Plotting time steps?

Question

I would like to plot the transition probabilities against time.

The dimension of the ["Activities"][1] matrix is ncol=144 and nrows=16533; act1_1...ac1_144 are time-steps, and time is represented in 10 minutes intervals (e.g. act1_1 = 4.10am; act1_2=4.20am..). Time start from 4am (act1_1) and ends at act1_144(4am).The columns are filled in with different activities, such 2=sleep, 48=watching Tv, 5=eating, etc.

Using this function I managed to calculate the transition probabilities between activities(Activities matrix).

I would like to plot on x axis time (10 minutes intervals) and y axis probabilities for example 2 to follow 3.

How can I do this?

Thanks

This is the plot that I am aiming for

[1]: https://i.stack.imgur.com/1UEUw.jpg

Answer 1

To plot the development of the transition probabilities over time, you (by definition) need multiple observations for the transition from one action a to another action b.

Once you have multiple transaction probability matrices, it is actually very straightforward to plot their development over time. In my example below, most of the code is actually devoted to (re-)create your data and the different transition probability matrices.

library(ggplot2)

num_samples <- 1000
num_actions <- 20

# 1. generate activities dataframe (dropped ID column):
activ <- data.frame(v1 = sample(1:num_actions, num_samples, replace = TRUE), 
                    v2 = sample(1:num_actions, num_samples, replace = TRUE), 
                    v3 = sample(1:num_actions, num_samples, replace = TRUE), 
                    v4 = sample(1:num_actions, num_samples, replace = TRUE), 
                    v5 = sample(1:num_actions, num_samples, replace = TRUE), 
                    v6 = sample(1:num_actions, num_samples, replace = TRUE), 
                    v7 = sample(1:num_actions, num_samples, replace = TRUE))

num_transp <- ncol(activ) - 1 

# 2. calculate transition probabilities for each time step:
l_transp <- vector("list", num_transp)
for (t in 1:num_transp){
  transp <- matrix(0, nrow = num_actions, ncol = num_actions)
  data = activ[, t:(t+1)]
  for (action in 1:num_actions){
    rows_to_keep <- data[,1] == action
    counts <- table(data[rows_to_keep,])
    probs <- as.data.frame(counts/sum(rows_to_keep))
    follow_actions <- as.integer(as.character(probs[,2]))
    transp[action, follow_actions] <- probs$Freq
  }
  l_transp[[t]] <- transp
}

# 3. get development of transition probability from action 2 to action 3 over time:
to_plot <- vector("numeric", num_transp)
for (i in 1:num_transp){
  to_plot[i] <- l_transp[[i]][2, 3]
}

# plot development of transition probability from action 2 to action 3 over time:
ggplot(data.frame(x=1:num_transp, y=to_plot), aes(x=x, y=y)) +
  geom_line() + 
  xlab("time") +
  ylab("transition probability")

Running this will give you something like

It looks very much like what one would expect from a scenario where 20 different actions were chosen randomly and independently over time.