Tracing Truth and Rumor Diffusions Over Mobile Social Networks: Who are the Initiators?

With the increasing popularity of mobile devices, each user is able to conveniently acquire messages from others, and share diverse forms of information, like texts, images, or videos through online mobile apps. The full freedom of speech makes a great amount of truth (i.e., true information) and rumor (i.e., false information) propagate rapidly in a hybrid way through mobile platforms. As a huge variety of information floods pouring over us each day, identifying the authenticity of massive events becomes a necessary task to maintain the stability of Mobile Social Networks (MSNs). An important way to realize it is to trace their diffusions and make judgements according to the reliability of sources. With this regard, this paper proposes a diffusion model that characterizes the simultaneous diffusion of both truth and rumor in realistic MSNs, and makes the first attempt to figure out their respective sources. The problem of interest can be stated as: Given an outcome of cascade of both truth and rumor in MSNs, i.e., a set of nodes that might be the ignorant, the spreader of truth or rumor, or simply the silent receiver, how can we infer both truth sources and rumor sources? Different from previous sources detection works considering single type of nodes, the interplay between truth diffusions and rumor diffusions makes the conventional methods not work. To answer this question, we aim to maximize the <italic>similarity index</italic>, i.e., the number of nodes possessing the same states between the resulting network triggered by our estimated sources with the proposed diffusion model and the given observation network. Compared with existing techniques to trace diffusions of truth or rumor, it is much harder to find two kinds of sets at the same time, including truth sources and rumor sources, due to two primary reasons: (i) our biset optimization makes the submodularity techniques fail; (ii) our objective function is proven to be non-bisubmodular. To overcome above limitations, we first convert the objective <italic>similarity index</italic> into a bisubmodular function by virtue of set covering. Based on this, we propose an approximation algorithm called Truth and Rumor Sources Detection (TRSD) algorithm via multiple reverse samplings with a provable <inline-formula><tex-math notation="LaTeX">$\frac{1}{4(1+\epsilon)^2}$</tex-math><alternatives><mml:math><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>4</mml:mn><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>ε</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:math><inline-graphic xlink:href="wang-ieq1-3119362.gif"/></alternatives></inline-formula> approximation ratio. Further, a novel “time reversal” sources optimization strategy is proposed to converge the number of output sources from TRSD to a steady state. The effectiveness of our models and algorithms are empirical validated in two various datasets, from which we observe an up to 15% of <italic>similarity index</italic> gain as well as a narrowed down gap 0.6% to the ground truth.