Networks Navigability: Theory and Applications

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Networks Navigability: Theory and Applications

  1. 1. Networks Navigability: Theory and Applications Denis Helic & Christoph Trattner KMI, TU Graz August 31, 2011Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 1 / 75
  2. 2. Internet of Things http://www.youtube.com/watch?v=sfEbMV295KkDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 2 / 75
  3. 3. Internet of Things We are heading towards a completely interconnected society Where people, devices, sensors are all connected to each other producing billions of billions of data each day...Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 3 / 75
  4. 4. Internet of Things One big challenge in this context is how we can find relevant information in such a networked world of data Hence, in this presentation: Latest research results on the navigability of such networks will be shownDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 4 / 75
  5. 5. Internet of Things In particular I will show: what are structural clues that make such networks navigable/searchable? In addition to this, I will present a framework that is able to measure network navigability. and I will present two algorithms to generate efficient navigational tools for that networks.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 5 / 75
  6. 6. Networks What are networks? Basically a network is a system that can be modeled with graphs. Graphs are mathematical structures consisting of vertices and edges connecting the vertices When we observe large graphs that exist in nature, societies, or systems we refer to them as networksDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 6 / 75
  7. 7. Networks What are popular examples of such networks? Social networks. Nodes are people and links are acquaintances, friendship, and so on. Communication networks. Internet: nodes are computers and links are cables connecting computers Biological networks. Metabolism: nodes are substances and links are metabolic reactions Information networks. Web: nodes are Web pages and links are hyperlinks connecting pagesDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 7 / 75
  8. 8. Networks 6 How to search in a small world Pajek Figure 2: HP Labs’ email communication (light grey lines) mapped onto the organizational Figure: Social network of lines). Note that communication tends to “cling” toof formal organizational hierarchy (black HP Labs constructed out the e-mail communication. chart. From: How to search a social network, Adamic, 2005. with one another. The h-distance, used to navigate the network, is computed as follows: individuals have h-distance one to their manager and to everyone they share a manager with. Distances are then recursively assigned, so that each individual has h-distance 2 to their first neighbor’s neighbors, and h-distance 3 to their secondDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 8 / 75
  9. 9. Networks Figure: Network of pages and hyperlinks on a Website. From: Networks, Mark Newman, 2011.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 9 / 75
  10. 10. Structure and Function of Networks One of the most important research questions in the study of networks: what is the relation between structure and function of networks For example, the Internet – how should the link structure of the Internet look like that supports efficient routing? Or how should the link structure of the Web look like to be efficient navigable? In this presentation we will focus on network navigability!Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 10 / 75
  11. 11. Network Navigability Definition Put simple, a network is navigable if and only if there is a short path between all or almost all pairs of nodes in the network. Formally: 1 There exist a giant component 2 The effective diameter is low – bounded by log (n), where n is the number of nodes in the networkDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 11 / 75
  12. 12. Network Navigability Knowledge Management Institute Navigability: Examples Example 1: Example 1: Not navigable: No giant component Figure: Network is not navigable because there is no giant component, i.e. the network is not connected. Example 2: Not navigable: giant component, BUT eff.diam: 7 > log2(8)Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 12 / 75
