Extension Of The Semi-Algebraic Framework For Approximate Cp Decompositions Via Non-Symmetric Simultaneous Matrix Diagonalization

With the increased importance of the CP decomposition (CAN-DECOMP / PARAFAC decomposition), efficient methods for its calculation are necessary. In this paper we present an extension of the SECSI (SEmi-algebraic framework for approximate CP decomposition via SImultaneous matrix diagonalization) that is based on new non-symmetric SMDs (Simultaneous Matrix Diagonalizations). Moreover, two different algorithms to calculate non-symmetric SMDs are presented as examples, the TEDIA (TEnsor DIAgonalization) algorithm and the IDIEM-NS (Improved DIagonalization using Equivalent Matrices- Non Symmetric) algorithm. The SECSI-TEDIA framework has an increased computational complexity but often achieves a better performance than the original SECSI framework. On the other hand, the SECSI-IDIEM framework offers a lower computational complexity while sacrificing some performance accuracy.