tried using ggalluvial

sankeychart.r

#install.packages("ggalluvial")
library("ggalluvial")
library("dplyr")
V_row=matrix(rexp(100*10),100,10)
V_col=matrix(rexp(100*10),100,10)

W_row = matrix(rexp(10*5),10,5)
cl_row = apply(V_row%*%W_row,1,which.max)

W_col = matrix(rexp(10*7),10,7)
cl_col = apply(V_col%*%W_col,1,which.max)

latent_row = apply(V_row,1,which.max)
latent_col = apply(V_col,1,which.max)

count_row = data.frame(cl_row, latent_row) %>% 
  group_by_all() %>% 
  tally() %>% 
  ungroup()

count_col = data.frame(latent_col, cl_col) %>% 
  group_by_all() %>% 
  tally() %>% 
  ungroup()

jointdf = full_join(count_row , count_col, 
                    by=c("latent_row"="latent_col"), 
                    relationship = "many-to-many") %>% 
  rename(latent = latent_row)

jointdf = mutate(jointdf, p_row = n.x/sum(n.x), p_col = n.y/sum(n.y)) %>% 
  mutate(p=p_row*p_col) %>% 
  mutate(p=p/sum(p))

ggplot(data = jointdf,
       aes(axis1 = paste("r", cl_row, sep = "-"),
           axis2 = paste("l", latent, sep="-"),
           axis3 = paste("c", cl_col, sep="-"), y = p)) +
  scale_x_discrete(limits = c("cl_row", "latent", "cl_col"),
                   expand = c(.2, .05)) +
  geom_alluvium(aes(fill=paste("l", latent, sep="-")), show.legend = FALSE)+
  geom_stratum() +
  geom_text(stat = "stratum", aes(label = after_stat(stratum))) +
  labs(y="relative frequnency")+theme_minimal(18)