Rumor Source Detection: A Group Testing Approach Ding-Zhu Du Department of Computer Science University of Texas at Dallas

OUTLINE Background Rumor Source Detection Problem Group Testing Approach

Social Networks > 1.3 billion users The 2nd largest “Country” in the world More visitors than Google > 800 million users 2013, 400 million users, 40% yearly increase 2009, 2 billion tweets per quarter 2010, 4 billion tweets per quarter 2011, 25 billion tweets per quarter Facebook Now Has more than one Billion Monthly Active Users Tencent QQ, popularly known as QQ, is an instant messaging software service QQ also offers a variety of services, including online social games, music, shopping, microblogging, and group and voice chat. As of 20 March 2013, there are 798.2 million active QQ accounts, with a peak of 176.4 million simultaneous online QQ users.[2] Pinterest is a tool for collecting and organizing things you love. Facebook , Pinterest, and teitter are dominating. More than 6 billion images Pinterest, with a traffic higher than Twitter and Google

A Trillion Dollar Opportunity Online Social networks have become a bridge to connect our daily physical life and the virtual web space On2Off Commerce[1] With the growth of local commerce on the Web, the links between online and physical commerce are becoming stronger. Think about the succefssful websites such as Groupon, priceline, OpenTable,Restaurant.com, and SpaFinder etc. What do they have in common? They grease the wheels of online-to-offline commerce. The key to O2O is that it finds consumers online and brings them into real-world stores. It has been predicted that it will create a trillion dollar opportunity via on 2 off e commerce. So online social networks provide good platforms for whose who want to move their physical business to online business. [Venture capitalists and entrepreneurs would be wise to think beyond cloning the “deal of the day” concept—and instead think about how the discovery, payment, and performance measurement of offline commerce can move online.] [1] Online to Offline is trillion dollar business http://techcrunch.com/2010/08/07/why-online2offline-commerce-is-a-trillion-dollar-opportunity/

Influence Propagation I hate Obama, the worst president ever I love Obama A fundamental understanding of communication has always been at the center of a politician's arsenal, but a firm grasp on the future of communication can be the secret weapon that wins the war. For Franklin D. Roosevelt, it was radio. For John F. Kennedy, it was television. And for Barack Obama, it is social media. The 2008 Obama Presidential campaign made history.  Not only was Obama the first African American to be elected president, but he was also the first presidential candidate to effectively use social media as a major campaign strategy. During his campaign, Obama has made his Web 2.0 presence known. He has over 1.5 million friends on MySpace and Facebook, and he currently has over 45,000 followers on Twitter. This personal activity in social networks allows him to quickly get the word out across multiple platforms. Positive Negative

What is Social Influence? Social influence occurs when one's opinions, emotions, or behaviors are affected by others, intentionally or unintentionally.[1] Informational social influence: to accept information from another; Normative social influence: to conform to the positive expectations of others. [1] http://en.wikipedia.org/wiki/Social_influence

Three Degree of Influence Six degree of separation[1] Three degree of Influence[2] Michael Gurevich conducted seminal work in his empirical study of the structure of social networks in 1961, everyone and everything is six or fewer steps away. Christakis and Fowler found that social networks have great influence on individuals' behavior. But social influence does not end with the people to whom a person is directly tied. our actions can influence people we have never met. The influence ceases to have a noticeable effect on people beyond three degrees of separation. 150*150*150=1,375,000 Each person may influence 150 persons [3] In total, you are able to influence about 1,000,000 (1503) persons in the world! [1] S. Milgram. The Small World Problem. Psychology Today, 1967, Vol. 2, 60–67 [2] J.H. Fowler and N.A. Christakis. The Dynamic Spread of Happiness in a Large Social Network: Longitudinal Analysis Over 20 Years in the Framingham Heart Study. British Medical Journal 2008; 337: a2338 [3] R. Dunbar. Neocortex size as a constraint on group size in primates. Human Evolution, 1992, 20: 469–493.

When misinformation or rumor spreads in social networks, what will happen? 5/26/2018

A misinformation said that the president of Syria is dead, and it hit the twitter greatly and was circulated fast among the population, leading to a sharp, quick increase in the price of oil. http://news.yahoo.com/blogs/technology-blog/twitter-rumor-leads-sharp-increase-price-oil-173027289.html 5/26/2018

In August, 2012, thousands of people in Ghazni province left their houses in the middle of the night in panic after the rumor of earthquake. http://www.pajhwok.com/en/2012/08/20/quake-rumour-sends-thousands-ghazni-streets In August, 2012, thousands of people in Ghazni province left their houses in the middle of the night in panic after the rumor of earthquake, which said that a major earthquake would hit the area until 5 am [3]. Believing in it, many people from the Ghazni city and some other districts of the province left their house and spent the whole night outside. The panic spread by the rumor was so intense that the people, who were in thousands, did not dare to return to their houses till morning. Mirwais, a resident of Ghazni city, talked to a news agency about this announcement. Later, the imams of the mosques had started believing in it and according to the statement made by Mirwais, Then, imams of mosques also started announcing about the earthquake. 5/26/2018

Control the spread of rumors 5/26/2018

OUTLINE Background Rumor Source Detection Problem Group Testing Approach

Motivation Rumors spread through the network We only see who received rumor but not where they got rumor from Can we locate the hidden rumor sources?

