Manifold Alignment of High- Dimensional Datasets Sridhar Mahadevan - - PowerPoint PPT Presentation

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Manifold Alignment of High- Dimensional Datasets Sridhar Mahadevan - - PowerPoint PPT Presentation

Nov 15, 2022 142 likes •502 views

Manifold Alignment of High- Dimensional Datasets Sridhar Mahadevan (PI) & Rui Wang (co-PI) Thomas Boucher, Clifton Carey, Stefan Dernbach, Blake Foster, Hoa Vu, Chang Wang (IBM) School of Computer Science University of Massachusetts,

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SLIDE 1

Manifold Alignment of High- Dimensional Datasets

Sridhar Mahadevan (PI) & Rui Wang (co-PI)

Thomas Boucher, Clifton Carey, Stefan Dernbach, Blake Foster, Hoa Vu, Chang Wang (IBM) School of Computer Science University of Massachusetts, Amherst

Thursday, December 13, 12

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SLIDE 2

Learning from Multiple Datasets

  • In many applications, multiple “views” or multiple datasets are

constructed

  • Bioinformatics
  • Activity recognition
  • Computer graphics
  • Scientific exploration (MARS rover)
  • Cross-lingual information retrieval
  • Spectral methods for learning latent variable models

Thursday, December 13, 12

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SLIDE 3

Canonical Correlation Analysis

(Hotelling, 1936)

Displacement Horsepower Weight Acceleration MPG

Thursday, December 13, 12

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SLIDE 4

Canonical Correlation Analysis

(Hotelling, 1936)

Displacement Horsepower Weight Acceleration MPG

Thursday, December 13, 12

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SLIDE 5

Canonical Correlation Analysis

(Hotelling, 1936)

Displacement Horsepower Weight Acceleration MPG

Thursday, December 13, 12

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SLIDE 6

Canonical Correlation Analysis

(Hotelling, 1936) Find u,v that maximizes

Displacement Horsepower Weight Acceleration MPG

Thursday, December 13, 12

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SLIDE 7

Canonical Correlation Analysis

(Hotelling, 1936) Find u,v that maximizes

Displacement Horsepower Weight Acceleration MPG

Thursday, December 13, 12

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SLIDE 8

Canonical Correlation Analysis

(Hotelling, 1936) Find u,v that maximizes

Displacement Horsepower Weight Acceleration MPG

Pioneer of the first two statistics departments in the US! UNC, Chapel Hill Columbia University

Thursday, December 13, 12

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SLIDE 9

FODAVA project: main contribution

  • We developed a new class of methods, called manifold

alignment, that outperforms CCA in many domains

  • Linear + Nonlinear
  • Local + Global
  • Supervised + Unsupervised
  • If you use multiple datasets, you should try manifold

alignment!

Thursday, December 13, 12

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SLIDE 10

Manifold Projections

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SLIDE 11

Manifold Projections

∑ ∑ ∑∑

− + − + − =

j i j i y j T i T j i j i x j T i T i j i j T i T j

W y y W x x W y x C C

, , 2 , , 2 , 2

) ( 5 . ) ( 5 . ) ( ) , ( where , ) , ( function cost the minimize to , functions mapping find want to We β β α α β α µ β α β α β α

Thursday, December 13, 12

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SLIDE 12

Manifold Projections

∑ ∑ ∑∑

− + − + − =

j i j i y j T i T j i j i x j T i T i j i j T i T j

W y y W x x W y x C C

, , 2 , , 2 , 2

) ( 5 . ) ( 5 . ) ( ) , ( where , ) , ( function cost the minimize to , functions mapping find want to We β β α α β α µ β α β α β α

Thursday, December 13, 12

slide-13
SLIDE 13

Manifold Projections

∑ ∑ ∑∑

− + − + − =

j i j i y j T i T j i j i x j T i T i j i j T i T j

W y y W x x W y x C C

, , 2 , , 2 , 2

) ( 5 . ) ( 5 . ) ( ) , ( where , ) , ( function cost the minimize to , functions mapping find want to We β β α α β α µ β α β α β α

