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ch5_MoreExamples.pdf

  1. 1. Example 1: PCA for genetic data “Genes mirror geography within Europe”, Nature 2008
  2. 2. Example 2: PCA for digit data Courtesy of Lester Mackey
  3. 3. Example 2: PCA for digit data Courtesy of Lester Mackey
  4. 4. Example 2: PCA for digit data Courtesy of Lester Mackey
  5. 5. Example 3: the data (many faces!) https://sandipanweb.wordpress.com/2018/01/06/eigenfaces-and-a-simple-face- detector-with-pca-svd-in-python/
  6. 6. Example 3: comparing PCA and NMF Eigenface Black: >0 White: 0 Red: <0 “Learning the parts of objects by non-negative matrix factorization”, Nature 1999
  7. 7. Example 3: comparing PCA and NMF Parts of the face Black: >0 White: 0 Red: <0 “Learning the parts of objects by non-negative matrix factorization”, Nature 1999
  8. 8. Example 3: PCA on faces x_bar nPC=1070 https://sandipanweb.wordpress.com/2018/01/06/eigenfaces-and-a-simple-face- detector-with-pca-svd-in-python/
  9. 9. Example 4: SVD and image compression Machine Learning: A Probabilistic perspective, Kevin P. Murphy Original Rank=2 Rank=20 Rank=5 Matlab source code: https://github.com/probml/pmtk3/blob/master/demos/svdImageDemo.m
  10. 10. Extensions of PCA • Probabilistic PCA • Ch12, Pattern Recognition and Machine Learning, Christopher Bishop • Exponential family PCA • Explicitly model binary, categorical and count data Nonlinear dimension reduction: • Kernel PCA • Variational Autoencoder (VAE) Courtesy of Percy Liang
  11. 11. Variational Autoencoder (VAE) • Non-linear dimension reduction method based on neural network
  12. 12. • In PCA, we can generate new 3 by varying • Similar concept applies to VAE <latexit sha1_base64="/JI5iynvNWOEKZjLq6ujHWhdsHw=">AAAB7nicbVDLSsNAFL2pr1pfVZduBovgqiQi1GXRjcsK9gFtKJPJpB06mYSZG6GEfoQbF4q49Xvc+TdO2yy09cDA4ZxzmXtPkEph0HW/ndLG5tb2Tnm3srd/cHhUPT7pmCTTjLdZIhPdC6jhUijeRoGS91LNaRxI3g0md3O/+8S1EYl6xGnK/ZiOlIgEo2il7kDaaEiH1Zpbdxcg68QrSA0KtIbVr0GYsCzmCpmkxvQ9N0U/pxoFk3xWGWSGp5RN6Ij3LVU05sbPF+vOyIVVQhIl2j6FZKH+nshpbMw0Dmwypjg2q95c/M/rZxjd+LlQaYZcseVHUSYJJmR+OwmF5gzl1BLKtLC7EjammjK0DVVsCd7qyeukc1X33Lr3cF1r3hZ1lOEMzuESPGhAE+6hBW1gMIFneIU3J3VenHfnYxktOcXMKfyB8/kDPMWPfQ==</latexit> <latexit sha1_base64="/JI5iynvNWOEKZjLq6ujHWhdsHw=">AAAB7nicbVDLSsNAFL2pr1pfVZduBovgqiQi1GXRjcsK9gFtKJPJpB06mYSZG6GEfoQbF4q49Xvc+TdO2yy09cDA4ZxzmXtPkEph0HW/ndLG5tb2Tnm3srd/cHhUPT7pmCTTjLdZIhPdC6jhUijeRoGS91LNaRxI3g0md3O/+8S1EYl6xGnK/ZiOlIgEo2il7kDaaEiH1Zpbdxcg68QrSA0KtIbVr0GYsCzmCpmkxvQ9N0U/pxoFk3xWGWSGp5RN6Ij3LVU05sbPF+vOyIVVQhIl2j6FZKH+nshpbMw0Dmwypjg2q95c/M/rZxjd+LlQaYZcseVHUSYJJmR+OwmF5gzl1BLKtLC7EjammjK0DVVsCd7qyeukc1X33Lr3cF1r3hZ1lOEMzuESPGhAE+6hBW1gMIFneIU3J3VenHfnYxktOcXMKfyB8/kDPMWPfQ==</latexit> <latexit sha1_base64="/JI5iynvNWOEKZjLq6ujHWhdsHw=">AAAB7nicbVDLSsNAFL2pr1pfVZduBovgqiQi1GXRjcsK9gFtKJPJpB06mYSZG6GEfoQbF4q49Xvc+TdO2yy09cDA4ZxzmXtPkEph0HW/ndLG5tb2Tnm3srd/cHhUPT7pmCTTjLdZIhPdC6jhUijeRoGS91LNaRxI3g0md3O/+8S1EYl6xGnK/ZiOlIgEo2il7kDaaEiH1Zpbdxcg68QrSA0KtIbVr0GYsCzmCpmkxvQ9N0U/pxoFk3xWGWSGp5RN6Ij3LVU05sbPF+vOyIVVQhIl2j6FZKH+nshpbMw0Dmwypjg2q95c/M/rZxjd+LlQaYZcseVHUSYJJmR+OwmF5gzl1BLKtLC7EjammjK0DVVsCd7qyeukc1X33Lr3cF1r3hZ1lOEMzuESPGhAE+6hBW1gMIFneIU3J3VenHfnYxktOcXMKfyB8/kDPMWPfQ==</latexit> <latexit sha1_base64="/JI5iynvNWOEKZjLq6ujHWhdsHw=">AAAB7nicbVDLSsNAFL2pr1pfVZduBovgqiQi1GXRjcsK9gFtKJPJpB06mYSZG6GEfoQbF4q49Xvc+TdO2yy09cDA4ZxzmXtPkEph0HW/ndLG5tb2Tnm3srd/cHhUPT7pmCTTjLdZIhPdC6jhUijeRoGS91LNaRxI3g0md3O/+8S1EYl6xGnK/ZiOlIgEo2il7kDaaEiH1Zpbdxcg68QrSA0KtIbVr0GYsCzmCpmkxvQ9N0U/pxoFk3xWGWSGp5RN6Ij3LVU05sbPF+vOyIVVQhIl2j6FZKH+nshpbMw0Dmwypjg2q95c/M/rZxjd+LlQaYZcseVHUSYJJmR+OwmF5gzl1BLKtLC7EjammjK0DVVsCd7qyeukc1X33Lr3cF1r3hZ1lOEMzuESPGhAE+6hBW1gMIFneIU3J3VenHfnYxktOcXMKfyB8/kDPMWPfQ==</latexit>
  13. 13. Example 5: VAE for image re-synthesis Variational inference & deep learning: a new synthesis, Diederik P. Kingma, 2017

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