  13. 13. Example 1: Network Navigability Not navigable: No giant component Example 2: Example 2: Not navigable: giant component, BUT Figure: Now, there is a giant component, i.e. the network is connected. However the network is not navigable because eff .diam = > log26 > log2 (8). eff.diam: 7 6, and (8) Denis Helic 2010 7Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 13 / 75
  14. 14. Network Navigability Knowledge Management Institute Navigability: Examples Example 3: Figure: The network is navigable because there is AND component and Navigable: Giant component a giant eff .diam = 2. Effective diamater is boundedlog2(10) eff.diam: 2 < by log2 (10). Is this efficiently navigable? There are short paths between all nodes, but can an agent or algorithm find them with local knowledge only?Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 14 / 75
  15. 15. Global Network Navigability We discussed so far global network navigability Suppose that the network is navigable and we have global knowledge of network Then it is easy to design efficient procedures to find an arbitrary target node from an arbitrary start node For example, breadth-first search is such an algorithm that has linear time complexity O(n + m), where m is the number of links Such procedures are called centralized searchDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 15 / 75
  16. 16. Local Network Navigability Let us now discuss local network navigability Suppose that the network is navigable but we have only local knowledge of network That means when we arrive at a particular node we know only outgoing links from that node and nothing beyond that For instance on Facebook we only know our friends or the friends of of our friends. These procedure are typically called decentralized searchDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 16 / 75
  17. 17. Local Network Navigability But, how efficient are people in such social search? As shown by Millgram’s experiment, people are very efficient in social search. As shown, people are able to find each other in less than seven hops (friends), ∝ log (n) Hence, people have an extremely efficient decentralized search procedureDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 17 / 75
  18. 18. Local Network Navigability How we are able to find other people efficiently? Or in other words, what are the properties of social networks, or networks in general that make efficient decentralized search possible? Are there some structural clues in the network which allows us to design sub-linear algorithms? And if yes, what are these structural clues?Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 18 / 75
  19. 19. Efficiently navigable Local Network Navigability A network is efficiently navigable iff: If there is an algorithm that can find a short path with only local knowledge, and the delivery time of the algorithm is bounded polynomially by logk(n). Example: B D A C Efficiently navigable, if the algorithm knows it needs to Figure: A is start node and D is target node. go through A B CJ. Kleinberg. The small-world phenomenon: An algorithmic perspective. Proc. 32nd ACM Symposium on Theory of Computing, 2000. Also appears as Cornell Computer ScienceTechnical Report 99-1776 (October 1999) Denis Helic 2010 9Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 19 / 75
  20. 20. Local A networkNavigability navigable iff: Network is efficiently If there is an algorithm that can find a short path with only local knowledge, and the delivery time of the algorithm is bounded polynomially by logk(n). Step 1: B D A C Figure: Efficiently navigable, if the algorithm knows it needs to There are two possible paths from A. Obviously, the optimal path leads to B. What is the structuralA go through property that can guide us in selecting B? B CJ. Kleinberg. The small-world phenomenon: An algorithmic perspective. Proc. 32nd ACM Symposium on Theory of Computing, 2000. Also appears as Cornell Computer ScienceTechnical Report 99-1776 (October 1999) Denis Helic 2010 10Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 20 / 75
