Predicting Positive and Negative Links in Online Social Networks

What’s waiting us for today: 1.Introduction 2.Dataset description 3.Predicting edge sign 4. Global structure of signed networks 5. Predicting positive edges 6. Conclusion

Introduction

*Majority of research has considered only positive relationships * Fundamental questions *Benefits of answering them

Edge Sign Prediction Extending Guha: 1.machine learning framework 2.investigate accros a range of datasets 3.compare to “balance and status” נתחיל מהבעיה הבסיסית, נניח שיש לנו רשת חברתית בה יש סימנים על כל הצלעות פרט לצלע אחת איך נוכל לקבוע מה הסימן שלה?

Generalization across Datasets. *Epinions, Slashdot, Wikipedia *Generalize: a. Sign prediction performance degrades only slightly b. Social-psychological theories agree and disagree with our learned-models u v (u,v)

DATASET DESCRIPTION

We consider three large online networks: Epinions, Slashdot, Wikipedia המידע נאסף בין השנים: Epnions 99-03 slashDot 2009 Wikipedia past-2008 בכל הרשתות ממוצע של 80 אחוז לינקים חיוביים

PREDICTING EDGE SIGN

A Machine-Learning Formulation Some signs: we let s(x, y) denote the sign of the edge (x, y) s(x, y) = 1 s(x, y) = −1 s(x, y) = 0 u v u v + u v - u v

s(x, y) = -1 is the opposite Sometimes we will be interested in the sign, regardless of its direction: s(x, y) = 1 1. 2. 3. s(x, y) = -1 is the opposite u v + + u v u v +

s(x, y) = -1 1. 2. 3. s(x, y) = 0 on all other cases u v - - u v u v -

Dividing our features into 2 classes: 1. 1st class features based on local relations of the node C(u,v) – number of common neighbors - u + + - + - v - +

The seven degree features: , , C(u,v), , 2 The seven degree features: , , C(u,v), , 2. 2nd class feature consider each triad involving the edge (u,v) and node w We encode it to 16-dimensional vector , , + + w +/- +/- u v

Learning Methodology and Results Our model :

Connections to Theories of Balance and Status Balance theory : “the enemy of my friend is my enemy” “the friend of my enemy is my enemy” “the enemy of my enemy is my friend” “the friend of my friend is my friend,” w v u - + w v u + - w v u - +

Status theory : w v u w v u S(u,w)+S(w,v)

Comparison of Balance and Status with the Learned Model

Comparison of Balance and Status with Reduced Models

All-positive subgraphs

Generalization across datasets How well the learned predictors generalize across the three datasets?

Heuristic Predictors • A balance heuristic • A status heuristic • An out-degree heuristic • An in-degree heuristic

GLOBAL STRUCTURE OF SIGNED NETWORKS

Balance and Status: From Local to Global We have 2 theories:

Searching for Evidence of Global Balance and Status We should expect: * network that is divided into two mutually opposed factions of friends * network whose edges respect a global ordering

Evaluating Global Balance and Status We try to find an evidence by using two baselines: 1. permuted-signs baseline 2. rewired-edges baseline

PREDICTING POSITIVE EDGES

how useful is it to know who a person’s enemies are, if we want to predict the presence of additional friends?

CONCLUSION