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Link Analysis: Current State of the Art Ronen Feldman Computer Science Department Bar-Ilan University, ISRAEL

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Presentation on theme: "Link Analysis: Current State of the Art Ronen Feldman Computer Science Department Bar-Ilan University, ISRAEL"— Presentation transcript:

1 Link Analysis: Current State of the Art Ronen Feldman Computer Science Department Bar-Ilan University, ISRAEL

2 Introduction to Text Mining

3 Find Documents matching the Query Display Information relevant to the Query Extract Information from within the documents Actual information buried inside documents Long lists of documents Aggregate over entire collection

4 Read Consolidate Absorb / Act Understand Find Material Let Text Mining Do the Legwork for You Text Mining

5 What Is Unique in Text Mining? Feature extraction. Very large number of features that represent each of the documents. The need for background knowledge. Even patterns supported by small number of document may be significant. Huge number of patterns, hence need for visualization, interactive exploration.

6 Document Types Structured documents –Output from CGI Semi-structured documents –Seminar announcements –Job listings –Ads Free format documents –News –Scientific papers

7 Text Representations Character Trigrams Words Linguistic Phrases Non-consecutive phrases Frames Scripts Role annotation Parse trees

8 The 100,000 foot Picture

9 Intelligent Auto-Tagging (c) 2001, Chicago Tribune. Visit the Chicago Tribune on the Internet at Distributed by Knight Ridder/Tribune Information Services. By Stephen J. Hedges and Cam Simpson Finsbury Park Mosque Abu Hamza al-Masri chief cleric Finsbury Park Mosque England Abu Hamza al-Masri London 1999 his alleged involvement in a Yemen bomb plot England France United States Belgium Abu Hamza al-Masri London ……. The Finsbury Park Mosque is the center of radical Muslim activism in England. Through its doors have passed at least three of the men now held on suspicion of terrorist activity in France, England and Belgium, as well as one Algerian man in prison in the United States. ``The mosque's chief cleric, Abu Hamza al- Masri lost two hands fighting the Soviet Union in Afghanistan and he advocates the elimination of Western influence from Muslim countries. He was arrested in London in 1999 for his alleged involvement in a Yemen bomb plot, but was set free after Yemen failed to produce enough evidence to have him extradited..'' ……

10 Intelligence Article

11 Google’s Article

12 Merger

13 Leveraging Content Investment Any type of content Unstructured textual content (current focus) Structured data; audio; video (future) From any source WWW; file systems; news feeds; etc. Single source or combined sources In any format Documents; PDFs; E-mails; articles; etc “Raw” or categorized Formal; informal; combination

14 Information Extraction

15 Relevant IE Definitions Entity: an object of interest such as a person or organization. Attribute: a property of an entity such as its name, alias, descriptor, or type. Fact: a relationship held between two or more entities such as Position of a Person in a Company. Event: an activity involving several entities such as a terrorist act, airline crash, management change, new product introduction.

16 IE Accuracy by Information Type Information Type Accuracy Entities90-98% Attributes80% Facts60-70% Events50-60%

17 MUC Conferences ConferenceYearTopic MUC 11987 Naval Operations MUC 21989 Naval Operations MUC 31991 Terrorist Activity MUC 41992 Terrorist Activity MUC 51993 Joint Venture and Micro Electronics MUC 61995 Management Changes MUC 71997 Spaces Vehicles and Missile Launches

18 Applications of Information Extraction Routing of Information Infrastructure for IR and for Categorization (higher level features) Event Based Summarization. Automatic Creation of Databases and Knowledge Bases.

19 Where would IE be useful? Semi-Structured Text Generic documents like News articles. Most of the information in the document is centered around a set of easily identifiable entities.

20 Approaches for Building IE Systems Knowledge Engineering Approach –Rules are crafted by linguists in cooperation with domain experts. –Most of the work is done by inspecting a set of relevant documents. –Can take a lot of time to fine tune the rule set. –Best results were achieved with KB based IE systems. –Skilled/gifted developers are needed. –A strong development environment is a MUST!

21 Approaches for Building IE Systems Automatically Trainable Systems –The techniques are based on pure statistics and almost no linguistic knowledge –They are language independent –The main input is an annotated corpus –Need a relatively small effort when building the rules, however creating the annotated corpus is extremely laborious. –Huge number of training examples is needed in order to achieve reasonable accuracy. –Hybrid approaches can utilize the user input in the development loop.

