A large amount of research has been done on algorithms utilizing the
fourth-order
cumulant tensor (see Section 4.3.5) for estimation of ICA
[20,21,22,29,27,36].
These are typically batch algorithms (non-adaptive), using
such tensorial techniques as eigenmatrix decomposition, which is a
generalization of eigenvalue decomposition for higher-order tensors.
Such a decomposition can be performed using ordinary algorithms
for eigen-value decomposition of matrices, but this requires matrices
of size
.
Since such matrices is often too large, specialized Lanczos type
algorithms of lower complexity have also been developed [20].
These algorithms often perform very efficiently on small dimensions.
However, in large dimensions, the memory requirements
may be prohibitive, because often the coefficients of the 4-th order
tensor must be stored in memory, which requires *O*(*m*^{4}) units of memory.
The algorithms also tend to be quite complicated to program, requiring
sophisticated matrix manipulations.