  Online social network has been one of the most important platforms for viral
marketing. Most of existing researches about diffusion of adoptions of new
products on networks are about one diffusion. That is, only one piece of
information about the product is spread on the network. However, in fact, one
product may have multiple features and the information about different features
may spread independently in social network. When a user would like to purchase
the product, he would consider all of the features of the product
comprehensively not just consider one. Based on this, we propose a novel
problem, multi-feature budgeted profit maximization (MBPM) problem, which first
considers budgeted profit maximization under multiple features propagation of
one product.
  Given a social network with each node having an activation cost and a profit,
MBPM problem seeks for a seed set with expected cost no more than the budget to
make the total expected profit as large as possible. We consider MBPM problem
under the adaptive setting, where seeds are chosen iteratively and next seed is
selected according to current diffusion results. We study adaptive MBPM problem
under two models, oracle model and noise model. The oracle model assumes
conditional expected marginal profit of any node could be obtained in O(1) time
and a (1-1/e) expected approximation policy is proposed. Under the noise model,
we estimate conditional expected marginal profit of a node by modifying the
EPIC algorithm and propose an efficient policy, which could return a
(1-exp({\epsilon}-1)) expected approximation ratio. Several experiments are
conducted on six realistic datasets to compare our proposed policies with their
corresponding non-adaptive algorithms and some heuristic adaptive policies.
Experimental results show efficiencies and superiorities of our policies.
