Dimensionality reduction is the representation of data using fewer coordinates while preserving selected features, such as variation or distances
(Cunningham and Ghahramani 2015). A linear method uses a linear
transformation to map 
to 
,
where 
, 
is a 
matrix, and 
denotes the real numbers.
Principal component analysis chooses directions that retain the most variance. A Tucker decomposition with a smaller core can give a compressed representation of a tensor (Kolda and Bader 2009, p. 475). The retained features depend on the mathematical objective of the method. Nonlinear methods include uniform manifold approximation and projection, which constructs a weighted graph of local similarities and computes a low-dimensional layout (McInnes et al. 2020).
