(pn) PR(X) PageRank of page X C(X) number of links going out of page X CS 331 - Data Mining 8 Naïve PageRank Model (from http://www.stanford.edu/class/cs345a/lectureslides/PageRank.pdf) The web in 1839 y = y /2 + a /2 y/2 a = y /2 + m Yahoo y m = a /2 a/2 y/2 m Amazon M’soft a/2 m a CS 331 - Data Mining 9 Solving the flow equations 3 equations, 3 unknowns, no constants No unique solution All solutions equivalent modulo scale factor Additional constraint forces uniqueness y+a+m = 1 y = 2/5, a = 2/5, m = 1/5 Gaussian elimination method works for small examples, but we need a better method for large graphs CS 331 - Data Mining 10 Matrix formulation Matrix M has one row and one column for each web page Suppose page j has n outlinks If j ! i, then Mij=1/n Else Mij=0 M is a column stochastic matrix Columns sum to 1 Suppose r is a vector with one entry per web page ri is the importance score of page i Call it the rank vector CS 331 - Data Mining 11 Example (from http://www.stanford.edu/class/cs345a/lectureslides/PageRank.pdf) Suppose page j links to 3 pages, including i j i i = 1/3 M r r CS 331 - Data Mining 12 Eigenvector formulation The flow equations can be written r = Mr So the rank vector is an eigenvector of the stochastic web matrix In fact, its first or principal eigenvector, with corresponding eigenvalue 1 CS 331 - Data Mining 13 Example (from http://www.stanford.edu/class/cs345a/lectureslides/PageRank.pdf) y a m Yahoo y 1/2 1/2 0 a 1/2 0 1 m 0 1/2 0 r = Mr Amazon M’soft y 1/2 1/2 0 y y = y /2 + a /2 a = 1/2 0 1 a a = y /2 + m m 0 1/2 0 m m = a /2 CS 331 - Data Mining 14 Power Iteration Simple iterative scheme (aka relaxation) Suppose there are N web pages Initialize: r0 = [1,….,1]T Iterate: rk+1 = Mrk Stop when |rk+1 - rk|1 < |x|1 = 1·i·N|xi| is the L1 norm Can use any other vector norm e.g., Euclidean CS 331 - Data Mining 15 Power Iteration Example (from http://www.stanford.edu/class/cs345a/lectureslides/PageRank.pdf) Yahoo y a m y 1/2 1/2 0 a 1/2 0 1 m 0 1/2 0 Amazon M’soft y 1 1 5/4 9/8 6/5 a = 1 3/2 1 22/24 . . . 6/5 m 1 1/2 3/4 1/2 3/5 CS 331 - Data Mining 16 Random Surfer Imagine a random web surfer At any time t, surfer is on some page P At time t+1, the surfer follows an outlink from P uniformly at random Ends up on some page Q linked from P Process repeats indefinitely Let p(t) be a vector whose ith component is the probability that the surfer is at page i at time t p(t) is a probability distribution on pages CS 331 - Data Mining 17 The stationary distribution Where is the surfer at time t+1? Follows a link uniformly at random p(t+1) = Mp(t) Suppose the random walk reaches a state such that p(t+1) = Mp(t) = p(t) Then p(t) is called a stationary distribution for the random walk Our rank vector r satisfies r = Mr So it is a stationary distribution for the random surfer CS 331 - Data Mining 18 Spider traps A group of pages is a spider trap if there are no links from within the group to outside the group Random surfer gets trapped Spider traps violate the conditions needed for the random walk theorem CS 331 - Data Mining 19 Microsoft becomes a spider trap (from http://www.stanford.edu/class/cs345a/lectureslides/PageRank.pdf) Yahoo y a m y 1/2 1/2 0 a 1/2 0 0 m 0 1/2 1 Amazon M’soft y 1 1 3/4 5/8 0 a = 1 1/2 1/2 3/8 ... 0 m 1 3/2 7/4 2 3 CS 331 - Data Mining 20 Random teleports The Google solution for spider traps At each time step, the random surfer has two options: With probability , follow a link at random With probability 1-, jump to some page uniformly at random Common values for are in the range 0.8 to 0.9 Surfer will teleport out of spider trap within a few time steps CS 331 - Data Mining 21 Matrix formulation Suppose there are N pages Consider a page j, with set of outlinks O(j) We have Mij = 1/|O(j)| when j!i and Mij = 0 otherwise The random teleport is equivalent to adding a teleport link from j to every other page with probability (1-)/N