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Our purpose Giving a query on the Web, how can we find the most authoritative (relevant) pages?

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The obstacles The quality of a search method necessarily requires human evaluation What is relevant, really? There are several types of query.

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The obstacles Query types: Specific queries: “Does Netscape support the JDK 1.1 codesigning API?” Broad-topic queries: “Find information about the Java programming language.” Similar-page queries: “Find pages ‘similar’ to java.sun.com.”

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The obstacles Specific queries raise a problem called Scarcity Problem – there are very few pages that contain the required information, and it is often difficult to determine the identity of these pages. Broad-topic queries raise a problem of Abundance – The number of pages that could reasonably be returned as relevant is far too large for a human user to digest.

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The obstacles Most importantly: How will we determine whether a certain page is relevant? - The Harvard problem - www.harvard.eduwww.harvard.edu - The search engine problem - lack of self description

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Using links Idea: use the links within the pages rather then the text. Using links gives us the someone’s judgment about the relevance of a page. Solves the problem: lack of self describing.

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Using links Disadvantage: Links can be used for various reasons – commercials or “for home page press here”. Finding balance between relevance and popularity

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Using links An idea: 1. Choose all pages that contain the query string. 2. Calculate the number of times each of them is being linked to. 3. Return C most linked pages. www.yahoo.com will be popular in respect to any query

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Using Links Hubs: Pages that have many links to related authorities Step 1: Build a base graph 1. relatively small 2. rich in relevant pages 3. contains most of the strongest authorities.

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Building a subgraph d = 50t = 200

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Building a subgraph |S| ≈ 1000 - 5000

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Building a subgraph |S| ≈ 1000 - 5000 Reducing the graph even farther: 1. Delete intrinsic links (transverse, intrinsic) 2. Only allow m pages from the same domain to point to a certain page.

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Computing Hubs and Authorities Now that we have a reasonably sized graph, we can find the most quality information using only link structure. This time, if we rank pages according to in-degree we’ll mostly get good results. But… search: java results: www.gamelan.comwww.gamelan.com java.sun.com Caribbean vacations commercials Amazon Good! Popular Good! Popular

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Computing Hubs and Authorities Maybe links are not enough then? Can we override the problem without an additional text-based algorithm? Hubs: pages that link to many related authorities

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Computing Hubs and Authorities Solution: Hubs can help discard irrelevant popular pages.

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Computing Hubs and Authorities Observation: a good hub is a page that points to many good authorities; a good authority is a page that is pointed to by many good hubs. We need to break down the circularity.

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Computing Hubs and Authorities The invariant that the weights: If p points to many pages with large x-values, then it should receive a large y-value; and if p is pointed to by many pages with large y-values, then it should receive a large x-value.

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Computing Hubs and Authorities 1) 2)

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Computing Hubs and Authorities

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Now we can filter the c best pages: 5 <= c <= 10 For an arbitrary large k, all values converge to fixed points.

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Computing Hubs and Authorities Small reminder – from linear algebra: Eigenvalues and eigenvectors: An eigenvector or characteristic vector of a square matrix A is a non-zero vector v that, when multiplied with A, yields a scalar multiple of itself. That is: The number λ is called the eigenvalue of A corresponding to v. Transope: the transpose of a matrix A is another matrix A T, such that.

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Computing Hubs and Authorities A is the matrix: The principal eigenvector is the vector that corresponds with the biggest |λ|.

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Computing Hubs and Authorities “Java”: “Search engines”:

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Computing Hubs and Authorities Censorship:

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Similar-Page Queries This algorithm can also be used to determine similarity between pages. Those can be very hard to answer via text-only. Change the algorithm: Instead of starting with: “find t pages that contain the string σ” start with : “find t pages pointing to p”.

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Similar-Page Queries Why not sort by in links now? searching www.honda.comwww.honda.com In-links only:

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Similar-Page Queries Using Hubs and authorities:

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Multiple Sets of Hubs and Authorities This algorithm is, in a sense, finding the most densely linked collection of hubs and authorities in the subgraph. Sometimes we wish to represent more than just one such collection.

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Multiple Sets of Hubs and Authorities The non-principal eigenvectors of and provide us with a natural way to extract additional densely linked collections of hubs and authorities from the base set.

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Multiple Sets of Hubs and Authorities Examples: searching “jaguar*” Principal eigenvector Atari jaguar product

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Multiple Sets of Hubs and Authorities 2 nd non-Principal eigenvector National football league team

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Multiple Sets of Hubs and Authorities 3 rd non-Principal eigenvector Jaguar cars

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Multiple Sets of Hubs and Authorities Examples: searching “abortion”

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Multiple Sets of Hubs and Authorities Examples: searching “randomized algorithms”

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Diffusion and Generalization For specific queries - the answer very often represents a natural generalization of the query string. Searching “www conferences”:

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Diffusion and Generalization searching “sigact.acm.org”:

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Diffusion and Generalization Taking the 11 th nonprincipal vector:

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Evaluation How can we evaluate the algorithm? Relevance is subjective Diversity of authoring styles Maybe it can’t even be assessed Comparison.

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Evaluation Testing CLEVER system: Yahoo!, Alta Vista 26 topics 10 pages per topic 5 tops hubs, 5 top authorities. 37 users. All the results were presented as one. “bad”, “fair”, “good” or “fantastic”

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Evaluation The results: 31% - Yahoo! And CLEVER were equivalent 19% - Yahoo! Was more successful. 50% - CLEVER was the more successful.

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Conclusion - The algorithm produces better results that text-based search. - It seems it serves better as a starting point for better and improved searching methods rather than a stand alone search.

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Link Analysis, PageRank and Search Engines on the Web

Link Analysis, PageRank and Search Engines on the Web

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