Midterm Presentation

Transcript

1. Midterm Presentation LIU MINGMOU Student ID: MG1533028 Email: mg1533028@smail.nju.edu.cn Group: TheoryGroup @NJU ڝ ก᧪
2. My Research Nearest Neighbor Search High-Dimensionally
3. My Research Nearest Neighbor Search …… 1000 1011 0110 0100 1100 …… High-Dimensionally
4. My Research Nearest Neighbor Search …… 1000 1011 0110 0100 1100 …… in Parallel / Distributed Computation High-Dimensionally
5. My Research Nearest Neighbor Search …… 1000 1011 0110 0100 1100 …… in Parallel / Distributed Computation High-Dimensionally
6. My Research Nearest Neighbor Search …… 1000 1011 0110 0100 1100 …… in Parallel / Distributed Computation High-Dimensionally
7. My Research Nearest Neighbor Search …… 1000 1011 0110 0100 1100 …… in Parallel / Distributed Computation High-Dimensionally
8. My Research Nearest Neighbor Search …… 1000 1011 0110 0100 1100 …… in Parallel / Distributed Computation High-Dimensionally
9. Nearest Neighbor Search Important and foundational problem in numerous fields of CS Pattern Recognition Statistical Classification Computer Vision Computational Geometry Databases etc. A Practical Example: Similar Picture Searching Theoretically, A Representation of high dimension problems
10. Publication and Award Mingmou Liu, Xiaoyin Pan, and Yitong Yin. 2016. Randomized Approximate Nearest Neighbor Search with Limited Adaptivity. In Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA '16). Best Paper Finalist of SPAA’16
11. Complexity Model …… 1000 1011 0110 0100 1100 …… Classical Cell-Probe Model: s memory units used w size of memory unit have to read t memory units
12. Complexity Model …… 1000 1011 0110 0100 1100 …… Classical Cell-Probe Model: s memory units used w size of memory unit have to read t memory units Space Complexity Limited by Machine Time Complexity
13. Complexity Model …… 1000 1011 0110 0100 1100 …… Classical Cell-Probe Model: s memory units used w size of memory unit have to read t memory units Access memory one by one
14. Complexity Model …… 1000 1011 0110 0100 1100 …… Classical Cell-Probe Model: s memory units used w size of memory unit have to read t memory units Access memory one by one
15. Complexity Model …… 1000 1011 0110 0100 1100 …… Classical Cell-Probe Model: s memory units used w size of memory unit have to read t memory units Access memory one by one
16. Complexity Model …… 1000 1011 0110 0100 1100 …… Classical Cell-Probe Model: s memory units used w size of memory unit have to read t memory units Access memory one by one
17. Complexity Model …… 1000 1011 0110 0100 1100 …… Classical Cell-Probe Model: s memory units used w size of memory unit have to read t memory units Access memory one by one
18. Complexity Model …… 1000 1011 0110 0100 1100 …… Access memory one by one Parallelized Cell-Probe Model: s memory units used w size of memory unit k time cost in real world have to read t memory units in total
19. Complexity Model …… 1000 1011 0110 0100 1100 …… Parallelized Cell-Probe Model: s memory units used w size of memory unit k time cost in real world have to read t memory units in total Access multiple unites at once
20. Complexity Model …… 1000 1011 0110 0100 1100 …… Parallelized Cell-Probe Model: s memory units used w size of memory unit k time cost in real world have to read t memory units in total Access multiple unites at once
21. Hardness of NNS People believe that NNS is hard if we have to find the exactly nearest neighbor or if we have to find the answer deterministically
22. Hardness of NNS People believe that NNS is hard if we have to find the exactly nearest neighbor or if we have to find the answer deterministically So called Curse of Dimensionality
23. Hardness of NNS People believe that NNS is hard if we have to find the exactly nearest neighbor or if we have to find the answer deterministically So called Curse of Dimensionality Toward removing the curse, we deal with NNS approximately and randomizedly.
