So what alternative method of dimensionality reduction does the author recommend? Considering that PCA works fine in the case that the dimensions form a proper

So what alternative method of dimensionality reduction does the author recommend? Considering that PCA works fine in the case that the dimensions form a proper vector space (e.g. geometrical space, stock market returns, temperature, etc, etc ,etc), it seems questionable to completely dismiss such a useful and historically important method.