CPD Computation via Recursive Eigenspace Decompositions

The Canonical Polyadic Decomposition (CPD) is a fundamental tensor decomposition which has widespread use in signal processing due to its ability to extract component information. A popular for algorithm CPD is the generalized eigenvalue decomposition (GEVD) which is based on the generalized eigenvectors of a subpencil of a tensor. GEVD plays an important role in applications as it provides strong algebraic initializations for optimization routines for CPD computation. In fact, using GEVD initializations can improve final accuracy and reduce computation time. However, despite GEVD’s success, the algorithm underperforms in some settings and exhibits pencil-based instability.We present a recursive generalized eigenspace decomposition (GESD) for CPD computation. Rather using one sub-pencil, GESD combines generalized eigenspace information from many subpencils to compute a CPD. GESD is more accurate than GEVD and thereby improves the reliability of the components extracted by CPD. We also give a Cramér-Rao based analysis for the accuracy of GESD.