Visualization of multiple Markov models

Question

Visualization of multiple Markov models

Andrew Brown

2020年3月5日 07:22

I am working on a project where we compare over 10 different Markov models, each representing a different treatment plan.

Most often single models are visualized with a decision tree or transition state diagram. However, with multiple different models what are potential visualizations that could communicate the transition states that differentiate each model?

I have seen other people use a table to depict different models and the transition states.

For clarity, I am not referring to a transition probabilities chart but a method of communicating the differences between multiple models.

Topic simulation markov-process visualization python r

Category Data Science

mikalai · Accepted Answer · 2020年3月5日 07:22

If we limit the question on comparing two graphs, I can propose a way based on adjacency matrices comparison. There is a sample notebook: graph_diff.ipynb

To summarize:

Having two graphs,

   A  B  C  D                  A  B  D  E  F
A  0  2  2  2               A  0  1  2  3  0
B  2  0  1  1               B  1  0  0  1  1
C  2  1  2  0               D  2  0  2  1  0
D  2  1  0  0               E  3  1  1  0  1
                            F  0  1  0  1  0

We can compare them and detect changes, producing result similar to diff output:

   A  B  C  D  E  F
A  1  0 -2  1  2  2
B  0  1 -2 -2  2  2
C -2 -2 -2 -2 -2 -2
D  1 -2 -2  2  2  2
E  2  2 -2  2  2  2
F  2  2 -2  2  2  2

Compare matrix nodes from both graphs. Edges values indicate change:

1 = same edge
0 = changed edge
-2 = removed edge
+2 = added edge

This matrix can be visualized as grid:

Or as graph:

which is more informative because shows also nodes changes:

green: new (added nodes E and F)
red: removed (removed C)
yellow: unaffected (A, B, D)

For simplicity, edges are unidirectional.

Visualization of multiple Markov models

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