REBUILD: Build an approximation of the tensor of any order

In PTAk: Principal Tensor Analysis on k Modes

Build an approximation of the tensor of any order

Description

Gives the approximation of a previously analysed tensor using its given decomposition.

Usage

 REBUILD(solutions,nTens=1:2,testvar=1 ,redundancy=FALSE)

Arguments

solutions	a PTAk object
nTens	a vector of identifying positions (numbers given in summary) for the choice of Principal Tensors to use
testvar	control within nTens used Principal Tensor with minimum percent of variability explained
redundancy	logical to take into account (within nTens) PT tested redundant during analysis (seealso RESUM) if TRUE.

Details

The function rebuilds the Principal Tensors, i.e. rank-one tensors of order the order of the tensor analysed, and add them up to build an approximation of the tensor analysed (according to the method used see method). This constitutes a best Least Squares (ordinary or "weighted" if metrics are used) approximation of datanam for a given orthogonal-rank r (number of principal tensors used), if and only if the singular values used are the r highest.

Value

A tensor with dimensions as solutions[[k]][["datanam"]].

Note

This function can be called for PARAFAC/CANDECOMP and PCAn. A specific rebuilt is implemented for this last one.

Author(s)

Didier G. Leibovici

See Also

PTAk

PTAk documentation built on March 31, 2023, 5:17 p.m.