Minor nit #2. I'd love to see a visualization of the "probability mixing" interpretation of markov chains and stationary distributions, which is what PageRank is really about. That is, it'd be really nice to have a visualization of the fact that Markov chains are ultimately memoryless (it eventually doesn't matter in which state you start for the distribution of events). I think it could be done by exchanging "probabilities conditioned on the past", which is most easily done by multiplying the entire probability vector by the stochastic matrix and visualizing that.
One way to get at what you're saying in #2 is to have a counter that accumulates the number of epochs spent in state 1, state 2, state 3, for one of these examples. Have a way to reset this counter, and compute the relative frequency (by normalizing the counts-in-each-epoch by the number of epochs so far).
Come to think of it, you could even calculate the first eigenvector of the transition matrix, and show this eigenvector next to the relative frequency mentioned above.
In fact, you could then plot an L1 distance of the relative frequency (above) to the eigenvector, with one point for each epoch. This distance would decrease (non-monotonically) towards zero as the number of epochs increases. I believe it is (in the expectation sense) exponentially fast, but with an exponent that depends on the transition matrix. (Typical transition matrices would exhibit fast mixing, http://en.wikipedia.org/wiki/Markov_chain_mixing_time).
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This is really nice.
Minor nit #1: https://www.dropbox.com/s/2meqa8hhen9ztba/Screenshot%202014-... Seems like the graph visualization is sticking to the wrong coordinates (dragging it to the left doesn't help; it moves back to the center)
Minor nit #2. I'd love to see a visualization of the "probability mixing" interpretation of markov chains and stationary distributions, which is what PageRank is really about. That is, it'd be really nice to have a visualization of the fact that Markov chains are ultimately memoryless (it eventually doesn't matter in which state you start for the distribution of events). I think it could be done by exchanging "probabilities conditioned on the past", which is most easily done by multiplying the entire probability vector by the stochastic matrix and visualizing that.
One way to get at what you're saying in #2 is to have a counter that accumulates the number of epochs spent in state 1, state 2, state 3, for one of these examples. Have a way to reset this counter, and compute the relative frequency (by normalizing the counts-in-each-epoch by the number of epochs so far).
Come to think of it, you could even calculate the first eigenvector of the transition matrix, and show this eigenvector next to the relative frequency mentioned above.
In fact, you could then plot an L1 distance of the relative frequency (above) to the eigenvector, with one point for each epoch. This distance would decrease (non-monotonically) towards zero as the number of epochs increases. I believe it is (in the expectation sense) exponentially fast, but with an exponent that depends on the transition matrix. (Typical transition matrices would exhibit fast mixing, http://en.wikipedia.org/wiki/Markov_chain_mixing_time).