24. Toward removing the curse, we deal with NNS approximately and randomizedly.
25. Our Result Toward removing the curse, we deal with NNS approximately and randomizedly.
26. Our Result Toward removing the curse, we deal with NNS approximately and randomizedly. if s = nO(1), w = dO(1) t = ⌦( 1 k (log d ) 1/k )
27. Our Result Toward removing the curse, we deal with NNS approximately and randomizedly. if s = nO(1), w = dO(1) t = O ( k (log d ) 1/k ) t = ⌦( 1 k (log d ) 1/k ) t = O ( k + ( 1 k log d ) O(1/k) ) s = nO(1), w = O(d) if
28. Our Result Toward removing the curse, we deal with NNS approximately and randomizedly. if s = nO(1), w = dO(1) t = O ( k (log d ) 1/k ) t = ⌦( 1 k (log d ) 1/k ) t = O ( k + ( 1 k log d ) O(1/k) ) Tight if k is constant or t=k s = nO(1), w = O(d) if
29. Our Result Toward removing the curse, we deal with NNS approximately and randomizedly. if s = nO(1), w = dO(1) t = O ( k (log d ) 1/k ) t = ⌦( 1 k (log d ) 1/k ) t = O ( k + ( 1 k log d ) O(1/k) ) Tight if k is constant or t=k t = ⇥( log log d log log log d) s = nO(1), w = O(d) if
30. Our Result Toward removing the curse, we deal with NNS approximately and randomizedly. if s = nO(1), w = dO(1) t = O ( k (log d ) 1/k ) t = ⌦( 1 k (log d ) 1/k ) t = O ( k + ( 1 k log d ) O(1/k) ) Tight if k is constant or t=k s = nO(1), w = O(d) if
31. Our Result Toward removing the curse, we deal with NNS approximately and randomizedly. if s = nO(1), w = dO(1) t = O ( k (log d ) 1/k ) t = ⌦( 1 k (log d ) 1/k ) t = O ( k + ( 1 k log d ) O(1/k) ) Tight if k is constant or t=k Asymptotically tight in other case s = nO(1), w = O(d) if
32. Publication Mingmou Liu, Xiaoyin Pan, and Yitong Yin. 2016. Randomized Approximate Nearest Neighbor Search with Limited Adaptivity. In Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA '16). Best Paper Finalist of SPAA’16
34. Furthermore - Seminar speaker in the seminar of Communication Complexity of Gap Hamming Distance. - Paper study on data structure and communication complexity. - Teaching Assistant of Randomized Algorithms in Fall 2015.
35. Grade Course Type Grade Teacher Ꮧॊኞ᝕᧍ A عץ ሴَ࿆ᒵ ӾࢵᇙᜋᐒտԆԎቘᦞӨਫ᪢ A 91 ਃԔ୩ Ḙظ௏ԆԎӨᐒտᑀ਍ොဩᦞ A 76 ᠗࿯ හഝ೵യ B 74 לಛ̵ୟڥ٠ ړ૲ୗᔮᕹ B 62 ᝞̵ً᰸ຶӾ ᦇᓒቘᦞ੕୚ B 76 ਟොභ ᕟݳහ਍ D 97 ੭Ӟ᭗ ᵋ๢ᓒဩ D 97 ੭Ӟ᭗ ړ૲ୗᓒဩفᳪ D 85 Ἆਜ Ꭵᴣቘᦞٌ݊ଫአ D 90 ᩶ᰂᆦ ཛྷୗᦩڦ D 88 ޓୌᰎ ݢᦇᓒ௔Өݢڣෙ௔ D 84 ࡎᜉ
36. Currently - Studying the λ-Near-Neighbor problem - The best known lower bound for λNN was given in 2006 - Trying to prove a better lower bound - λNN is a decision problem - Any better result will be the highest lower bound among any decision problem
37. Q&A
38. Thank you LIU MINGMOU Student ID: MG1533028 Email: mg1533028@smail.nju.edu.cn Group: TheoryGroup @NJU ڝ ก᧪