  21. 21. Local A networkNavigability navigable iff: Network is efficiently If there is an algorithm that can find a short path with only local knowledge, and the delivery time of the algorithm is bounded polynomially by logk(n). Step 1: B D A C Figure: Efficiently navigable, if the algorithm knows it needs to There are two possible paths from A. Obviously, the optimal path leads to B. What is the structuralA go through property that can guide us in selecting B? B CJ. Kleinberg. The small-world phenomenon: An algorithmic perspective. Proc. 32nd ACM Symposium on Theory of Computing, 2000. Also appears as Cornell Computer ScienceTechnical Report 99-1776 (October 1999) Denis Helic 2010 Nodes degree 10Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 20 / 75
  22. 22. Local A networkNavigability navigable iff: Network is efficiently If there is an algorithm that can find a short path with only local knowledge, and the delivery time of the algorithm is bounded polynomially by logk(n). Step 2: B D A C Figure: Efficiently navigable,paths from B. Obviously, the it needs to leads There are seven possible if the algorithm knows optimal path to C. What is through A property that can guide us in selecting C? go the structural B CJ. Kleinberg. The small-world phenomenon: An algorithmic perspective. Proc. 32nd ACM Symposium on Theory of Computing, 2000. Also appears as Cornell Computer ScienceTechnical Report 99-1776 (October 1999) Denis Helic 2010 11Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 21 / 75
  23. 23. Local A networkNavigability navigable iff: Network is efficiently If there is an algorithm that can find a short path with only local knowledge, and the delivery time of the algorithm is bounded polynomially by logk(n). Step 2: B D A C Figure: Efficiently navigable,paths from B. Obviously, the it needs to leads There are seven possible if the algorithm knows optimal path to C. What is through A property that can guide us in selecting C? go the structural B CJ. Kleinberg. The small-world phenomenon: An algorithmic perspective. Proc. 32nd ACM Symposium on Theory of Computing, 2000. Also appears as Cornell Computer ScienceTechnical Report 99-1776 (October 1999) Denis Helic 2010 Nodes clustering 11Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 21 / 75
  24. 24. Local Network Navigability Summarizing, local network navigability requires: 1 Existence of network hubs that are connected to many nodes 2 Existence of network clusters where nodes are highly interlinkedDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 22 / 75
  25. 25. Local Network Navigability Formally: 1 Power-low degree distribution with exponent γ 2 High clustering coefficient CDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 23 / 75
  26. 26. γ=2.2 γ=2.6 α=1.5 free nor clustered success proγ=2.3γ=2.4 γ=2.7 α=2.0 γ=2.8 α=3.0 Local Network Navigabilityγ=2.5 γ=2.9 α=1.1 0.2 α=5.0 γ=3.0 0 IV. AIR TRAV 3 4 5 2 2.2 2.4 2.6 2.8 3 10 network size (N) 10 10 degree exponent (γ) A 3 non-navigable region degree exponent (γ) We illustrate th 2.5 structure of netwo Web of trust Metabolic an example of pa Internet to travel from Tok α=5.0 2 Airports the public air tran navigable region work are airports, 3 4 50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 10 10 10 is at least one flig network size (N) clustering coefficient (C) ing to the greedy Success probability of greedy routing. Left the underlying me Figure: Navigable networks in γ, C space. the next-hop airpoccess probability ps as a function of network size Nent values of γ with weak (top) and strong (bottom) nation. Under thg. The top-right plot shows ps as a function of γ Bethel, then to Anr networks of fixed size N ≈ 105 . In the bottom- to Paris, then to Vt, parameter α is mapped to Navigability: Theorycoefficient Networks clustering Denis Helic & Christoph Trattner (KMI, TU Graz) and Applications August 31, 2011 24 / 75
  27. 27. A network is efficiently navigable iff: Local If there is an algorithm that can find a short path with Network Navigability only local knowledge, and the delivery time of the algorithm is bounded polynomially by logk(n). Revisiting Step 2: B D A E CJ. Kleinberg. The small-world phenomenon: An algorithmic perspective. Proc. 32nd ACM Symposium on Theory of Computing, 2000. Also appears as Cornell Computer ScienceTechnical Report 99-1776 (October 1999) Figure: There are seven possible paths from B. Obviously, the optimal path leads Denis Helic 2010 to C. What is an additional hint that can guide us in selecting C over E? 12Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 25 / 75
