CP decomposition of semi-nonnegative semisymmetric tensors based on QR matrix factorization

Lu Wang (1, 2) , Laurent Albera (1, 2, 3) , Amar Kachenoura (1) , Huazhong Shu (2, 4) , Lotfi Senhadji (1, 2)

1 LTSI - Laboratoire Traitement du Signal et de l'Image
2 CRIBS - Centre de Recherche en Information Biomédicale sino-français
3 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
4 LIST - Laboratory of Image Science and Technology [Nanjing]

The problem of Canonical Polyadic (CP) decomposition of semi-nonnegative semi-symmetric three-way arrays is often encountered in Independent Component Analysis (ICA), where the cumulant of a nonnegative mixing process is frequently involved, such as the Magnetic Resonance Spectroscopy (MRS). We propose a new method, called JD+QR, to solve such a problem. The nonnegativity constraint is imposed by means of a square change of variable. Then the high-dimensional optimization problem is decomposed into several sequential rational subproblems using QR matrix factorization. A numerical experiment on simulated arrays emphasizes its good performance. A BSS application on MRS data confirms the validity and improvement of the proposed method.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Analyse numérique [math.NA]

Lu Wang, Laurent Albera, Amar Kachenoura, Huazhong Shu, Lotfi Senhadji. CP decomposition of semi-nonnegative semisymmetric tensors based on QR matrix factorization. The eighth IEEE Sensor Array and Multi-Channel Signal Processing Workshop, Jun 2014, A Coruna, Spain. 4 p. ⟨hal-01012125⟩