A limitation is a derivative of what you mentioned: how to pick a proper kernel to make the data linearly separable? How do we check we have made our data set linearly separable?
PCA can sometimes make linear classification harder if the class separation information is not aligned with the principal components. This is not a "failure" of PCA, but rather a mismatch between PCA's objective (variance preservation) and the downstream task's requirement (class separation).
A limitation is a derivative of what you mentioned: how to pick a proper kernel to make the data linearly separable? How do we check we have made our data set linearly separable?
Rightly said, Giorgio :)
I vividly remember looking around for the answers myself once I was stuck. There are some great answers here if you wish to read: https://stats.stackexchange.com/questions/131142/how-to-choose-a-kernel-for-kernel-pca.
Thank you, good links
You put in admirable efforts to offer a new angle on data science, each day! Well done
Thanks for appreciating, Giorgio. Really appreciate the kind words :)
I beg to differ a bit.
PCA can sometimes make linear classification harder if the class separation information is not aligned with the principal components. This is not a "failure" of PCA, but rather a mismatch between PCA's objective (variance preservation) and the downstream task's requirement (class separation).