Algorithm 1. EM algorithm

Procedure EM algorithm returns activation and pose of the capsules in layer l + 1 based on activations and poses of capsules in layer l. $V_{ij}^h$ is the $h^{th}$ dimension of the vote from capsule i with activation $a_i$ in layer l to capsule j in layer L + 1. $m_j^h$ is the hth dimension of the pose from capsule j. $R_{ij}$ is initialized to $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\left|I_{l+1}\right|$}\right.$.

M-STEP for one higher-level capsule $R_{ij}=a_i{R}_{ij}$, $\forall i\in I_l$ $m_j^h=\frac{{{\displaystyle \sum }}_i{R}_{ij}{V}_{ij}^h}{{{\displaystyle \sum }}_i{R}_{ij}}$, $\forall h$ ${\left({\sigma }_j^h\right)}^2=\frac{{{\displaystyle \sum }}_i{R}_{ij}{V}_{ij}^h}{{{\displaystyle \sum }}_i{R}_{ij}}$, $\forall h$ $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}cos{t}^h=\left({\gamma }_u+log\left({\sigma }_j^h\right)\right){{\displaystyle \sum }}_i{R}_{ij}$ $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{a}_j=logistic\left(\rho \left({\gamma }_v-{{\displaystyle \sum }}_{h}cos{t}^h\right)\right)$ E-STEP for one lower-level capsule $p_j=\frac{1}{\sqrt{{{\displaystyle \prod }}_{h}2\pi {\left({\sigma }_j^h\right)}^2}}{e}^{\left(-{{\displaystyle \sum }}_h\frac{{\left(V_{ij}^h-m_j^h\right)}^2}{2{\left({\sigma }_j^h\right)}^2}\right)}$, $\forall j\in I_{l+1}$ $R_{ij}=\frac{a_j{p}_j}{{{\displaystyle \sum }}_{n\in I_{l+1}}{a}_n{p}_n}$, $\forall j\in I_{l+1}$