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Orpailleur -- triclustering talk

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Dmitrii Ignatov
Dmitrii Ignatov

An informal talk on triclustering for Orpailleur team, LORIA, Nancy, France

TechnologyEducation
1 of 27
Dmitry V. Gnatyshak, Dmitry I. Ignatov*, Sergei O. Kuznetsov School of Applied Mathematics and Information Science & Intelligence Systems and Structural Analysis Lab NRU Higher School of Economics, Moscow, Russia LORIA Orpailleur meeting, Nancy, France, 2013
Outline 1. Motivation and problem setting 2. FCA basic definitions 3. Triclustering methods 4. Experiments 5. Conclusion 2
Motivation  A large amount of structured and unstructured data generates triadic data.  Example: folksonomy is a set of triples (user, object, tag)  Examples:  Bibsonomy.org (user, bookmark, tag)  Social networking sites (user, group, interest)  Delicious (user, link, tag) 3
Main goals 1. Comparison of some triclustering methods 2. Development of a toolbox for triclustering experiments 3. New possibly better methods 4. Possible applications 4
FCA: basic definitions Biology Mathematics Computer Science Chemistry Kate x x Mike x x x Alex x x Pete x x x 5  (R. Wille, 1982; B. Ganter, R. Wille, 1999)
FCA: basic definitions  6 Biology Mathematics Computer Science Chemistry Kate x x Mike x x x Alex x x Pete x x x
FCA: basic definitions  7 Biology Mathematics Computer Science Chemistry Kate x x Mike x x x Alex x x Pete x x x
Triadic FCA: basic definitions  8 (F. Lehmann, R. Wille, 1995)
OAC-triclusters (based on box operators)  Box operators 9 (D. Ignatov et al., 2011) … … … …
OAC-triclusters (based on prime operators)  Prime-operators of singletons 10
OAC-triclustering  11
TriBox  12 (A. Kramarenko & B. Mirkin, 2011)
Spectral Triclustering: SpecTric  13 (D. Ignatov & Z. Sekinaeva, 2011; Ignatov et al. 2013)
Spectral Triclustering: SpecTric 14 (D. Ignatov & Z. Sekinaeva, 2011; Ignatov et al. 2013)
TRIAS  15 (R. Jäschke, 2006)
Experiments  Main goals:  Fault-tolerance test  Comparison by criteria: time, quantity, mean density, coverage and diversity  For TriBox and OAC-triclustering we implemented their parallel versions  They were included to the comparison 16
Data  17
Comparison Criteria  18
Results (fault-tolerance) 19
OAC-prime triclustering example  IMDB 20
Results (time, quantity, average density, coverage, diversity) Method T,ms # OAC (box) 407 73 9,88 100,00 0,00 0,00 0,00 0,00 OAC (prime) 312 2659 32,23 100,00 92,51 60,07 59,80 59,45 SepcTric 277 5 8,74 8,84 100,00 100,00 100,00 100,00 TriBox 6218 1011 74,00 96,02 97,42 66,25 79,53 84,80 TRIAS 29367 38356 100,00 100,00 99,99 99,93 4,07 3,51 IMDB OAC (box) 2314 1500 1,84 100,00 15,65 9,67 0,70 7,87 OAC (prime) 547 1274 53,85 100,00 96,55 94,56 92,14 28,52 Spectric 98799 21 17,07 20,88 100,00 100,00 100,00 100,00 TriBox 197136 328 91,65 98,90 98,89 98,46 95,21 30,94 TRIAS 102554 1956 100,00 100,0 99,89 99,69 52,52 26,18 BibSonomy OAC (box) 19297 398 4,16 100,00 79,59 67,28 42,83 79,54 OAC (prime) 13556 1289 94,66 100,00 99,74 88,58 99,51 99,53 SpecTric 5906563 2 50,00 100,00 100,00 100,00 100,00 100,00 TriBox Time> 24 hours TRIAS 110554 1305 100,00 100,00 99,98 91,70 99,78 99,92 21
Method Time Quantity Average density Coverage Diversity Efficiency of parallel version OAC(box) average large low high~very low very low~average high OAC (prime) small large average high~average average~high low SpecTric Small for small contexts small low average~high 1 – TriBox high average high high high high TRIAS very large 1 high~low high~low – 22 Results (time, quantity, average density, coverage, diversity)
Conclusion  There is no a winner according to the comparison criteria  Method TriBox shows best results but it takes huge computational time  OAC-triclustering based on prime operators gives the second best results and it is sufficiently fast 23
Conclusion  There is no a winner according to the comparison criteria  Details by methods:  TRIAS  High elapsed time  Too large number of small well-interpreted triclusters (triconcepts) 24
Conclusion  OAC (box operators)  Large triclusters of low density  High density, small diversity  An efficient parallelization  OAC (prime-operators)  High speed of computations  Large number of dense well-interpreted triclusters  Low efficiency of parallelization 25
Conclusion  Spectral Triclustering  High computational speed on small contexts  Well-interpreted triclusters but of the low density  Diversity is always equals to 1, but it causes too low coverage  TriBox  A moderate number of well-interpreted triclusters  High elapsed time  Efficient parallelization  Reasonably high coverage and diversity 26
Merci beaucoup! Questions? 27

