Autors: Kountchev, R. K., Mironov, R. P., Kountcheva R. Title: Complexity Estimation of Cubical Tensor Represented through 3D FrequencyOrdered Hierarchical KLT Keywords: cubical tensor decomposition; 3D hierarchical adaptive PCA transform; 3D FrequencyOrdered Hierarchical KLT; computational complexity Abstract: In this work is introduced one new hierarchical decomposition for cubical tensor of size 2n, based on the wellknown orthogonal transforms Principal Component Analysis and Karhunen–Loeve Transform. The decomposition is called 3D FrequencyOrdered Hierarchical KLT (3DFOHKLT). It is separable, and its calculation is based on the onedimensional FrequencyOrdered Hierarchical KLT (1DFOHKLT) applied on a sequence of matrices. The transform matrix is the product of n sparse matrices, symmetrical at the point of their main diagonal. In particular, for the case in which the angles which define the transform coecients for the couples of matrices in each hierarchical level of 1DFOHKLT are equal to /4, the transform coincides with this of the frequencyordered 1D Walsh–Hadamard. Compared to the hierarchical decompositions of Tucker (HTucker) and the TensorTrain (TT), the oered approach does not ensure full decorrelation between its components, but is close to the maximum. References Issue

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