Algorithm 1 PFBP-STP

Input:  vectors $x_1$, $x_2$ and $x_3$; Output:  vector $z_{12}$, $z_{13}$;   1:Factorize the projection matrix: ${\mathbf{W}}_i={\mathbf{U}}_i⋉{\mathbf{V}}_i^T$.   2:Projecting: ${\sum }_{i=1}^o{x}_2^T{\mathbf{U}}_i⋉{\mathbf{V}}_i^T{x}_1$ and ${\sum }_{i=1}^o{x}_3^T{\overline{\mathbf{U}}}_i⋉{\overline{\mathbf{V}}}_i^T{x}_1$.   3:STP-pooling: z12 = STP-pooling $\left(y_{12}⋉w_0,h\right)$, z13 = STP-pooling $\left(y_{13}⋉w_0,h\right)$.   4:Soft fusion: ${\mathbf{S}}_z\left(c\right)={\mathbf{W}}_{12}·{\mathbf{S}}_{12}\left(c\right)+{\mathbf{W}}_{13}·{\mathbf{S}}_{13}\left(c\right).$   5:Return ${\mathbf{S}}_z\left(c\right)$.