  For tensor decompositions such as HOSVD and ParaFac, the objective functions
are nonconvex. This implies, theoretically, there exists a large number of
local optimas: starting from different starting point, the iteratively improved
solution will converge to different local solutions. This non-uniqueness
present a stability and reliability problem for image compression and
retrieval. In this paper, we present the results of a comprehensive
investigation of this problem. We found that although all tensor decomposition
algorithms fail to reach a unique global solution on random data and severely
scrambled data; surprisingly however, on all real life several data sets (even
with substantial scramble and occlusions), HOSVD always produce the unique
global solution in the parameter region suitable to practical applications,
while ParaFac produce non-unique solutions. We provide an eigenvalue based rule
for the assessing the solution uniqueness.
