# Link Analysis in Web Mining

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1 Problem formulation (998) Link Analysis in Web Mining Hubs and Authorities Spam Detection Suppose we are given a collection of documents on some broad topic e.g., stanford, evolution, iraq perhaps obtained through a text search Can we organize these documents in some manner? Page rank offers one solution HITS (Hypertext-Induced Topic Selection) is another proposed at approx the same time HITS Model Idealized view Interesting documents fall into two classes. Authorities are pages containing useful information course home pages home pages of auto manufacturers. Hubs are pages that link to authorities course bulletin list of US auto manufacturers Hubs Authorities Mutually recursive definition A good hub links to many good authorities A good authority is linked from many good hubs Model using two scores for each node Hub score and Authority score Represented as vectors h and a Transition Matrix A HITS uses a matrix A[i, j] = if page i links to page j, 0 if not A T, the transpose of A, is similar to the PageRank matrix M, but A T has s where M has fractions

2 Example Hub and Authority Equations Amazon Yahoo A = M soft y a m y a 0 m 0 0 The hub score of page P is proportional to the sum of the authority scores of the pages it links to h = λaa Constant λ is a scale factor The authority score of page P is proportional to the sum of the hub scores of the pages it is linked from a = µa T h Constant µ is scale factor Iterative algorithm Example Initialize h, a to all s h = Aa Scale h so that its max entry is.0 a = A T h Scale a so that its max entry is.0 Continue until h, a converge A = a(yahoo) a(amazon) a(m soft) 0 A T = 0 0 = = = 4/ h(yahoo) = h(amazon) = h(m soft) = /3 / Existence and Uniqueness Bipartite cores h = λaa a = µa T h h = λµaa T h a = λµa T A a Hubs Authorities Most densely-connected core (primary core) Under reasonable assumptions about A, the dual iterative algorithm converges to vectors h* and a* such that: h* is the principal eigenvector of the matrix AA T a* is the principal eigenvector of the matrix A T A Less densely-connected core (secondary core)

3 Secondary cores A single topic can have many bipartite cores corresponding to different meanings, or points of view abortion: pro-choice, pro-life evolution: darwinian, intelligent design jaguar: auto, Mac, NFL team, panthera onca How to find such secondary cores? Non-primary eigenvectors AA T and A T A have the same set of eigenvalues An eigenpair is the pair of eigenvectors with the same eigenvalue The primary eigenpair (largest eigenvalue) is what we get from the iterative algorithm Non-primary eigenpairs correspond to other bipartite cores The eigenvalue is a measure of the density of links in the core Finding secondary cores Once we find the primary core, we can remove its links from the graph Repeat HITS algorithm on residual graph to find the next bipartite core Technically, not exactly equivalent to non-primary eigenpair model Creating the graph for HITS We need a well-connected graph of pages for HITS to work well Page Rank and HITS Page Rank and HITS are two solutions to the same problem What is the value of an inlink from S to D? In the page rank model, the value of the link depends on the links into S In the HITS model, it depends on the value of the other links out of S The destinies of Page Rank and HITS post-998 were very different Why? Web Spam Search has become the default gateway to the web Very high premium to appear on the first page of search results e.g., e-commerce sites advertising-driven sites 3

4 What is web spam? Spamming = any deliberate action solely in order to boost a web page s position in search engine results, incommensurate with page s real value Spam = web pages that are the result of spamming This is a very broad defintion SEO industry might disagree! SEO = search engine optimization Approximately 0-5% of web pages are spam Web Spam Taxonomy We follow the treatment by Gyongyi and Garcia-Molina [004] Boosting techniques Techniques for achieving high relevance/importance for a web page Hiding techniques Techniques to hide the use of boosting From humans and web crawlers Boosting techniques Term spamming Manipulating the text of web pages in order to appear relevant to queries Link spamming Creating link structures that boost page rank or hubs and authorities scores Term Spamming Repetition of one or a few specific terms e.g., free, cheap, sale, promotion, Goal is to subvert if-idf ranking schemes The tf idf weight (term frequency inverse document frequency) is a weight often used in information retrieval and text mining. This weight is a statistical measure used to evaluate how important a word is to a document in a collection or corpus (a large and structured set of texts). The importance increases proportionally to the number of times a word appears in the document but is offset by the frequency of the word in the corpus. Variations of the tf idf weighting scheme are often used by search engines to score and rank a document's relevance given a user query. Term Spamming Repetition Dumping of a large number of unrelated terms e.g., copy entire dictionaries Weaving Copy legitimate pages and insert spam terms at random positions Phrase Stitching Glue together sentences and phrases from different sources Term spam targets Body of web page Title URL HTML meta tags Anchor text 4

5 Link spam Three kinds of web pages from a spammer s point of view pages Accessible pages e.g., web log comments pages spammer can post links to his pages Own pages Completely controlled by spammer May span multiple domain names Link Farms Spammer s goal Maximize the page rank of target page t Technique Get as many links from accessible pages as possible to target page t Construct link farm to get page rank multiplier effect Link Farms Analysis Accessible t Own One of the most common and effective organizations for a link farm M Accessible Suppose rank contributed by accessible pages = x Let page rank of target page = y Rank of each farm page = βy/m + (-β)/n y = x + βm[βy/m + (-β)/n] + (-β)/n = x + β y + β(-β)m/n + (-β)/n Very small; ignore y = x/(-β ) + cm/n where c = β/(+β) t Own M Analysis Accessible y = x/(-β ) + cm/n where c = β/(+β) For β = 0.85, /(-β )= 3.6 Multiplier effect for acquired page rank By making M large, we can make y as large as we want t Own M Hiding techniques Content hiding Use same color for text and page background Cloaking Return different page to crawlers and browsers Redirection Alternative to cloaking Redirects are followed by browsers but not crawlers 5

7 Picking the seed set Two conflicting considerations Human has to inspect each seed page, so seed set must be as small as possible Must ensure every good page gets adequate trust rank, so need make all good pages reachable from seed set by short paths Approaches to picking seed set Suppose we want to pick a seed set of k pages PageRank Pick the top k pages by page rank Assume high page rank pages are close to other highly ranked pages We care more about high page rank good pages 7

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