reducing the probability of following each outlink from 1/|O(j)| to /|O(j)| Equivalent: tax each page a fraction (1-) of its score and redistribute evenly Mining CS 331 - Data 22 Page Rank Construct the NxN matrix A as follows Aij = Mij + (1-)/N Verify that A is a stochastic matrix The page rank vector r is the principal eigenvector of this matrix satisfying r = Ar Equivalently, r is the stationary distribution of the random walk with teleports CS 331 - Data Mining 23 Previous example with =0.8 (from http://www.stanford.edu/class/cs345a/lectureslides/PageRank.pdf) 1/2 1/2 0 1/3 1/3 1/3 Yahoo 0.8 1/2 0 0 + 0.2 1/3 1/3 1/3 0 1/2 1 1/3 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 Amazon M’soft y 1 1.00 0.84 0.776 7/11 a = 1 0.60 0.60 0.536 . . . 5/11 m 1 1.40 1.56 1.688 21/11 CS 331 - Data Mining 24 Dead ends Pages with no outlinks are “dead ends” for the random surfer Nowhere to go on next step CS 331 - Data Mining 25 Microsoft becomes a dead end (from http://www.stanford.edu/class/cs345a/lectureslides/PageRank.pdf) 1/2 1/2 0 1/3 1/3 1/3 Yahoo 0.8 1/2 0 0 + 0.2 1/3 1/3 1/3 0 1/2 0 1/3 1/3 1/3 y 7/15 7/15 1/15 a 7/15 1/15 1/15 m 1/15 7/15 1/15 Amazon M’soft y Non- 1 1 0.787 0.648 0 a = stochastic! 1 0.6 0.547 0.430 . . . 0 m 1 0.6 0.387 0.333 0 CS 331 - Data Mining 26 Dealing with dead-ends Teleport Follow random teleport links with probability 1.0 from dead-ends Adjust matrix accordingly Prune and propagate Preprocess the graph to eliminate dead-ends Might require multiple passes Compute page rank on reduced graph Approximate values for dead ends by propagating values from reduced graph CS 331 - Data Mining 27 Anchor Text Can be more accurate description of target site than target site’s text itself Can point at non-HTTP or non-text Images Videos Databases Possible for non-crawled pages to be returned in the process CS 331 - Data Mining 28 Other Features List of occurrences of a particular word in a particular document (Hit List) Location information and proximity Keeps track of visual presentation details: Font size of words Capitalization Bold/Italic/Underlined/etc. Full raw HTML of all pages is available in repository CS 331 - Data Mining 29 Google Architecture (from http://www.ics.uci.edu/~scott/google.htm) Implemented in C and C++ on Solaris and Linux CS 331 - Data Mining 30 Google Architecture (from http://www.ics.uci.edu/~scott/google.htm) Multiple crawlers run in parallel. Keeps track of URLs Each crawler keeps its own DNS Compresses and that have and need lookup cache and ~300 open stores web pages to be crawled connections open at once. Stores each link and text surrounding link. Converts relative URLs into absolute URLs. Uncompresses and parses Contains full html of every web link documents. Stores- Data Mining CS 331 page. Each document is prefixed 31 information in anchors file. by docID, length, and URL. Google Architecture (from http://www.ics.uci.edu/~scott/google.htm) Maps absolute URLs into docIDs stored in Doc Parses & distributes hit lists into Index. Stores anchor text in “barrels”. “barrels.” Generates database of links (pairs of docIds). Partially sorted forward indexes sorted by docID. Each barrel stores hitlists for a given range of wordIDs. In-memory hash table that maps words to wordIds. Contains pointer to doclist in barrel which wordId falls into. Creates inverted index whereby document list containing docID and hitlists can be retrieved given wordID. DocID keyed index where each entry includes info such as pointer to doc in repository, checksum, statistics, status, etc. Also contains URL info if doc 32 CS 331 - Data Mining has been crawled. If not just contains URL. Google Architecture (from http://www.ics.uci.edu/~scott/google.htm) 2 kinds of barrels. Short barrell which contain hit list which include title or anchor hits. Long barrell for all hit lists. List of wordIds produced by Sorter and lexicon created by Indexer used New lexicon keyed by to create new lexicon wordID, inverted doc used by searcher. Lexicon index keyed by docID, stores ~14 million words. and PageRanks used to answer queries CS 331 - Data Mining 33 Google Query Evaluation 1. Parse the query. 