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For tensor decompositions such as HOSVD and ParaFac, the objective functionsare nonconvex. This implies, theoretically, there exists a large number oflocal optimas: starting from different starting point, the iteratively improvedsolution will converge to different local solutions. This non-uniquenesspresent a stability and reliability problem for image compression andretrieval. In this paper, we present the results of a comprehensiveinvestigation of this problem. We found that although all tensor decompositionalgorithms fail to reach a unique global solution on random data and severelyscrambled data; surprisingly however, on all real life several data sets (evenwith substantial scramble and occlusions), HOSVD always produce the uniqueglobal solution in the parameter region suitable to practical applications,while ParaFac produce non-unique solutions. We provide an eigenvalue based rulefor the assessing the solution uniqueness.

Are Tensor Decomposition Solutions Unique? On the global convergence of HOSVD and ParaFac algorithms