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Spectral Dimensionality Reduction via Maximum Entropy, incl. discussion by Laurens van der Maaten
Published on May 06, 20115414 Views
We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian random fields (GRFs). Our unifying perspective is based on the maximum entropy principle whi
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Chapter list
Spectral Dimensionality Reduction via Maximum Entropy00:00
Outline00:35
Maximum Entropy Unfolding00:38
Spectral Approaches (1)00:39
Spectral Approaches (2)01:06
Spectral Approaches (3)01:35
Spectral Approaches (4)01:52
Spectral Approaches (5)01:54
Classical MDS and KPCA (1)02:15
Classical MDS and KPCA (2)02:40
Classical MDS and KPCA (3)02:55
Maximum Variance Unfolding (1)03:41
Maximum Variance Unfolding (2)03:50
Maximum Variance Unfolding (2)03:51
Maximum Variance Unfolding (3)03:52
Maximum Variance Unfolding (4)03:58
Maximum Entropy Unfolding (1)04:35
Maximum Entropy Unfolding (2)04:49
Maximum Entropy Unfolding (3)05:00
Maximum Entropy Unfolding (4)05:02
Maximum Entropy Unfolding (5)05:34
Maximum Entropy Unfolding (6)06:16
Gaussian Random Field (1)06:51
Gaussian Random Field (2)07:21
Gaussian Random Field (3)07:37
Gaussian Random Field (4)07:54
Gaussian Random Field (5)08:01
Data Feature Independence08:20
Blessing of Dimensionality (1)09:11
Blessing of Dimensionality (2)09:15
Blessing of Dimensionality (3)09:16
Blessing of Dimensionality (4)09:20
Blessing of Dimensionality (4)09:22
Blessing of Dimensionality (5)09:28
Blessing of Dimensionality (6)09:52
Relations to Other Spectral Methods10:16
Relationship to Laplacian Eigenmaps (1)10:18
Relationship to Laplacian Eigenmaps (2)10:19
Relationship to Laplacian Eigenmaps (3)10:20
Relationship to Laplacian Eigenmaps (4)10:20
Relationship to Laplacian Eigenmaps (5)10:21
Relationship to Laplacian Eigenmaps (6)10:22
Locally Linear Embedding (1)11:19
Locally Linear Embedding (2)11:23
Locally Linear Embedding (3)11:30
Locally Linear Embedding (4)11:43
Locally Linear Embedding (5)11:45
Locally Linear Embedding (6)12:10
Locally Linear Embedding (7)12:16
Locally Linear Embedding (8)12:25
LLE Approximates MEU (1)12:37
LLE Approximates MEU (2)12:48
LLE Approximates MEU (3)12:50
LLE Approximates MEU (4)12:54
LLE Approximates MEU (5)13:00
LLE Approximates MEU (6)13:05
LLE and PC (1)13:12
LLE and PC (2)13:15
LLE and PC (3)13:17
LLE and PC (4)13:19
Isomap (1)13:54
Isomap (2)13:58
Isomap (3)14:00
Isomap (4)14:01
Isomap (5)14:02
Relation to GP-LVM (1)14:34
Relation to GP-LVM (2)14:35
Relation to GP-LVM (3)14:36
Relation to GP-LVM (4)14:37
Experiments14:38
Simple Experiments14:41
Motion Capture Data14:44
Laplacian Eigenmaps and LLE15:06
Isomap and MVU15:15
MEU15:20
Motion Capture: Model Scores15:24
Robot Navigation Example15:52
Laplacian Eigenmaps and LLE16:17
Isomap and MVU16:19
MEU16:25
Robot Navigation: Model Scores16:48
Discussion and Conclusions16:59
Stages of Spectral Dimensionality Reduction (1)17:04
Stages of Spectral Dimensionality Reduction (2)17:11
Stages of Spectral Dimensionality Reduction (3)17:26
Stages of Spectral Dimensionality Reduction (4)17:45
Our Perspective (1)18:34
Our Perspective (2)18:35
Our Perspective (3)18:36
Our Perspective (4)18:37
Our Perspective (5)18:39
Advantages of Existing Approaches (1)18:42
Advantages of Existing Approaches (2)18:45
Advantages of Existing Approaches (3)18:53
Acknowledgements19:14
Discussion of “Spectral Dimensionality Reduction via Maximum Entropy”19:30
Timeline19:43
Manifold learning vs. generative modeling (1)21:24
Manifold learning vs. generative modeling (2)22:42
Manifold learning vs. generative modeling (3)23:38
Rank minimization (1)25:02
Rank minimization (2)26:01