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Orpailleur -- triclustering talk

  • 1. Dmitry V. Gnatyshak, Dmitry I. Ignatov*, Sergei O. Kuznetsov School of Applied Mathematics and Information Science & Intelligence Systems and Structural Analysis Lab NRU Higher School of Economics, Moscow, Russia LORIA Orpailleur meeting, Nancy, France, 2013
  • 2. Outline 1. Motivation and problem setting 2. FCA basic definitions 3. Triclustering methods 4. Experiments 5. Conclusion 2
  • 3. Motivation  A large amount of structured and unstructured data generates triadic data.  Example: folksonomy is a set of triples (user, object, tag)  Examples:  Bibsonomy.org (user, bookmark, tag)  Social networking sites (user, group, interest)  Delicious (user, link, tag) 3
  • 4. Main goals 1. Comparison of some triclustering methods 2. Development of a toolbox for triclustering experiments 3. New possibly better methods 4. Possible applications 4
  • 5. FCA: basic definitions Biology Mathematics Computer Science Chemistry Kate x x Mike x x x Alex x x Pete x x x 5  (R. Wille, 1982; B. Ganter, R. Wille, 1999)
  • 6. FCA: basic definitions  6 Biology Mathematics Computer Science Chemistry Kate x x Mike x x x Alex x x Pete x x x
  • 7. FCA: basic definitions  7 Biology Mathematics Computer Science Chemistry Kate x x Mike x x x Alex x x Pete x x x
  • 8. Triadic FCA: basic definitions  8 (F. Lehmann, R. Wille, 1995)
  • 9. OAC-triclusters (based on box operators)  Box operators 9 (D. Ignatov et al., 2011) … … … …
  • 10. OAC-triclusters (based on prime operators)  Prime-operators of singletons 10
  • 12. TriBox  12 (A. Kramarenko & B. Mirkin, 2011)
  • 13. Spectral Triclustering: SpecTric  13 (D. Ignatov & Z. Sekinaeva, 2011; Ignatov et al. 2013)
  • 14. Spectral Triclustering: SpecTric 14 (D. Ignatov & Z. Sekinaeva, 2011; Ignatov et al. 2013)
  • 16. Experiments  Main goals:  Fault-tolerance test  Comparison by criteria: time, quantity, mean density, coverage and diversity  For TriBox and OAC-triclustering we implemented their parallel versions  They were included to the comparison 16
  • 21. Results (time, quantity, average density, coverage, diversity) Method T,ms # OAC (box) 407 73 9,88 100,00 0,00 0,00 0,00 0,00 OAC (prime) 312 2659 32,23 100,00 92,51 60,07 59,80 59,45 SepcTric 277 5 8,74 8,84 100,00 100,00 100,00 100,00 TriBox 6218 1011 74,00 96,02 97,42 66,25 79,53 84,80 TRIAS 29367 38356 100,00 100,00 99,99 99,93 4,07 3,51 IMDB OAC (box) 2314 1500 1,84 100,00 15,65 9,67 0,70 7,87 OAC (prime) 547 1274 53,85 100,00 96,55 94,56 92,14 28,52 Spectric 98799 21 17,07 20,88 100,00 100,00 100,00 100,00 TriBox 197136 328 91,65 98,90 98,89 98,46 95,21 30,94 TRIAS 102554 1956 100,00 100,0 99,89 99,69 52,52 26,18 BibSonomy OAC (box) 19297 398 4,16 100,00 79,59 67,28 42,83 79,54 OAC (prime) 13556 1289 94,66 100,00 99,74 88,58 99,51 99,53 SpecTric 5906563 2 50,00 100,00 100,00 100,00 100,00 100,00 TriBox Time> 24 hours TRIAS 110554 1305 100,00 100,00 99,98 91,70 99,78 99,92 21
  • 22. Method Time Quantity Average density Coverage Diversity Efficiency of parallel version OAC(box) average large low high~very low very low~average high OAC (prime) small large average high~average average~high low SpecTric Small for small contexts small low average~high 1 – TriBox high average high high high high TRIAS very large 1 high~low high~low – 22 Results (time, quantity, average density, coverage, diversity)
  • 23. Conclusion  There is no a winner according to the comparison criteria  Method TriBox shows best results but it takes huge computational time  OAC-triclustering based on prime operators gives the second best results and it is sufficiently fast 23
  • 24. Conclusion  There is no a winner according to the comparison criteria  Details by methods:  TRIAS  High elapsed time  Too large number of small well-interpreted triclusters (triconcepts) 24
  • 25. Conclusion  OAC (box operators)  Large triclusters of low density  High density, small diversity  An efficient parallelization  OAC (prime-operators)  High speed of computations  Large number of dense well-interpreted triclusters  Low efficiency of parallelization 25
  • 26. Conclusion  Spectral Triclustering  High computational speed on small contexts  Well-interpreted triclusters but of the low density  Diversity is always equals to 1, but it causes too low coverage  TriBox  A moderate number of well-interpreted triclusters  High elapsed time  Efficient parallelization  Reasonably high coverage and diversity 26