I understand that PCA takes a data set with input size, with output labels, and reduces the inputs to a set of principal components size r, where r < n.
My question is whether or not this can be applied beyond a simple classification problem where the outputs are not simply labels. For instance, in sheet metal forming of a part, the inputs could be temperature, initial thickness, applied force, etc. while the output is thickness.
Could we use PCA (or kernel PCA) to reduce the inputs to a smaller number while relating them to the output as a thickness and not a label?