  28. 28. A network is efficiently navigable iff: Local If there is an algorithm that can find a short path with Network Navigability only local knowledge, and the delivery time of the algorithm is bounded polynomially by logk(n). Revisiting Step 2: B D A E CJ. Kleinberg. The small-world phenomenon: An algorithmic perspective. Proc. 32nd ACM Symposium on Theory of Computing, 2000. Also appears as Cornell Computer ScienceTechnical Report 99-1776 (October 1999) Figure: There are seven possible paths from B. Obviously, the optimal path leads Denis Helic 2010 to C. What is an additional hint that can guide us in selecting C over E? 12 Nodes similarityDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 25 / 75
  29. 29. Local Network Navigability Nodes similarity is external to the network It is derived from some additional information that we have about network nodes In Millgram’s experiment people selected the next person according to their occupation or geographyDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 26 / 75
  30. 30. Local Network Navigability All of this information, i.e. degrees, clustering, similarity can be understood as a kind of our background knowledge about the network We use this background knowledge to guide us in our search for a target node When we have more than one link to follow we consult the background knowledge and ask which of the links will lead us with highest probability to a given target nodeDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 27 / 75
  31. 31. Greedy Decentralized Search On the next abstraction level we can say that background knowledge defines a notion of distance between nodes In other words, background knowledge is a metric space where each node has unique coordinates and we can calculate the distance between nodes Or in other words, we can abstract background knowledge as a black-box executing a simple function: getDistance(node, target node)Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 28 / 75
  32. 32. Greedy Decentralized Search Let us now take an algorithmic perspective on decentralized search We start at an arbitrary node and need to find as fast as possible a target node having only local knowledge of the network In addition, we have background knowledge represented through getDistance(node, target node) function At each search step we have to make a decision which of the available links to followDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 29 / 75
  33. 33. Greedy Decentralized Search In order to maximize the probability of finding the target node we always select a node which has the smallest distance to the target node It has been shown that the greedy algorithm is very efficient, i.e. the number of steps to reach an arbitrary target node is ∝ log (n) Kleinberg proved it theoretically, Watts by simulation Watts was able to reproduce Millgram’s experiment with proper selection of parameters: Identity and Search in Social Networks, 2002Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 30 / 75
  34. 34. Background Knowledge Now, how does our background knowledge of people typically look like? It is a metric space, e.g. 1-D spaces, 2-D vector spaces, 3-D Euclidean spaces, hyperbolic spaces, ... or does it look like completely different? Actually, it was observed by Kleinberg and also by Watts that a hierarchy of nodes is also a very good approximation of how people think Hence, we will also use hierarchical background knowledgeDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 31 / 75
  35. 35. Hierarchy as a Metric Space 2 3 2 3 3 23 24 21 4 4 4 4 1 1 15 22 25 3 5 5 5 5 1 1 11 12 13 14 31 32 33 Figure: Node distances in a hierarchy. Distance: d(i, j) = h(i) + h(j) − 2h(lca(i, j)) − 1Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 32 / 75
  36. 36. Example of a Greedy Navigation 3 2 2 3 3 23 24 21 2 3 4 4 4 4 1 1 15 22 25 3 4 1 5 5 5 5 1 1 11 12 13 14 31 32 33 11 2 21 3 31 12 1 1 22 2 3 4 13 23 25 32 33 14 15 24 Figure: Greedy search.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 33 / 75
  37. 37. Calculating Network Navigability Now in order to measure network navigability, we developed a theoretical framework to estimate network navigability by simulations As input we take a network, e.g. information network like Wikipedia, or Delicious and a suitable hierarchy that models background knowledge For example, Wikipedia categories or Delicious folksonomy and simulate decentralized search on 106 start and target node pairsDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 34 / 75
