Algorithm 1.

Learning algorithm based on Gibbs sampling.

1:   procedure Gibbs_Sampling (a, p, o, c, w, A)

2:    Setting of hyperparameters {α}, {β}, λ, γ

3:    Initialization of parameters and latent variables {π}, {ϕ}, θ, {z}, F

4:    for j = 1 to iteration_number do

5:     πo ∼ Dir(πo | zo, αo)   // equation (12)

6:     πc ∼ Dir(πc| zc, αc)     // equation (13)

7:     πp ∼ Dir(πp| zp, αp)    // equation (14)

8:     πa ∼ Dir(πa| za, αa)    // equation (15)

9:     for k = 1 to Ko do

10:      ${\varphi }_k^{\text{o}}\sim \text{GIW}\left({\varphi }_k^{\text{o}}\mathrm{|}{o}_k,{\beta }^{\text{o}}\right)$   // equation (16)

11:     end for

12:     for k = 1 to Kc do

13:      ${\varphi }_k^{\text{c}}\sim \text{GIW}\left({\varphi }_k^{\text{c}}\mathrm{|}{c}_k,{\beta }^{\text{c}}\right)$   // equation (17)

14:     end for

15:     for k = 1 to Kp do

16:      ${\varphi }_k^{\text{p}}\sim \text{GIW}\left({\varphi }_k^{\text{p}}\mathrm{|}{p}_k,{\beta }^{\text{p}}\right)$   // equation (18)

17:     end for

18:     for k = 1 to Ka do

19:      ${\varphi }_k^{\text{a}}\sim \text{GIW}\left({\varphi }_k^{\text{a}}\mathrm{|}{a}_k^{\prime },{\beta }^{\text{a}}\right)$   // equation (19)

20:     end for

21:     for $l=\left(F_{\mathit{dn}},z_{{\mathit{dA}}_d}^{F_{\mathit{dn}}}\right)\text{in}\left\{\left(F_{\mathit{dn}},z_{\mathit{dm}}^{F_{\mathit{dn}}}\right)\mathrm{|}{F}_{\mathit{dn}}\in \left\{\text{o},\text{c},\text{p},\text{a}\right\},\right.$ $\left.z_{\mathit{dm}}^{F_{\mathit{dn}}}\in \left\{\text{1},\text{2},\dots ,K^{F_{\mathit{dn}}}\right\}\right\}$ do

22:      θl ∼ Dir(θl | wl, γ)   // equation (20)

23:     end for

24:     for d = 1 to D do

25:      for m = 1 to Md do

26:       $z_{\mathit{dm}}^{\text{o}}\sim {\prod }_{n=1}^{N_d}\text{\hspace{1em}Cat}\left(w_{\mathit{dn}}\mathrm{|}{\theta }_{l=\left(F_{\mathit{dn}},z_{d{A}_d}^{F_{\mathit{dn}}}\right)}\right)\text{Gauss}\left(o_{\mathit{dm}}\mathrm{|}{\varphi }_{z_{\mathit{dm}}^{\text{o}}}^{\text{o}}\right)\text{Cat}\left(z_{\mathit{dm}}^{\text{o}}\mathrm{|}{\pi }^{\text{o}}\right)$   // equation (21)

27:       $z_{\mathit{dm}}^{\text{c}}\sim {\prod }_{n=1}^{N_d}\text{\hspace{1em}Cat}\left(w_{\mathit{dn}}\mathrm{|}{\theta }_{l=\left(F_{\mathit{dn}},z_{d{A}_d}^{F_{\mathit{dn}}}\right)}\right)\text{Gauss}\left(c_{\mathit{dm}}\mathrm{|}{\varphi }_{z_{\mathit{dm}}^{\text{c}}}^{\text{c}}\right)\text{Cat}\left(z_{\mathit{dm}}^{\text{c}}\mathrm{|}{\pi }^{\text{c}}\right)$   // equation (22)

28:       $z_{\mathit{dm}}^{\text{p}}\sim {\prod }_{n=1}^{N_d}\text{\hspace{1em}Cat}\left(w_{\mathit{dn}}\mathrm{|}{\theta }_{l=\left(F_{\mathit{dn}},z_{d{A}_d}^{F_{\mathit{dn}}}\right)}\right)\text{Gauss}\left(p_{\mathit{dm}}\mathrm{|}{\varphi }_{z_{\mathit{dm}}^{\text{p}}}^{\text{p}}\right)\text{Cat}\left(z_{\mathit{dm}}^{\text{p}}\mathrm{|}{\pi }^{\text{p}}\right)$   // equation (23)

29:      end for

30:      $z_d^{\text{a}}\sim {\prod }_{n=\text{1}}^{N_d}\text{\hspace{1em}Cat}\left(w_{\mathit{dn}}\mathrm{|}{\theta }_{l=\left(F_{\mathit{dn}},z_{d{A}_d}^{F_{\mathit{dn}}}\right)}\right)\text{Gauss}\left(a_d\mathrm{|}{\varphi }_{z_d^{\text{a}}}^{{\text{a}}^{\prime }}\right)\text{Cat}\left(z_d^{\text{a}}\mathrm{|}{\pi }^{\text{a}}\right)$   // equation (24)

31:      $F_d\sim {\prod }_{n=1}^{N_d}\text{\hspace{1em}Cat}\left(w_{\mathit{dn}}\mathrm{|}{\theta }_{l=\left(F_{\mathit{dn}},z_{d{A}_d}^{F_{\mathit{dn}}}\right)}\right)\text{Unif}\left(F_d\mathrm{|}\lambda \right)$ // equation (25)

32:     end for

33:    end for

34:    return {π}, {ϕ}, θ, {z}, F

35:   end procedure