In [[multilinear algebra]], the '''higher-order singular value decomposition''' ('''HOSVD''') is a misnomer. sincethereThere does not exist a single tensor decomposition that retains all the defining properties of the matrix SVD. The matrix SVD simultaneously yields a rank-𝑅 decomposition and computes orthonormal subspaces for the row and column spaces and a diagonal matrix. These properties are not realized within a single algorithm for higher-order tensors, but are instead realized by two distinct algorithmic developments and represent two distinct research directions. Harshman, as well as, the team of Carol and Chang proposed [[Canonical polyadic decomposition]] (CPD), which is a variant of the [[tensor rank decomposition]], in which a tensor is approximated as a sum of ''K rank-1'' tensors for a user-specified ''K''. [[L. R. Tucker]] proposed a strategy for computing orthonormal subspaces for third order tensors. Aspecsts of these algorithms can be traced as far back as [[F. L. Hitchcock]] in 1928.<ref name=":0">{{Cite journal|last=Hitchcock|first=Frank L|date=1928-04-01|title=Multiple Invariants and Generalized Rank of a M-Way Array or Tensor|journal=Journal of Mathematics and Physics|language=en|volume=7|issue=1–4|pages=39–79|doi=10.1002/sapm19287139|issn=1467-9590}}</ref>
