14:25 summarizes very well what KPCA is up to. It's identical to PCA, only that instead of weighting values of variables by corresponding eigenvector weights, the eigenvector weights are applied to the kernel of data points. Why apply to kernels instead of the original variables? So that we can benefit from the kernel trick, which means we can compute in the original dimensional space but basically figure out what's "going on" in higher-D even if we do not know the exact function in higher D. The kernel trick is not exclusive to KPCA but is also seen in techniques such as support vector machines and other kernel methods.
Great lecture! thank you! I believe there's a small typo at 13:30 . In the bottom row, the subscript of the first x in the third addend should be j rather than i.
I don't know if an answer after two years would help, but basically, apply linear PCA and plot it. If the linear PCA worked perfectly, then your data has a linear structure and vise versa.
Hi, the reference should be corrected as Tanenbaum et al., Science 22, 2000 not 2009. Took me a while to find. Great video and thanks a lot!
Outstanding speaker and communicator.
Very well explain and presented ,
really quite helpful
14:25 summarizes very well what KPCA is up to. It's identical to PCA, only that instead of weighting values of variables by corresponding eigenvector weights, the eigenvector weights are applied to the kernel of data points. Why apply to kernels instead of the original variables? So that we can benefit from the kernel trick, which means we can compute in the original dimensional space but basically figure out what's "going on" in higher-D even if we do not know the exact function in higher D. The kernel trick is not exclusive to KPCA but is also seen in techniques such as support vector machines and other kernel methods.
Excelente, me encanto!
Great lecture! thank you!
I believe there's a small typo at 13:30 . In the bottom row, the subscript of the first x in the third addend should be j rather than i.
Thank you so help full
Thank you very much!
Very well presented. Thank you.
awesome!
Can you give the playlist where lectures are in sequence?
How do you know beforhand that your dataset has a non-linear structure if you are a dimension higher than 3?
I have never understood this. All examples that I come across are with toy datasets and that does not help me.
@@sau002 Depends on what you want to do. Try linear approach and if it fails you might consider using non linear ones ?
If your linear methods result in bad accuracy, you can try non linear methods. although you will not know for certain
I don't know if an answer after two years would help, but basically, apply linear PCA and plot it. If the linear PCA worked perfectly, then your data has a linear structure and vise versa.
@@scholar7558 Ok thank you very much for the help! :) I really apreciate it
Poor pedagogy...