  38. 38. Network Navigability Simulation Framework The metrics we measure by our framework are success rate s and stretch τ For both metrics we calculate distributions over global shortest path Definition Stretch: τ = h , where h is the number of simulator steps and l is the l global shortest path.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 35 / 75
  39. 39. Evaluating hierarchies The framework lets you e.g. estimate the quality of a hierarchy to serve as background knowledge A hierarchy with better navigational properties will have better success rate and stretch in comparison with other hierarchies For example, Wikipedia categories versus Delicious tags For example, different folksonomies for navigating social tagging systems, see Helic et al.: Pragmatic Evaluation of Folksonomies, 2011Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 36 / 75
  40. 40. Evaluating Navigational Tools But we can use framework to estimate the effects of changes in the network on its navigational properties For example, how navigable is Wikipedia now? How navigable will be Wikipedia if we include Delicious tags? How navigable will be Wikipedia if we include breadcrumbs? We take Wikipedia as the starting network and create new links in the network to emulate Delicious tags, breadcrumbs, etc.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 37 / 75
  41. 41. Evaluating folksonomies A folksonomy is a hierarchy that is automatically generated from a tagging system Today there are several folksonomy algorithms, see e.g. Heymann 2008, or Benz 2010 In addition, you can produce folksonomies by using standard hierarchical clustering methods such as K-Means or Affinity PropagationDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 38 / 75
  42. 42. Evaluating folksonomies In Helic et al.: Pragmatic Evaluation of Folksonomies, WWW2011 we took 5 tagging datasets and 5 different folksonomy algorithms We produced 5x5 folksonomies and simulated (100.000 samples) greedy decentralized search on the datasets We measured the success rate and stretch to see if some folksonomies perform better than the other ones.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 39 / 75
  43. 43. Evaluating folksonomies Greedy Search Success Rate: BibSonomy 100 Folksonomy Random Aff.Prop. Success Rate (Percentage) 80 K-Means Deg/Cooc Clo/Cos 60 40 20 0 1 2 3 4 5 6 7 Shortest path Figure: Success Rate of different folksonomies in BibSonomyDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 40 / 75
  44. 44. Evaluating folksonomies Greedy Search Success Rate: CiteULike 100 Folksonomy Random Aff.Prop. Success Rate (Percentage) 80 K-Means Deg/Cooc Clo/Cos 60 40 20 0 1 2 3 4 5 6 7 Shortest path Figure: Success Rate of different folksonomies in CiteULikeDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 41 / 75
  45. 45. Evaluating folksonomies Greedy Search Success Rate: Delicious 100 Folksonomy Random Aff.Prop. Success Rate (Percentage) 80 K-Means Deg/Cooc Clo/Cos 60 40 20 0 1 2 3 4 5 6 7 Shortest path Figure: Success Rate of different folksonomies in DeliciousDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 42 / 75
  46. 46. Evaluating folksonomies Greedy Search Success Rate: Flickr 100 Folksonomy Random Aff.Prop. Success Rate (Percentage) 80 K-Means Deg/Cooc Clo/Cos 60 40 20 0 1 2 3 4 5 6 Shortest path Figure: Success Rate of different folksonomies in FlickrDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 43 / 75
  47. 47. Evaluating folksonomies Greedy Search Success Rate: LastFM 100 Folksonomy Random Aff.Prop. Success Rate (Percentage) 80 K-Means Deg/Cooc Clo/Cos 60 40 20 0 1 2 3 4 5 Shortest path Figure: Success Rate of different folksonomies in LastFMDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 44 / 75
  48. 48. Evaluating folksonomies Centrality-based algorithms such as Heymann 2008 or Benz 2010 outperform traditional methods However, these are all theoretical results Because, what is if we wanted to embed folksonomies in the user interface (UI) to support users in their navigation tasks and the space in user interface is limited?Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 45 / 75
