Agents interactions in a social network are dynamic and stochastic. We model
the dynamic interactions using the hidden Markov model, a probability model
which has a wide array of applications. The transition matrix with three states,
forgetting, reinforcement and exploration is estimated using simulation. Singular
value decomposition estimates the observation matrix for emission of
low, medium and high interaction rates. This is achieved when the rank approximation
is applied to the transition matrix. The initial state probabilities
are then estimated with rank approximation of the observation matrix. The
transition and the observation matrices estimate the state and observed symbols
in the model. Agents interactions in a social network account for between
20% and 50% of all the activities in the network. Noise contributes to the other
portion due to interaction dynamics and rapid changes observable from the
agents transitions in the network. In the model, the interaction proportions
are low with 11%, medium with 56% and high with 33%. Hidden Markov
model has a strong statistical and mathematical structure to model interactions
in a social network.
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