Thursday, December 13, 12

slide-14
SLIDE 14

Manifold Projections

∑ ∑ ∑∑

− + − + − =

j i j i y j T i T j i j i x j T i T i j i j T i T j

W y y W x x W y x C C

, , 2 , , 2 , 2

) ( 5 . ) ( 5 . ) ( ) , ( where , ) , ( function cost the minimize to , functions mapping find want to We β β α α β α µ β α β α β α

Preserve correspondences

Thursday, December 13, 12

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SLIDE 15

Manifold Projections

∑ ∑ ∑∑

− + − + − =

j i j i y j T i T j i j i x j T i T i j i j T i T j

W y y W x x W y x C C

, , 2 , , 2 , 2

) ( 5 . ) ( 5 . ) ( ) , ( where , ) , ( function cost the minimize to , functions mapping find want to We β β α α β α µ β α β α β α

Preserve correspondences

Thursday, December 13, 12

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SLIDE 16

Manifold Projections

∑ ∑ ∑∑

− + − + − =

j i j i y j T i T j i j i x j T i T i j i j T i T j

W y y W x x W y x C C

, , 2 , , 2 , 2

) ( 5 . ) ( 5 . ) ( ) , ( where , ) , ( function cost the minimize to , functions mapping find want to We β β α α β α µ β α β α β α

Preserve correspondences Preserve local geometry

Thursday, December 13, 12

slide-17
SLIDE 17

Manifold Projections

∑ ∑ ∑∑

− + − + − =

j i j i y j T i T j i j i x j T i T i j i j T i T j

W y y W x x W y x C C

, , 2 , , 2 , 2

) ( 5 . ) ( 5 . ) ( ) , ( where , ) , ( function cost the minimize to , functions mapping find want to We β β α α β α µ β α β α β α

Preserve correspondences Preserve local geometry

  • f

s eigenvalue smallest the to ing correspond rs eigenvecto the by given are minimize to : 1 Theorem (2) . ) , ( , γ λ γ β α β α

T T

ZDZ ZLZ C =

Thursday, December 13, 12

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SLIDE 18

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SLIDE 19

A Summary of Manifold Alignment Approaches

Given correspondences Given labels Unsupervised alignment Preserve Local geometry Preserve Global geometry One-step alignment Two-step alignment Feature-level Instance-level Procrustes alignment Manifold Projections (MP) Extensions of MP

Thursday, December 13, 12

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SLIDE 20

Manifold Warping

(Hoa, Carey, Mahadevan: AAAI, 2012)

Dynamic Time Warping Manifold Alignment + Iterate:

  • Find projection to lower-dimensional

space

  • Find new set of correspondences

Thursday, December 13, 12

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SLIDE 21

Activity Recognition

  • ’
  • The resulted alignment path of manifold warping is much closer to the ground truth alignment

Vu, Carey, and Mahadevan, AAAI 2012 CCA+DTW (Zhou, NIPS 2009)

Thursday, December 13, 12

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SLIDE 22

Social Network Alignment

  • Sparse Manifold Alignment

Use Lasso to find a sparse solution.

  • ’
  • Wang, Liu, Vu, and Mahadevan, 2012

DBLP Social Network

Thursday, December 13, 12

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SLIDE 23

Cross-Lingual Transfer in IR

Thursday, December 13, 12

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SLIDE 24

Cross-Lingual Transfer in IR

Signora Presidente, intervengo per una mozione d'ordine.Come avrà letto sui giornali o sentito alla televisione, in Sri Lanka si sono verificati numerosi assassinii ed esplosioni di ordigni. Madam President, on a point of order. You will be aware from the press and television that there have been a number of bomb explosions and killings in Sri Lanka.

English documents Italian documents

Frau Präsidentin, zur Geschäftsordnung. Wie Sie sicher aus der Presse und dem Fernsehen wissen, gab es in Sri Lanka mehrere Bombenexplosionen mit zahlreichen Toten.

German documents

Thursday, December 13, 12

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SLIDE 25

Cross-Lingual Transfer in IR

Signora Presidente, intervengo per una mozione d'ordine.Come avrà letto sui giornali o sentito alla televisione, in Sri Lanka si sono verificati numerosi assassinii ed esplosioni di ordigni. Madam President, on a point of order. You will be aware from the press and television that there have been a number of bomb explosions and killings in Sri Lanka.