  49. 49. Embedding folksonomies in UI Google Directory - Computers > Internet > On the Web > Online Communities Directory Help Online Communities Computers > Internet > On the Web > Online Communities Go to Directory Home Categories Bulletin Board Directories (9) PowerPets (6) Systems (132) Events (1) Second Life (119) By Region (8) Mailing Lists (85) Social Networking By Subject (204) Message Boards (222) Chat (745) (154) Software and Community MySpace (28) Services (27) Management (36) Neopets (171) The Palace (51) Community Zetapets (3) Providers (14) Related Categories: Society > Activism > Community Building (26) Society > Organizations (16987) Society > People > Personal Homepages (8890) Society > Relationships > Cyber Relationships (59) Society > Subcultures > Cyberculture (162) Web Pages Viewing in Google PageRank order View in alphabetical order Talk City - http://www.talkcity.com/ Figure: Directory Based Navigation technology, health and other Participate in discussions about relationships, hobbies, business, topics. Socialize with friends, or start your own chat group. Whyville - http://www.whyville.net/ A virtual 3-D world for curious minds where you can own land, build your own house, play simulation games, win prizes, chat, and help the community grow. Buzznet - http://www.buzznet.com/Denis Helic & Christoph Trattner (KMI, TU Graz) create communitiesTheory and Applications Users can Networks Navigability: and share blogs and photographs. August 31, 2011 46 / 75
  50. 50. Embedding folksonomies in UI We have breadcrumbs connecting each node all the way up to the root node We have limited number of subcategories (n) We have limited number of related categories (m) Now we embed folksonomy as in Benz 2010 and apply different restrictionsDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 47 / 75
  51. 51. Embedding folksonomies in UI - Greedy Navigator (1000000 Runs) - l=3.585123, h=5.936013, sg=0.005548, τg=1.655735 Success Rate (s) 3 Stretch (τ) 2.5 2 s, τ 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 Shortest Path Figure: Success Rate and stretch in BibSonomy with n = 20 and m = 20Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 48 / 75
  52. 52. Embedding folksonomies in UI - Greedy Navigator (1000000 Runs) - l=3.634634, h=6.536937, sg=0.001110, τg=1.798513 9 Success Rate (s) Stretch (τ) 8 7 6 5 s, τ 4 3 2 1 0 1 2 3 4 5 6 7 8 9 Shortest Path Figure: Success Rate and stretch in CiteULike with n = 20 and m = 20Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 49 / 75
  53. 53. Embedding folksonomies in UI - Greedy Navigator (1000000 Runs) - l=3.518932, h=5.557032, sg=0.000903, τg=1.579181 7 Success Rate (s) Stretch (τ) 6 5 4 s, τ 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 Shortest Path Figure: Success Rate and stretch in Delicious with n = 20 and m = 20Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 50 / 75
  54. 54. Embedding folksonomies in UI - Greedy Navigator (1000000 Runs) - l=3.467684, h=4.162304, sg=0.000382, τg=1.200312 Success Rate (s) 7 Stretch (τ) 6 5 s, τ 4 3 2 1 0 1 2 3 4 5 6 7 8 9 Shortest Path Figure: Success Rate and stretch in Flickr with n = 20 and m = 20Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 51 / 75
  55. 55. Embedding folksonomies in UI - Greedy Navigator (1000000 Runs) - l=3.197477, h=6.662900, sg=0.001062, τg=2.083799 Success Rate (s) 6 Stretch (τ) 5 4 s, τ 3 2 1 0 1 2 3 4 5 6 Shortest Path Figure: Success Rate and stretch in LastFM with n = 20 and m = 20Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 52 / 75
  56. 56. Embedding folksonomies in UI Under this restriction the navigator in Considering practical user interface restriction folksonomies are useless for supporting navigation. The success rate drops below 1%.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 53 / 75
  57. 57. Embedding folksonomies in UI Thus, folksonomies (unlimited) are useful theoretically but useless practically The problem is that top nodes have many children (possibly thousands) and UI restrictions cut to many children nodes off Hence, we need a new algorithm that takes into account these UI restrictions Technically, we need to able to determine the branching factor for the hierarchy We developed such an algorithm and published in CIKM2011. Helic et al. Building Directories for Social Tagging Systems We were able to almost recover theoretical navigabilityDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 54 / 75
