The curse of dimensionality describes the apparent paradox of “neighborhoods” in higher dimensions, if the neighborhoods are “local,” then they are almost surely “empty,” whereas if a neighborhood is not “empty,” then it is not “local.” If the bandwidth is large enough to include enough data to hold down the variance, the bias is intolerable due to the large neighborhood, and vice versa. The presence of rank deficiencies in the multivariate data, rather than the fact of high dimensions per se, is the more important component of the curse of dimensionality. This chapter focuses on the recognition of rank deficiencies and corresponding projection algorithms and deals with dimension reduction technology. Dimension‐reduction transformations based on prior knowledge are common in applied sciences.