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Ali Ghodsi Department of Statistics and Actuarial Science University of Waterloo October 2006

Learning from Shadows Dimensionality Reduction and its Application in Artificial Intelligence, Signal Processing and Robotics. Ali Ghodsi Department of Statistics and Actuarial Science University of Waterloo October 2006. Dimensionality Reduction. Dimensionality Reduction.

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Ali Ghodsi Department of Statistics and Actuarial Science University of Waterloo October 2006

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  1. Learning from ShadowsDimensionality Reduction and its Application in Artificial Intelligence, Signal Processing and Robotics Ali Ghodsi Department of Statistics and Actuarial Science University of Waterloo October 2006

  2. Dimensionality Reduction

  3. Dimensionality Reduction

  4. Manifold and Hidden Variables

  5. Data Representation

  6. Data Representation

  7. Data Representation

  8. -2.19 -3.19 -0.02 1.02 2 by 103 644 by 103 644 by 2 23 by 28 2 by 1 2 by 1 23 by 28

  9. Hastie, Tibshirani, Friedman 2001

  10. The Big Picture

  11. Uses of Dimensionality Reduction(Manifold Learning)

  12. Denoising Mika et. al. 1999 Zhu and Ghodsi 2005

  13. Tenenbaum, V de Silva, Langford 2001

  14. Roweis and. Saul 2000

  15. Roweis and Saul 2000 Arranging words: Each word was initially represented by a high-dimensional vector that counted the number of times it appeared in different encyclopedia articles. Words with similar contexts are collocated

  16. Hinton and Roweis 2002

  17. Embedding of Sparse Music Similarity Graph Platt, 2004

  18. Pattern Recognition Ghodsi, Huang, Schuurmans 2004

  19. Pattern Recognition

  20. Clustering

  21. Glasses vs. No Glasses

  22. Beard vs. No Beard

  23. Beard Distinction Ghodsi , Wilkinson, Southey 2006

  24. Glasses Distinction

  25. Multiple-Attribute Metric

  26. Reinforcement Learning Mahadevan and Maggioini, 2005

  27. Semi-supervised Learning Use graph-based discretization of manifold to infer missing labels. Belkin & Niyogi, 2004; Zien et al, Eds., 2005 Build classifiers from bottom eigenvectors of graph Laplacian.

  28. Ham et al, 2003, 2005 Learning Correspondences How can we learn manifold structure that is shared across multiple data sets?

  29. Mapping and Robot Localization • Bowling, Ghodsi, Wilkinson 2005 Ham, Lin, D.D. 2005

  30. Action Respecting Embedding Joint Work with Michael Bowling and Dana Wilkinson

  31. Modelling Temporal Data and Actions

  32. Outline • Background • PCA • Kernel PCA • Action Respecting Embedding (ARE) • Prediction and Planning • Probabilistic Actions • Future Work

  33. Principal Component Analysis (PCA)

  34. Principal Component Analysis (PCA)

  35. Kernel Methods

  36. Kernel Trick

  37. Observed, Feature and Embedded Spaces

  38. Kernel PCA

  39. Problem

  40. Idea

  41. Action Respecting Embedding (ARE)

  42. Action Respecting Constraint

  43. Local Distances Constraint Preserve distances between each point and its k nearest neighbors.

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