${\mathbb{A}}_{1}=\left\{1,2,3\right\}$ ${\stackrel{̂}{\mathbit{W}}}_{\mathit{\text{lr}}\left(1,2,3\right)}$ ${\stackrel{̂}{\Lambda }}_{\left(1,2,3\right)}$ r 123 Vector
${\mathbb{A}}_{1}=\left\{1\right\}$, ${\mathbb{A}}_{2}=\left\{2\right\}$, ${\mathbb{A}}_{3}=\left\{3\right\}$ ${\stackrel{̂}{\mathbit{W}}}_{\mathit{\text{lr}}\left(1/2/3\right)}$ ${\stackrel{̂}{\Lambda }}_{\left(1/2/3\right)}$ r1, r2, r3 HOSVD
${\mathbb{A}}_{1}=\left\{1,2\right\}$, ${\mathbb{A}}_{2}=\left\{3\right\}$ ${\stackrel{̂}{\mathbit{W}}}_{\mathit{\text{lr}}\left(1,2/3\right)}$ ${\stackrel{̂}{\Lambda }}_{\left(1,2/3\right)}$ r12, r3 AU-HOSVD
${\mathbb{A}}_{1}=\left\{1\right\}$, ${\mathbb{A}}_{2}=\left\{2,3\right\}$ ${\stackrel{̂}{\mathbit{W}}}_{\mathit{\text{lr}}\left(1/2,3\right)}$ ${\stackrel{̂}{\Lambda }}_{\left(1/2,3\right)}$ r1, r23 AU-HOSVD
${\mathbb{A}}_{1}=\left\{1,3\right\}$, ${\mathbb{A}}_{2}=\left\{2\right\}$ ${\stackrel{̂}{\mathbit{W}}}_{\mathit{\text{lr}}\left(1,3/2\right)}$ ${\stackrel{̂}{\Lambda }}_{\left(1,3/2\right)}$ r13, r2 AU-HOSVD 