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Subspace Learning
Published on Aug 26, 20135480 Views
This work deals with the problem of linear subspace estimation in a general, Hilbert space setting. We provide bounds that are considerably sharper than existing ones, under equal assumptions. These b
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Chapter list
Subspace Learning00:00
Outline00:23
Introduction - 100:24
Introduction - 200:40
Setting: Why a Hilbert Space H00:47
Example 1: PCA - Kernel PCA01:30
Example 2: Kernel Support Estimation02:13
Problem definition03:31
Covariance Lemma in the continuous case04:01
Truncated estimator04:16
Which metric?04:45
Metric for Kernel PCA05:39
Metric for Support Estimation06:20
More on General metric07:37
Main results08:43
Learning rate for the general metric - 108:44
Learning rate for the general metric - 209:35
Learning Rates for Kernel PCA and Reconstruction error10:14
Rates comparison on Kernel PCA10:30
Learning Rates for Kernel Support Estimation12:11
Rates comparison on Kernel Support Estimation12:42
Numerics13:52
Experiments:Simulation on Kernel PCA - 113:53
Experiments: Numerical tradeoff in Kernel PCA - 315:20
Experiments:Simulation on Kernel PCA - 215:25
Contribution16:42
References17:20