Dimension Reduction
Simon Foucart · Cambridge University Press eBooks · 2022
The high dimensionality of datapoints often constitutes an obstacle to efficient computations. This chapter investigates three workarounds that replace the datapoints by some substitutes selected in a lower dimensional set. The first workaround is principal component analysis, where the lower dimensional set is a linear space spanned by the top singular vectors of the data matrix. The second workaround is a Johnson–Lindenstrauss projection, where the lower dimensional set is a random linear space. The third workaround is locally linear embedding, where the lower dimensional set is not chosen as a linear space anymore.