Discuss the differences between dimensionality reduction based on aggrega- tion and dimensionality reduction based on techniques such as PCA and SVD.

What will be an ideal response?

The dimensionality of PCA or SVD can be viewed as a projection of the
data onto a reduced set of dimensions. In aggregation, groups of dimensions
are combined. In some cases, as when days are aggregated into months or
the sales of a product are aggregated by store location, the aggregation can
be viewed as a change of scale. In contrast, the dimensionality reduction
provided by PCA and SVD do not have such an interpretation.