22 Components of IE System

23 Why is IE Difficult? Different Languages –Morphology is very easy in English, much harder in German and Hebrew. –Identifying word and sentence boundaries is fairly easy in European language, much harder in Chinese and Japanese. –Some languages use orthography (like english) while others (like hebrew, arabic etc) do no have it. Different types of style –Scientific papers –Newspapers –memos –Emails –Speech transcripts Type of Document –Tables –Graphics –Small messages vs. Books

24 Link Analysis on Large Textual Networks Social Network Analysis

25 The Kevin Bacon Game The game works as follows: given any actor, find a path between the actor and Kevin Bacon that has less than 6 edges. For instance, Kevin Costner links to Kevin Bacon by using one direct link: Both were in JFK. Julia Louis-Dreyfus of TV's Seinfeld, however, needs two links to make a path: Julia Louis- Dreyfus was in Christmas Vacation (1989) with Keith MacKechnie. Keith MacKechnie was in We Married Margo (2000) with Kevin Bacon.Julia Louis- DreyfusChristmas Vacation (1989) Keith MacKechnie We Married Margo (2000)Kevin Bacon You can play the game by using the following URL

26 The Erdos Number A similar idea is also used in the mathematical society and is called the Erdös number of a researcher. Paul Erdös (1913–1996), wrote hundreds of mathematical research papers in many different areas, many in collaboration with others.Paul Erdös There is a link between any two mathematicians if they co-authored a paper. Paul Erdös is the root of the mathematical research network and his Erdös number is 0. Erdös’s co-authors have Erdös number 1. People other than Erdös who have written a joint paper with someone with Erdös number 1 but not with Erdös have Erdös number 2, and so on.

27 Running Example

28 Hijackers by Flight Flight 77 : PentagonFlight 11 : WTC 1Flight 175 : WTC 2Flight 93: PA Khalid Al-Midhar Satam Al Suqami Marwan Al-Shehhi Saeed Alghamdi Majed Moqed Waleed M. Alshehri Fayez Ahmed Ahmed Alhaznawi Nawaq Alhamzi Wail Alshehri Ahmed Alghamdi Ahmed Alnami Salem Alhamzi Mohamed Atta Hamza Alghamdi Ziad Jarrahi Hani Hanjour Abdulaziz Alomari Mohald Alshehri

29 Automatic layout of networks Pretty Graph Drawing

30 Motivation I In order to display large networks on the screen we need to use automatic layout algorithms. These algorithms display the graphs in an aesthetic way without any user intervention. The most commonly used aesthetic criteria are to expose symmetries and make drawing as compact as possible or alternatively fill the space available for the drawing.

31 Motivation II Many of the “higher-level” aesthetic criteria are implicit consequences of: –minimized number of edge crossings –evenly distributed edge length –evenly distributed vertex positions on the graph area –sufficiently large vertex-edge distances –sufficiently large angular resolution between edges.

32 Disadvantages of the Spring based methods They are computationally expensive and hence minimizing the energy function when dealing with large graphs is computationally prohibitive. Since all methods rely on heuristics, there is no guarantee that the “best” layout will be found. The methods behave as black boxes and hence it is almost impossible to integrate additional constraints on the layout (such as fixing the positions of certain vertices, or specifying the relative ordering of the vertices) Even when the graphs are planar it is quite possible that we will get edge crossings. The methods try to optimize just the placement of vertices and edges while ignoring the exact shape of the vertices or the fact the vertices may have labels.

33 Kamada and Kawai’s (KK) Method

34 Fruchterman Reingold (FR) Method

35 Classic Graph Operations

36 Finding the shortest Path (from Atta)

37 A better Visualization

38 Centrality

39 Degree If the graph is undirected then the degree of a vertex v  V is the number of other vertices that are directly connected to it. –degree(v) = |{(v1, v2)  E | v1 = v or v2 = v}| If the graph is directed then we can talk about in-degree or out-degree. An edge (v1,v2)  E in the directed graph is leading from vertex v1 to v2. –In-degree(v) = |{(v1, v)  E }| –Out-degree(v) = |{(v, v2)  E }|

40 Degree of the Hijackers

41 Closeness Centrality - Motivation Degree centrality measures might be criticized because they only take into account the direct connections that an entity has, rather than indirect connections to all other entities. One entity might be directly connected to a large number of entities that might be pretty isolated from the network. Such an entity is central only in a local neighborhood of the network.

42 Closeness Centrality This measure is based on the calculation of the geodesic distance between the entity and all other entities in the network. We can either use directed or undirected geodesic distances between the entities. The sum of these geodesic distances for each entity is the "farness" of the entity from all other entities. We can convert this into a measure of closeness centrality by taking the reciprocal. In addition, we can normalize the closeness measure by dividing it by the closeness measure of the most central entity.

43 Closeness : Formally let d(v1,v2) = the minimal distance between v1 and v2, i.e., the minimal number of vertices that we need to pass on the way from v1 to v2.

