Maximizing positive influence spread in online social networks via fluid dynamics

Highlights

• This paper proposes a novel influence spread model via the fluid dynamics theory.

• We formulate the Maximizing Positive Influenced Users problem.

• The Fluidspread greedy algorithm is presented which attempts the MPIU problem.

• The experimental results reveal the time evolving dynamic influence process.

• The experimental results show the effectiveness and efficiency of our algorithm.

Abstract

In online social networks, many application problems can be generalized as influence maximization problem, which targets at finding the top-$k$ influential users. Most of the existing influence spread models ignore user’s attitude and interaction and cannot model the dynamic influence process. We propose a novel influence spread model called Fluidspread, using the fluid dynamics theory to reveal the time-evolving influence spread process. In this paper, we model the influence spread process as the fluid update process in three dimensions: the fluid height difference, the fluid temperature and the temperature difference. To the best of our knowledge, this is first attempt of using the fluid dynamics theory in this field. Moreover, we formulate the Maximizing Positive Influenced Users (MPIU) problem and design the Fluidspread greedy algorithm to solve it. Through the experimental results, we demonstrate the effectiveness and efficiency of our Fluidspread model and Fluidspread greedy algorithm.

Introduction

With the development of web technology and network infrastructure, Online Social Networks (OSNs) have become an integral part of every user’s daily life [1], [2]. The wide spread researches in influence and information propagation pave the way for a large amount of applications such as viral marketing [3], [4], [5], community formation, evolution and detection [6], outbreak detection [7] and many more. The key problem in this field is Influence Maximization (IM), which aims at finding the top-$k$ influential users (seed users) from the social network. Firstly, most existing influence spread models did not consider the attitude of user. These models suppose users believe both the positive and negative information. Any kind of information can active the users, but it is not in line with practical situation. Then the existing models suppose the user always perceives the information from others, but he may just perceive the information from another user three-tenths of the chance. Thus, we need consider different attitudes and interactions in the influence spread process. Moreover, the previous models cannot reflect the dynamic influence spread process.

In reality, due to users’ preference, product quality or other reasons, people may have different attitudes towards an entity (products, news, etc.). For example, the users may have different attitudes (positive/neutral/negative) towards a message when the message appears in social network. It will also lead different interactions between users. Then the process of influence spread will become complicated. To overcome these challenges, our goal is selecting the top-$k$ influential users to maximize the active users with positive attitude, rather than the overall active users. To better simulate the attitude variation and interaction process, we emphasize the time-evolving spread process using the fluid dynamics theory.

In the existing models, the most obvious problem lies in the simulation process of influence spread. The problem is three fold - (1) Lack of attitude: The previous works lack the capability to incorporate the emergence and propagation of attitudes into the influence diffusion process. Each user is supposed to be positive contribute to the influence spread without the consideration of the user’s personal attitudes. But the user may be negative or neutral attitude towards the entity. (2) Lack of ability to capture interaction: The previous models ignore to distinguish which information can be perceived with the consideration of users’ interaction. Each user is supposed to perceive the information with the same probability, while the users may not perceive the information owing to the interaction between users. (3) Cannot model the dynamic process: The existing models suppose the active users have only one chance to activate the neighbor inactive users. And the users in active state cannot turn to inactive state, but these assumptions are not true in real situation. Actually the influence always exists, and the process of influence is a continuous process. To better illustrate these problems, we provide a sample example shown in Fig. 1.

Example 1

Fig. 1 shows a snapshot of social network consisting five nodes. The parameter$p_{AB}$ denotes the influence probability from node A to B. The parameter${\varphi }_{AB}$ denotes the interaction probability between node A and B. We can obtain that node B and D follow node A, node A and node D follow node C, node B and D follow node E. The number in the node denotes the attitude ($a$) towards an entity, ranges in [−1, 1]. The value of$a$ greater than zero denotes the node has positive attitude, then less than zero means the node has negative attitude. The specific values denote the attitude strength. Thus,$a_A=0.6$ means node A has positive attitude.$a_D=0$ means node D has neutral attitude, and$a_E=-0.3$ denotes node E has negative attitude. The other nodes can be calculated in a similar way.

On the basis of above discussion, we propose a novel Fluidspread mechanism via the theory of fluid dynamics, which can model the time-evolving influence spread process. Our Fluidspread mechanism can capture attitude variation and the interaction between users, which matches the real situation better. We formulate the problem of Maximizing Positive Influenced Users (MPIU) and design an efficient algorithm to solve it. We try to maximize the active users with positive attitude in the process of influence spread, rather than the overall active users.

Based on the fluid dynamics theory, we model the influence spread process as a fluid dynamic system. We use a container with enough volume to denote each user. The volume of fluid in the container denotes the user’s influence strength. Each edge corresponds to the pipe that connects two containers. We install each pipe at the bottom of the container, and we set a valve in each pipe. The connectivity of each pipe is decided by the influence probability and interaction probability. We can capture the process of influence spread as the flowed fluid in three dimensions: the fluid height difference between two containers is taken as the influence probability, the temperature of fluid in each container is deemed as the user’s attitude, and the fluid temperature difference between two containers can be denoted as the interaction probability. Moreover, we set a plug at the bottom of the container, through which the fluid will leak a little. This reflects users’ influences will gradually discount over time. Fig. 2 illustrates the mapping relationship from the features of influence spread to the fluid dynamic system.

In the Fluidspread model, each container has some fluids, and the fluids flow originate from the seed containers. When the temperature difference and the height difference both satisfy the conditions of fluid flowing, then the fluids can flow from one container to another. And the fluids in the lower fluid height container will be mixed with the flowed fluids. Thus, the fluid temperature will be updated which reflects the time-evolving process of users’ attitude variation. But we should restore the volume of fluids in the containers to the previous situation at the end of each update round. Because the strength of users’ influences cannot be changed during influence propagation process in the real-world situation. We apply a discretized method to measure the variation of each container’s fluids over time. The results of influence spread are based on the collection of sampled fluid temperatures.

To summarize, we present our main contributions as follows.

• We propose a novel Fluidspread mechanism to simulate the influence spread process using the fluid dynamics theory. This may be the first attempt in the field of influence spread. We emphasize the features of influence spread: the influence probability, the user’s attitude and the interaction probability. The influence spread process is modeled as the fluid update in three dimensions: the fluid height difference, the fluid temperature and the fluid temperature difference.

• We formulate the problem of Maximizing Positive Influenced Users (MPIU) and design the Fluidspread greedy algorithm to solve it. We aim at identifying the seed users can maximize the spread of positive active state. Corresponding to the Fluidspread model, we apply the fluid update process to model the influence spread. In this way, the influence spread process can be modeled naturally and gracefully.

• We conduct the experiments on four real world datasets. We calculate the range of influence spread with/without the consideration of user’s attitudes, compare the running time with other existing algorithms, and measure the variation of users’ attitudes and states. Through the experimental results, we demonstrate the effectiveness and efficiency of the Fluidspread model and algorithm. And the results reveal the time-evolving dynamic influence process.

The rest of this paper is organized as follows: we review the related works in Section 2. We present the statement of problem in Section 3. Section 4 shows the Fluidspread framework. We describe the details of Fluidspread mechanisms in Section 5. We present the experimental results in Section 6. Finally, we conclude our work and provide the future direction in Section 7.