My understanding after scanning the code examples is the technique expands the dimensionality of each data point with a set consisting of the quadratic coefficients of its existing dimensions. I thought it sounded like kernel PCA.
I think that kernel PCA is a strict superset of PCA. That would make it trivially true that it beats PCA.
I think that kernel PCA is a strict superset of PCA. That would make it trivially true that it beats PCA.