English documents Italian documents

Frau Präsidentin, zur Geschäftsordnung. Wie Sie sicher aus der Presse und dem Fernsehen wissen, gab es in Sri Lanka mehrere Bombenexplosionen mit zahlreichen Toten.

German documents

Proceedings of the EU

Thursday, December 13, 12

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SLIDE 26

Cross-lingual IR

Thursday, December 13, 12

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SLIDE 27

Cross-lingual IR

Thursday, December 13, 12

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SLIDE 28

Impact of Work

Thursday, December 13, 12

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SLIDE 29

Impact of Work

  • The most useful research I have done in 20 years!

Thursday, December 13, 12

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SLIDE 30

Impact of Work

  • The most useful research I have done in 20 years!
  • Led to several new collaborations

Thursday, December 13, 12

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SLIDE 31

Impact of Work

  • The most useful research I have done in 20 years!
  • Led to several new collaborations
  • Mars rover Curiosity (Darby Dyar, Mount Holyoke, NASA/

JPL scientific team)

Thursday, December 13, 12

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SLIDE 32

Impact of Work

  • The most useful research I have done in 20 years!
  • Led to several new collaborations
  • Mars rover Curiosity (Darby Dyar, Mount Holyoke, NASA/

JPL scientific team)

  • Proposals submitted to CDS&E and BIGDATA

Thursday, December 13, 12

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SLIDE 33

Impact of Work

  • The most useful research I have done in 20 years!
  • Led to several new collaborations
  • Mars rover Curiosity (Darby Dyar, Mount Holyoke, NASA/

JPL scientific team)

  • Proposals submitted to CDS&E and BIGDATA
  • Papers: 100+ citations on Google Scholar

Thursday, December 13, 12

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SLIDE 34

Impact of Work

  • The most useful research I have done in 20 years!
  • Led to several new collaborations
  • Mars rover Curiosity (Darby Dyar, Mount Holyoke, NASA/

JPL scientific team)

  • Proposals submitted to CDS&E and BIGDATA
  • Papers: 100+ citations on Google Scholar
  • Many many applications (bioinformatics, graphics, robotics,

science, IR)

Thursday, December 13, 12

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SLIDE 35

Publications

Hoa Vu, CJ Carey, and Sridhar Mahadevan, “ Manifold Warping: Manifold Alignment over Time " , Proceedings of the 26th Conference on Artificial Intelligence (AAAI), July 22-26, 2012, Toronto, Canada. Chang Wang and Sridhar Mahadevan, “ Manifold Alignment Preserving Global Geometry " , Technical Report, UMass Computer Science Department UM- CS-2012-031, 2012. Chang Wang, Bo Liu, Hoa Vu, and Sridhar Mahadevan, “ Sparse Manifold Alignment " , Technical Report, UMass Computer Science UM-2012-030, 2012. Chang Wang and Sridhar Mahadevan, “ Heterogeneous Domain Adaptation using Manifold Alignment " , Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), July 18-23, 2011, Barcelona, Spain. Chang Wang and Sridhar Mahadevan, “ Jointly Learning Data-Depdendent Label and Locality-Preserving Projections " , Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), July 18-23, 2011, Barcelona, Spain. Blake Foster, Sridhar Mahadevan, and Rui Wang, “ GPU-Based Approximate SVD Algorithm " , 9th International Conference on Parallel Programming and Mathematics, Torun, Poland, September 11-14, 2011 (also available as Technical Report UM-CS-2011-025, Univ. of Massachusetts, Amherst). Chang Wang, Peter Krafft, and Sridhar Mahadevan, “ Manifold Alignment ", appearing in Manifold Learning: Theory and Applications, Taylor and Francis CRC Press. Chang Wang and Sridhar Mahadevan, "Multiscale Manifold Alignment" , Univ. of Massachusetts TR UM-CS-2010-049, 2010. Chang Wang and Sridhar Mahadevan, "Learning Locality Preserving Discriminative Features" , Univ. of Massachusetts TR UM-CS-2010-048, 2010.

Thursday, December 13, 12