lecture17-linkanalysis-handout-6-per

Matrix p tells us where we go next from state i so

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Unformatted text preview: ains Introduc)on to Informa)on Retrieval Sec. 21.2.1 Ergodic Markov chains n   Clearly, for all i, ∑ Pij = 1. j =1   Markov chains are abstrac*ons of random walks.   Exercise: represent the telepor*ng random walk from 3 slides ago as a Markov chain, for this case: Introduc)on to Informa)on Retrieval Sec. 21.2.1   For any (ergodic) Markov chain, there is a unique long ­term visit rate for each state.   Steady ­state probability distribu)on.   Over a long *me ­period, we visit each state in propor*on to this rate.   It doesn t ma\er where we start. Introduc)on to Informa)on Retrieval Sec. 21.2.1 Probability vectors Change in probability vector   A probability (row) vector x = (x1, … xn) tells us where the walk is at any point.   If the probability vector is x = (x1, … xn) at this step, what is it at th...
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