  58. 58. Embedding folksonomies in UI - Greedy Navigator (1000000 Runs) - l=3.585123, h=8.691685, sg=1.000000, τg=2.424376 7 Success Rate (s) Stretch (τ) 6 5 4 s, τ 3 2 1 0 1 2 3 4 5 6 7 8 9 Shortest Path Figure: Success Rate and stretch in BibSonomy with new folksonomy algorithmDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 55 / 75
  59. 59. Embedding folksonomies in UI - Greedy Navigator (1000000 Runs) - l=3.634634, h=9.163688, sg=1.000000, τg=2.521213 7 Success Rate (s) Stretch (τ) 6 5 4 s, τ 3 2 1 0 1 2 3 4 5 6 7 8 9 Shortest Path Figure: Success Rate and stretch in CiteULike with new folksonomy algorithmDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 56 / 75
  60. 60. Embedding folksonomies in UI - Greedy Navigator (1000000 Runs) - l=3.518932, h=9.720769, sg=1.000000, τg=2.762420 6 Success Rate (s) Stretch (τ) 5 4 s, τ 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 Shortest Path Figure: Success Rate and stretch in Delicious with new folksonomy algorithmDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 57 / 75
  61. 61. Embedding folksonomies in UI - Greedy Navigator (1000000 Runs) - l=3.467684, h=8.886960, sg=0.996066, τg=2.562794 Success Rate (s) 6 Stretch (τ) 5 4 s, τ 3 2 1 0 1 2 3 4 5 6 7 8 9 Shortest Path Figure: Success Rate and stretch in Flickr with new folksonomy algorithmDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 58 / 75
  62. 62. Embedding folksonomies in UI - Greedy Navigator (1000000 Runs) - l=3.197477, h=9.830726, sg=1.000000, τg=3.074526 6 Success Rate (s) Stretch (τ) 5 4 s, τ 3 2 1 0 1 2 3 4 5 6 Shortest Path Figure: Success Rate and stretch in LastFM with new folksonomy algorithmDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 59 / 75
  63. 63. Why usefulness of folksonomies for navigation is limited? Even if folksonomies allow the user to navigate to related concepts in an efficient manner navigation to a particular resource is still a problem As shown related work, in tagging systems the tag-resource distribution follows a power-law function, i.e. there are many tags that refer to a large number of resources. In BibSonomy or CiteULike for instance there are tags, which refer to hundreds or even thousands of resources. To display such long resource lists, developers typically paginate the resource lists in a tagging system by a certain factor kDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 60 / 75
  64. 64. Why usefulness of folksonomies for navigation is limited? (a) Austria-Forum (b) BibSonomy (c) CiteULike Figure: Tag distributions.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 61 / 75
  65. 65. Creating tag-resource Taxonomies To support the user not only to navigate to related tags in efficient manner but also to the resources of a tagging system, we invented the approach of the so-called tag-resource taxonomies. Car Car Tire Motor Tire Motor Mercedes VOLVO VW BMW VW BMW VW BMW (a) Folksonomy (b) Tag-Resource Taxonomy Figure: Folksonomy vs. Tag-Resource Taxonomy. In a Folksonomy tags appear only once. However, resources can be referred by different tags. In a tag-resource taxonomy on the other hand resources can occur only once while tags can appear on multiple and on different levels.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 62 / 75
  66. 66. Why usefulness of folksonomies for navigation is limited? In the worst case a user would have to click max{click(Ttag )} times to reach a desired resource with the help of a Folksonomy. c1 |r | max{click(Ttag )} = + logb/2 (c2 · |r |), b ≥ 2 (1) k or c1 · |r | max{click(Ttag )} ≈ (2) k c1 ·|r | supposing that logb/2 (c2 · |r |) kDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 63 / 75
  67. 67. Why usefulness of folksonomies for navigation is limited? The worst case scenario of a tag-resource taxonomy is significantly better. In the worst case a user would have to click max{click(Tres )} times to reach a desired target resource. max{click(Tres )} = max{depth(Tres )} = logk/2 |r | , k ≥ 2 (3) Then for large values of |r | we have: c1 · |r | logk/2 |r | (4) kDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 64 / 75