2. Convert words into wordIDs. 3. Seek to the start of the doclist in the short barrel for every word. 4. Scan through the doclists until there is a document that matches all the search terms. 5. Compute the rank of that document for the query. 6. If we are in the short barrels and at the end of any doclist, seek to the start of the doclist in the full barrel for every word and go to step 4. 7. If we are not at the end of any doclist go to step 4. 8. Sort the documents that have matched by rank and return the top k. CS 331 - Data Mining 34 Single Word Query Ranking Hitlist is retrieved for single word Each hit can be one of several types: title, anchor, URL, large font, small font, etc. Each hit type is assigned its own weight Type-weights make up vector of weights Number of hits of each type is counted to form count-weight vector Dot product of type-weight and count-weight vectors is used to compute IR score IR score is combined with PageRank to compute final rank CS 331 - Data Mining 35 Multi-word Query Ranking Similar to single-word ranking except now must analyze proximity of words in a document Hits occurring closer together are weighted higher than those farther apart Each proximity relation is classified into 1 of 10 bins ranging from a “phrase match” to “not even close” Each type and proximity pair has a type-prox weight Counts converted into count-weights Take dot product of count-weights and type-prox weights to computer for IR score CS 331 - Data Mining 36 Scalability Cluster architecture combined with Moore’s Law make for high scalability. At time of writing: ~ 24 million documents indexed in one week ~518 million hyperlinks indexed Four crawlers collected 100 documents/sec CS 331 - Data Mining 37 Key Optimization Techniques Each crawler maintains its own DNS lookup cache Use flex to generate lexical analyzer with own stack for parsing documents Parallelization of indexing phase In-memory lexicon Compression of repository Compact encoding of hit lists for space saving Indexer is optimized so it is just faster than the crawler so that crawling is the bottleneck Document index is updated in bulk Critical data structures placed on local disk Overall architecture designed avoid to disk seeks wherever possible CS 331 - Data Mining 38 Storage Requirements (from http://www.ics.uci.edu/~scott/google.htm) At the time of publication, Google had the following statistical breakdown for storage requirements: CS 331 - Data Mining 39 Conclusions Search is far from perfect Topic/Domain-specific PageRank Machine translation in search Non-hypertext search Business potential Brin and Page worth around $15 billion each… at 32 years old! If you have a better idea than how Google does search, please remember me when you’re hiring software engineers! CS 331 - Data Mining 40 Possible Exam Questions Given a web/link graph, formulate a Naïve PageRank link matrix and do a few steps of power iteration. Slides 14 – 16 What are spider traps and dead ends, and how does Google deal with these? Spider Trap: Slides 19 – 21 Dead End: Slides 25 – 27 Explain difference between single and multiple word search query evaluation. Slides 35 – 36 CS 331 - Data Mining 41 References Brin, Page. The Anatomy of a Large-Scale Hypertextual Web Search Engine. Brin, Page, Motwani, Winograd. The PageRank Citation Ranking: Bringing Order to the Web. http://www.stanford.edu/class/cs345a/lectureslid es/PageRank.pdf www.cs.duke.edu/~junyang/courses/cps296.1- 2002-spring/lectures/02-web-search.pdf http://www.ics.uci.edu/~scott/google.htm CS 331 - Data Mining 42 Thank you! CS 331 - Data Mining 43

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