How to Analyse Social Network? : Part 2 Power Laws and Rich-Get-Richer Phenomena Thank you for all referred contexts and figures

Introduction A person's behavior or decisions always depend on the choices made by other people  The choices of other people convey information that is useful in the decision-making process. Conclusion: behavior is correlated across a population 2 Source: The fire caused a panic in the city…!!

Introduction Popularity is a phenomenon characterized by extreme imbalances: A few people achieve wider visibility A very, very few attain global name recognition 3 …compared to normal people

Introduction Power laws seem to dominate in cases where the quantity being measured can be viewed as a type of popularity. 4 Remark: Scale-Free Networks Some nodes are more highly connected than others are, which are called popular nodes. Popularity: High in-Degree value

Rich-Get-Richer Models Decision-making: People have a tendency to copy the decisions of people who act before them. 5 Ice Bucket Challenge

Rich-Get-Richer Models Example: Creation of links among Web pages  Pages are created in order, and named 1, 2, 3, …..,N.  When page j is created, it produces a link to an earlier Web page according to the following probabilistic rule With probability p, page j chooses a page i uniformly at random from among all earlier pages, and creates a link to this page i. With probability 1-p, page j instead chooses a page i uniformly at random from among all earlier pages, and creates a link to the page that i points to. 6

Rich-Get-Richer Models Example: Creation of links among Web pages After finding a random earlier page i in the population, the author of page j does not link to i, but instead copies the decision made by the author of page i -- linking to the same page that i did. This describes the creation of a single link from page j; one can repeat this process to create multiple, independently generated links from page j. With probability 1 - p, page j chooses a page i with probability proportional to i's current number of in-links, and creates a link to i. 7

Rich-Get-Richer Models Why do we call this a “rich-get-richer” rule?  Because: the probability that page i experiences an increase in popularity is directly proportional to i's current popularity. This phenomenon is also known as preferential attachment  Links are formed “preferentially” to pages that already have high popularity.  The copying model provides an operational story for why popularity should exhibit such rich-get-richer dynamics. The more well-known someone is, the more likely you are to hear their name 8

Applying “Preferential Attachment Concept” in Social Network Application” 9

10 Example: What are recommender systems? Recommender systems are systems which provide recommendations to a user  Too much information (information overload)  Users have too many choices Recommend different products for users, suited to their tastes.  Assist users in finding information  Reduce search and navigation time

11 Case Study: Amazon

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15 Personalized Product Recommendation?

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19 Which Sources of Information? Sources of information for recommendations: Browsing and searching data Purchase data Feedback provided by the users Textual comments Expert recommendations Rating

20 Type of Recommendations User-based  “Users who bought X like Y.”  Each user is represented by a vector indicating his ratings for each product.  Users with a small distance between each other are similar.  Find a similar user and recommend things they like that you haven’t rated.

21 Type of Recommendations Item-to-item  Content-based  One item is recommended based on the user’s indication that they like another item. If you like Lord of the Rings, you’ll like Legend.

22 Type of Recommendations Population-based => TREND!!  The most popular news articles, or searches, or downloads  Frequently add content  No user tracking needed.

Population-based Recommender System Preferential attachment is like some trendiness force:  a item that is well known in the market would have a greater probability to be chosen by a user. Movie Song Etc. 23

Population-based Recommender System REVIEW: Preferential Attachment  Nodes with higher degrees (i.e., with more links) acquire new links at higher rates than low-degree nodes  The probability that a link will connect a new node j with another existing node i is linearly proportional to the actual degree of i: 24

Population-based Recommender System A rating network is a bipartite network between persons and items they have rated.  The nodes are persons and items, and each edge connects a person with an item, and is annotated with a rating. 25 Source: U: Nodes V: Items

Population-based Recommender System A higher probability of selecting a popular item than an unknown one goods being sold depend on trendiness  Items that are well-known will have a higher probability of being bought 26 iPhone 6 Nokia 225

Population-based Recommender System REVIEW: Preferential Attachment 27 Small number of well-known items compared to regular ones

Rich-Get-Richer Models How to recommend items?  User Similarity Measure Distance Similarity: Euclidean Distance, City Block Distance..etc  Distance between a target user and any other users.  A vector is created for each user, accounting for his/her selected items. the closeness of users related with that item 28

Rich-Get-Richer Models How to recommend items?  Items in the top of the list are the best for the target user, and should be submitted to his/her attention Population-based Recommended Items 29 Problem: New Items?

Reference David Easley and Jon Kleinberg, Networks, Crowds, and Markets: Reasoning About a Highly Connected World, Cambridge University Press, Zanin, M., Cano P., Celma Ò., & Buldú J. M.,Preferential attachment, aging and weights in recommendation systems, International Journal of Bifurcation and Chaos, vol. 19, iss.2, pp ,