# Influence Maximization with Spontaneous User Adoption

## TL;DR

This paper introduces a new influence propagation model incorporating spontaneous self-activation, along with scalable algorithms for influence maximization problems that outperform existing methods on real-world data.

## Contribution

It proposes the SAIC model with self-activation, formulates PIM and BPIM problems, and develops approximation algorithms with proven guarantees and superior performance.

## Key findings

- Algorithms achieve near-optimal approximation ratios.
- Methods outperform baselines in real-world graph tests.
- Self-activation significantly enhances influence spread modeling.

## Abstract

We incorporate self activation into influence propagation and propose the self-activation independent cascade (SAIC) model: nodes may be self activated besides being selected as seeds, and influence propagates from both selected seeds and self activated nodes. Self activation reflects the real-world scenarios such as people naturally share product recommendations with their friends even without marketing intervention. It also leads to two new forms of optimization problems: (a) {\em preemptive influence maximization (PIM)}, which aims to find $k$ nodes that, if self-activated, can reach the most number of nodes before other self-activated nodes; and (b) {\em boosted preemptive influence maximization (BPIM)}, which aims to select $k$ seeds that are guaranteed to be activated and can reach the most number of nodes before other self-activated nodes. We propose scalable algorithms for PIM and BPIM and prove that they achieve $1-\varepsilon$ approximation for PIM and $1-1/e-\varepsilon$ approximation for BPIM, for any $\varepsilon > 0$. Through extensive tests on real-world graphs, we demonstrate that our algorithms outperform the baseline algorithms significantly for the PIM problem in solution quality, and also outperform the baselines for BPIM when self-activation behaviors are non-uniform across nodes.