Exercise:Independent Component Analysis

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(Step 4: Optimization)
(Step 4: Optimization)
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In step 4, you will optimize for the orthonormal ICA objective using gradient descent with backtracking line search (the code for which has already been provided for you. For more details on the backtracking line search, you may wish to consult the [[Exercise:Independent Component Analysis#Appendix| appendix ]] of this exercise). The orthonormality constraint should be enforced with a projection, which you should fill in.
In step 4, you will optimize for the orthonormal ICA objective using gradient descent with backtracking line search (the code for which has already been provided for you. For more details on the backtracking line search, you may wish to consult the [[Exercise:Independent Component Analysis#Appendix| appendix ]] of this exercise). The orthonormality constraint should be enforced with a projection, which you should fill in.
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Once you have filled in the code for the projection, check that it is correct by using the verification code provided. Once you have verified that your projection is correct, comment out the verification code and run the optimization. 10 000 iterations of gradient descent should take around 2 hours, and produce a basis which looks like the following:
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Once you have filled in the code for the projection, check that it is correct by using the verification code provided. Once you have verified that your projection is correct, comment out the verification code and run the optimization. 1000 iterations of gradient descent should take less than 15 minutes, and produce a basis which looks like the following:
[[File:OrthonormalICAFeatures.png | 350px]]
[[File:OrthonormalICAFeatures.png | 350px]]

Revision as of 04:29, 4 October 2011

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