Transition due to preferential cluster growth of collective emotions in online communities

摘要

We consider a preferential cluster growth in a stochastic model describing the dynamics of a binary Markovnchain with an additional long-range memory. The model is driven by data describing emotional patterns observednin online community discussions with binary states corresponding to emotional valences. Numerical simulationsnand approximate analytical calculations show that the pattern of frequencies depends on a preference exponentnrelated to the memory strength in our model. For low values of this exponent in the majority of simulatedndiscussion threads both emotions are observed with similar frequencies. When the exponent increases an orderednphase emerges in the majority of threads, i.e., only one emotion is represented from a certain moment. Similarnchanges are observed with increase of a single-step Markov memory value. The transition becomes discontinuousnin the thermodynamical limit when discussions are infinitely long and even an infinitely small preference exponentnleads to ordered behavior in each discussion thread. Numerical simulations are in a good agreement with thenapproximated analytical formula. The model resembles a dynamical phase transition observed in other Markovnmodels with a long memory where persistent dynamics follows from a transition to a superdiffusion phase. Thenordered patterns predicted by our model have been found in the Blog06 dataset although their number is limitednby fluctuations and sentiment classification errors.