  68. 68. Why usefulness of folksonomies for navigation is limited?xxx Austria-Forum BibSonomy CiteULike max{click(Ttag )} 184 5,278 20,799 max{click(Tres )} 6.1 7.7 8.5 Table: Tag Taxonomy vs. Tag-Resource Taxonomy: Maximum number of clicks for k = 10.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 65 / 75
  69. 69. Why usefulness of folksonomies for navigation is limited? To calculate the number of tags suffering from the so-called pagination effect, we can user the following equation: 1 α 1 (α) |tp | = |t| · − (5) k k Austria-Forum BibSonomy CiteULike |tp | (%) 5079 (38%) 7401 (28%) 51748 (32%) Table: Number of paginated tags for k = 10.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 66 / 75
  70. 70. Why usefulness of folksonomies for navigation is limited? The mean number of clicks is calculated as follows: Tag-Resource Taxonomy: mean{click(Tres )} = logk (|r |) |t| Folksonomy: mean{click(Ttag )} = logk (|t|) + |t| i=1 ri 1 k k Austria-Forum BibSonomy CiteULike mean{click(Tres )} 2 14.2 17.8 19.8 mean{click(Ttag )} 2 29.5 22.4 30.7 mean{click(Tres )} 5 6.1 7.6 8.5 mean{click(Ttag )} 5 11.6 9.2 12.3 mean{click(Tres )} 10 4.3 5.3 5.9 mean{click(Ttag )} 10 6.4 5.6 7.3 Table: Tag Taxonomy vs. Tag-Resource Taxonomy: Mean number of clicks for different branching factors k.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 67 / 75
  71. 71. Creating tag-resource Taxonomies 1. Computer Degree centrality of the resource-to-resource tag network 2. Take most general resource as root an attach max. b resources as childs. Child-nodes are selected according their cos-sim values. 3. After that we take the resource taxonomy and apply labels (tags) to the resource (top-down, in left-order) 3.1 We calculate candidate labels by the method of co-occurance, i.e. we take the tags of the related resources into account to rank the actual tags of the currently processed resource. 3.2. If the candidate tag has already been applied to one of the parent resources of the currently processed resource we take the next candidate tag from the co-occurance vector and try to apply it.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 68 / 75
  72. 72. Evaluating Tag-Resource Taxonomies In the first experiment we measured the average and maximum number of clicks and the drop rate Name b n max{click(Tres )} mean{click(Tres )} Res2 2 19,430 17 12.45 Res5 5 19,430 10 5.93 Res10 10 19,430 8 4.44 Table: max{click(Tres )} and mean{click(Tres )} for different branching factors b.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 69 / 75
  73. 73. Evaluating Tag-Resource Taxonomies In the second experiment we measured the number of collisions Name b n CR (%) Res2 2 19,430 0.1% Res5 5 19,430 0.2% Res10 10 19,430 0.2% Table: Collision Rates (CR) for different resource taxonomies with different branching factor b.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 70 / 75
  74. 74. Evaluating Tag-Resource Taxonomies In the third experiment we measured the semantic structure of the tag-resource taxonomy compared to popular folksonomy induction algorithms such as Heymann, K-Means, Affinity Propagation and Co-Occurance As measure for this experiment we used Taxonomic Recall/Prec. and overlap. Ground truth: Germanet ontholoy 0.4 Taxonomic F−Measure 0.35 Taxonomic Overlap 0.3 Count (1 = 100%) 0.25 0.2 0.15 0.1 0.05 0 Res2 Res5 Res10 Deg/Cooc Aff. Prop K−Means HeymannDenis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 71 / 75
  75. 75. Evaluating Tag-Resource Taxonomies In the fourth and last experiment a user study was conducted to test weather the approach is also useful for humans or not As ground truth for the experiment the best so far known folksonomy generation approach was used All over we had 9 test users who had to judge 200 tag trails extracted from both hierarchies Name b Correct (%) Related (%) Equivalent (%) Not Related (% Deg/Cooc10 10 33.2 27.3 13 21.9 Res10 10 27.3 36.2 12.3 19.8 Table: Results of the empirical analysis of the tag-resource taxonomy with branching factor b = 10 compared to a Deg/Cooc folksonomy with branching factor b = 10.Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 72 / 75
  76. 76. End of presentation Thank you very much for your attention! Christoph Trattner (ctrattner@iicm.edu)Denis Helic & Christoph Trattner (KMI, TU Graz) Networks Navigability: Theory and Applications August 31, 2011 73 / 75

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