Tucker3 Tensor Decomposition for the Standardized Residual Hypermatrix on Three-Way Correspondence Analysis

Lestari, Karunia Eka
Yudhanegara, Mokhammad Ridwan
Nugraha, Edwin Setiawan
Sylviani, Sisilia

Journal of the Indonesian Mathematical Society
Vol. 31 No. 2 (2025): JUNE

This study investigates the theoretical and practical mathematical aspects of Tucker3 tensor decomposition from the three-way correspondence analysis point of view. Since the standardized residual hypermatrix represents the association of the three categorical variables, this study focused on (1) Tucker3 tensor decomposition for the standardized residual hypermatrix, (2) some mathematical properties of Tucker3 tensor decomposition, and (3) constructing the correspondence plot via Tucker3 tensor decomposition. Some mathematical results are presented in lemmas, theorems and algorithms, while a practical result is exhibited at the end of the discussion.