  Modeling interpersonal influence on different sentimental polarities is a
fundamental problem in opinion formation and viral marketing. There has not
been seen an effective solution for learning sentimental influences from users'
behaviors yet. Previous related works on information propagation directly
define interpersonal influence between each pair of users as a parameter, which
is independent from each others, even if the influences come from or affect the
same user. And influences are learned from user's propagation behaviors, namely
temporal cascades, while sentiments are not associated with them. Thus we
propose to model the interpersonal influence by latent influence and
susceptibility matrices defined on individual users and sentiment polarities.
Such low-dimensional and distributed representations naturally make the
interpersonal influences related to the same user coupled with each other, and
in turn, reduce the model complexity. Sentiments act on different rows of
parameter matrices, depicting their effects in modeling cascades. With the
iterative optimization algorithm of projected stochastic gradient descent over
shuffled mini-batches and Adadelta update rule, negative cases are repeatedly
sampled with the distribution of infection frequencies users, for reducing
computation cost and optimization imbalance. Experiments are conducted on
Microblog dataset. The results show that our model achieves better performance
than the state-of-the-art and pair-wise models. Besides, analyzing the
distribution of learned users' sentimental influences and susceptibilities
results some interesting discoveries.