Motivation Rumors spread through the network We only see who received rumor but not where they got rumor from Can we locate the hidden rumor sources?

Problem Description Given Goal Question Applications Social network structure Infection time of monitors Goal Select a subset of vertices with minimum cardinality such that the rumor source can be uniquely located. Question Which set of vertices should we select? Applications Epidemiology: Virus Social Media: Rumor

Related Work Shah and Zaman, 2010, 2011, 2012: Luo and Tay, 2012: “Rumor Centrality”-single source, Susceptible-Infected (SI) model Luo and Tay, 2012: Multiple sources, Susceptible-Infected-Recovered (SIR) model Zhu and Ying, 2013: Single source estimation for SIR model Seo et al., 2012; Karamchandani and Franceschetti, 2013; Luo and Tay, 2013; Zhu and Ying, 2014: Partial observations

OUTLINE Background Rumor Source Detection Problem Group Testing Approach

What is Group Testing? Part I

An Example There are 9 items with 1 defective. Please identify the defective item with the minimum number of tests. Each test on a subset of items can tell whether the subset contains the defective item or not.

3 tests are enough? 1 2 3 4 5 6 7 8 9 1 2 3 4 5 4 5

No, sometime you need 4 tests. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 1 2 3 1 2

Minimum # of Tests Goal: minimize # of tests in the worst case. So, for bisecting on 9 items with 1 defective, the # of tests in the worst case is 4. For bisecting on n items with 1 defective, require tests

This is the best you can do! There are totally n outcomes. Each tests has two outcomes, which divides a subset of outcomes into two smaller subsets. Suppose k tests are enough. Then

Two Defective Items Need at least tests. For some n, the lower bound can be reached. But, for some n, the lower bound can not be reached. This case is complicated.

3 or more defective items Very hard to find the optimal algorithm for determine tests!!!

Classical Group Testing Given n items with some positive ones, identify all positive ones by less number of tests. Each test is on a subset of items. Test outcome is positive iff there is a positive item in the subset.

Idea of Group Testing (GT) _ _ _ _ _ _ _ _ _ _ _ + _ _ _ _ _ + positive negative

History During World War II, to test syphilitic antigen, David Rosenblatt first proposed the idea. In 1943, Robert Dorfman published the first paper on Group Testing. After 1943, there are many papers published and many applications discovered.

Group Testing Sequential Group Testing Nonadaptive Group Testing Pooling Design (Biology)

Example 1 - Sequential 1 2 3 4 5 6 7 8 9 1 2 3 4 5 4 5

Example 2 – Non-adaptive p4 p5 p6 O( ) tests for n items

Sequential and Non-adaptive Sequential GT needs less number of tests, but longer time. Non-adaptive GT needs more tests, but shorter time. In molecular biology, non-adaptive GT is usually taken. Why?

Los Alamos Labs in 1998 Face 220,000 clones to do screening. If test individually, need 220,000 tests. Actually, use 376 tests. What is the technique?

Methodology for Rumor Source Detection Definition (Set Resolving Set (SRS)). Node set K ⊆ V is an SRS if any different detectable node sets A,B ∈ V are distinguishable by K. Two node sets A,B ⊆ V are distinguishable by K if there exist two nodes x, y ∈ K such that : the time that node x received the rumor from A,

Influence Propagation Model Rumor propagates from the sources to any vertex through shortest paths in the network. As soon as a vertex receives the information, it sends the information to all its neighbors simultaneously, which takes one time unit. Thus, the time that a rumor initiated at node u is received by node v is ru(v) = s(u) + d(u, v). Rumor is initiated at different locations at time t, but t is unknown but uniform.

An Example of Set Resolving Set (SRS) {A,B,C} is a SRS. A E F D B C A B C r(A)-r(B) r(A)-r(C) r(B)-r(C) 1 -1 2 -2 D E F

An Example of Set Resolving Set (SRS) {A,C} is not a SRS. A E F D B C A C r(A)-r(C) E 1 F 2

Active Source & Inactive Source Only active source is detectable.

Theorem For any graph, there exists a SRS

Problem Definition MULTI-RUMOR-SOURCE DETECTION problem (MRSD): find a SRS K with the smallest cardinality.

Greedy Algorithm & Its Approximation Ratio Theorem . Algorithm1 correctly computes a SRS with provable approximation ratio of at most (1 + r ln n + ln log2 ). r : upper bound for the number of sources : maximum number of equivalence classes divided by one node-pair. we present a greedy algorithm for MRSD. The algorithm starts from T = ∅, and iteratively adds into T node-pairs with the highest efficiency (which will be defined later) until all sets can be distinguished by some node-pair in T . Its is polynomial time if there is a constant upper bound r for the number of sources.

Thank you very much!