44 Closeness of the Hijackers NameCloseness Abdulaziz Alomari0.6 Ahmed Alghamdi0.5454545 Ziad Jarrahi0.5294118 Fayez Ahmed0.5294118 Mohamed Atta0.5142857 Majed Moqed0.5142857 Salem Alhamzi0.5142857 Hani Hanjour0.5 Marwan Al Shehhi0.4615385 Satam Al Suqami0.4615385 Waleed M. Alshehri0.4615385 Wail Alshehri0.4615385 Hamza Alghamdi0.45 Khalid Al Midhar0.4390244 Mohald Alshehri0.4390244 Nawaq Alhamzi0.3673469 Saeed Alghamdi0.3396226 Ahmed Alnami0.2571429 Ahmed Alhaznawi0.2571429

45 Betweeness Centrality The betweeness centrality measures the effectiveness in which the vertex connects the various parts of the network. The main idea behind betweeness centrality is that entities that are mediators have more power. Entities that are on many geodesic paths between other pairs of entities are more powerful since they control the flow of information between the pairs.

46 Betweeness - Formally Highest Possible Betweeness g jk = the number of geodetic paths that connect v j with v k g jk (v i ) = the number of geodetic paths that connect v j with v k and pass via v i.

47 Betweenness of the Hijackers

48 Eigen Vector Centrality The main idea behind eigenvector centrality is that entities receiving many communications from other well connected entities, will be better and more valuable sources of information, and hence be considered central. The Eigenvector centrality scores correspond to the values of the principal eigenvector of the adjacency matrix M. Formally, the vector v satisfies the equation where is the corresponding eigenvalue and M is the adjacency matrix.

49 EigenVector centralities of the hijackers NameE1 Mohamed Atta0.518 Marwan Al-Shehhi0.489 Abdulaziz Alomari0.296 Ziad Jarrahi0.246 Fayez Ahmed0.246 Satam Al Suqami0.241 Waleed M. Alshehri0.241 Wail Alshehri0.241 Salem Alhamzi0.179 Majed Moqed0.165 Hani Hanjour0.151 Khalid Al-Midhar0.114 Ahmed Alghamdi0.085 Nawaq Alhamzi0.064 Mohald Alshehri0.054 Hamza Alghamdi0.015 Saeed Alghamdi0.002 Ahmed Alnami0 Ahmed Alhaznawi0

50 Power Centrality Given an adjacency matrix M, the power centrality of vertex i (denoted ci), is given by  is used to normalize the score; the normalization parameter is automatically selected so that the sum of squares of the vertices’s centralities is equal to the number of vertices in the network.  is an attenuation factor that controls the effect that the power centralities of the neighboring vertices should have on the power centrality of the vertex.

51 Power - Motivation In a similar way to the eigenvector centrality, the power centrality of each vertex is determined by the centrality of the vertices it is connected to. By specifying positive or negative values to  the user can control if the fact that a vertex is connected to powerful vertices should have a positive effect on its score or a negative effect. The rational for specifying a positive  is that if you are connected to powerful colleagues it makes you more powerful. On the other hand, the rational for a negative  is that powerful colleagues have many connections and hence are not controlled by you, while isolated colleagues have no other sources of information and hence are pretty much controlled by you.

52 Power of the Hijackers Power :  = 0.99Power :  = -0.99 Mohamed Atta2.2542.214 Marwan Al-Shehhi2.1210.969 Abdulaziz Alomari1.2961.494 Ziad Jarrahi1.071.087 Fayez Ahmed1.071.087 Satam Al Suqami1.0470.861 Waleed M. Alshehri1.0470.861 Wail Alshehri1.0470.861 Salem Alhamzi0.7951.153 Majed Moqed0.731.029 Hani Hanjour0.6731.334 Khalid Al-Midhar0.5030.596 Ahmed Alghamdi0.380.672 Nawaq Alhamzi0.2880.574 Mohald Alshehri0.2360.467 Hamza Alghamdi0.070.566 Saeed Alghamdi0.0120.656 Ahmed Alnami0.0030.183 Ahmed Alhaznawi0.0030.183

53 Network Centralization In addition to the individual vertex centralization measures, we can assign a number between 0 and 1 that will signal the level of centralization of the whole network. The network centralization measures will be computed based on the centralization values of its vertices and hence we will have for type of individual centralization measure an associated network centralization measure. A network that is structured like a circle will have a network centralization value of 0 (since all vertices have the same centralization value), while a network that structured like a star will have a network centralization value of 1. We will now provide some of the formulas for the different network centralization measures.

54 Degree For the Hijackers network Net Degree = 0.31

55 Betweenness For the Hijackers network Net Bet = 0.24

56 Summary Diagram

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