Graph Mining: Introduction

Transcription

1 Graph Mining: Introduction Davide Mottin, Konstantina Lazaridou HassoPlattner Institute Graph Mining course Winter Semester 2016

2 Lecture road Course Information Introduction to graph mining Graphs: models and basic concepts 2

3 Organization of the lecture Lecture and slides in English Tuesday Two mandatory assignments: [Individual] One presentation of a paper of choice among a list of papers about topics covered in the lectures. Two slots: 13/12 (first part) 07/02 (second part) [Individual] One small project of graph analytics to be completed before the end of the course Examination (in English!): Oral exam (in the first three weeks after the lecture period) Grading scheme: 20%: Presentation 10%: Project 70%: Exam Lectures will be recorded and online (tele-task) There is no official textbook for the course Registration is required for this lecture, notify the studienreferat and myself: davide.mottin@hpi.de 3

4 About the lecturers Davide Mottin Postdoctoral Knowledge Discovery and Data Mining PhD in 2015, University of Trento Research Interests: Graph Mining, Data Mining, Graph databases, Preference models, Query paradigms Konstantina Lazaridou PhD Information Systems Research - Web Science MSc in 2015, University Ioannina Research Interests: Graph Mining, Social Network Analysis, Web data Mining, Opinion and Sentiment Analysis, Data Stream Mining 4

5 Course Web site Lecture material (slides, papers, books, tutorials, assignments, ) available online hing/aktuelle-vorlesung/ws- 1617/graph-mining.html The slides are also available in the intranet! 5

6 Objectives Understanding Where graphs are, why they are important, and what are new applications The main challenges from data mining perspective Learn How to efficiently query, and store a graph using graph mining techniques Analyze networks to understand the properties and the behaviors of individuals Think in a research perspective (novelty, clarity, ) Solve practical problems Work on real scale data and existing tools 6

7 Prerequisites Basic computer science and programming. Data-mining knowledge is a plus but is not strictly required. Basic probability theory and linear algebra are beneficial, although a small recap of the main concepts will be done at the beginning of the required lectures. 7

8 Schedule (tentative) Introduction to graph mining Social network analysis - Diffusion Graph Querying: exact, approximate, and reachability Frequent subgraph mining Graph indexing HPI-Kolloquium Invited speaker: prof. Danai Koutra Node classification Some practical graph mining framework Project assignment Link prediction Student paper presentation [first part] Christmas break Christmas break Non overlapping communities Overlapping communities Anomaly detection Graph summarization Report handover Summary of algorithms for different graph models Student paper presentation [second part] 8

9 Course Material - 1 There is no official book in the course. However, the slides are based on materials from these books: Aggarwal, C.C. and Wang, H. eds., 2010.Managing and mining graph data (Vol. 40). New York: Springer. Chakrabarti, D. and Faloutsos, C., Graph mining: laws, tools, and case studies. Synthesis Lectures on Data Mining and Knowledge Discovery, 7(1), pp Easley, D. and Kleinberg, J., Networks, crowds, and markets: Reasoning about a highly connected world. Cambridge University Press. 9

10 Course Material - 2 Some material is inspired, imported and modified from several existing courses. Graph Mining and Exploration at Scale (prof. Danai Koutra) Social and Information Network Analysis (prof. Jure Leskovec) Online Social Networks and Media (prof. Evaggelia Pitoura, prof. Panayotis Tsaparas) Data Mining meets Graph Mining (prof. Leman Akoglu) 10

11 How to send s To: Subject: Problem Help Text: Dear Dr. Davide Mottin, Your sincerely, BigBug92 I m a student at the third year, attending the course, number of shoes, quantity of food To: eaten davide.mottin@hpi.de yesterday The slides are not clear. I don t understand Subject: [GraphMining] the things Subgraph isomorphism theres. Text: Hi Davide, the subgraph isomorphism concept is not entirely clear to me. Why is the function bijective? Thanks, [First Name-Last Name] 11

12 Some rule of thumbs I m available for any kind of concern Use the mailing list: Seldom send to me directly, unless it is a very important concern Be quick and precise in the s Ask me questions in the course, or right after/before the lecture. If the question requires more time ask for a meeting with me: Better if you cluster and come in group instead of alone so I can answer to many questions at the same time If you think the course load/organization is unfair please let me know before the end of the semester. After that there will be NO possibility for discussion. 12

13 Feedback The course is taught for the first time: Any feedback is appreciated Any comments on slides and clarity as well There might be some mistake here and there (but we will do our best) Ask questions if you don t understand something. Better a question in class than a doubt during the exam! 13

14 (There's) no such thing as a stupid question 14

15 Content of the course First part Second part Background concepts: probability theory/statistics, basic linear algebra, basic graph concepts (morphisms, degrees, matrix representation,...) Social network analysis: Diffusion Power laws Influence propagation Graph querying and indexing: Exact and approximate queries Reachability queries Frequent subgraph mining Graph indexing Node classification and node similarity Link prediction Communities and anomalies Overlapping/Non overlapping communities Anomaly detection Graph summarization Summary of algorithms for different models (graph streams, evolving graphs, probabilistic graphs, colored graphs) Graph mining frameworks 15

16 About the presentations The presentation will be 15 mins in total 10 minutes presentation 5 minutes questions The group will be divided into two halves: One half will present on December 13 papers regarding the first part of the course The other half will present on February 7 regarding the second part of the course Every person presents one paper First come first served if two people ask to present the same paper, the second has to change the choice Paper list for the first part of the course: 16

17 Questions? 17

18 Lecture road Course Information Introduction to graph mining Graphs: models and basic concepts 18

19 The web August 2016 >= 50 billions of pages At least 4.73 billion pages indexed by search engines Source: 19

20 Social graphs facebook 1.5 Bln users 450 Bln Relationships 600 Mln groups 10.5 USD per user Twitter 313 Mln users 500 Mln Tweets/day Avg 208 followers/user They are complex: Groups, links, preferences, attributes 20

21 Knowledge graphs 20Mln entities 100Mln relationships 2500 types of relationships Other knowledge graphs: YAGO DBPedia DBLP Pubmed Linkmdb Connect entities such as persons, organizations, countries, objects through semantic relationships (e.g. owns a company) 21

22 Biological networks Protein-protein interaction networks Nodes: Proteins Edges: Physical interactions Metabolic networks Nodes: Metabolites and enzymes Edges: Chemical reactions 22

23 What else? Source: Source: Anything that involves relationships (implicit or explicit) can be modeled as a graph! 23

24 Graphs are everywhere Social Networks Complex Ubiquituous Large Valuable Road Networks Recommendation Graphs Knowledge Graphs 24

25 Why Graphs? Why now? Describe complex data with a simple structure Nature, social, concepts, roads, circuits Same representation for many disciplines Computer science, biology, physics, economics,... Availability of (BIG) data Large networks are now available and require complex algorithms Networks are evolving over time (e.g., new users/friends in Facebook) Usefulness Analysis will discover non trivial patterns, and allow simple smooth explorations They reveal user behaviors They are valuable (Facebook, Twitter, Amazon... All of them based on graphs!!!) 25

26 Graph mining is the process of discovering, retrieving and analyzing non trivial patterns in graph shaped data Graph mining 26

27 What can we do with graph mining? Compressing graphs without losing information Finding complex structures fast Recognizing communities and social patterns Study the propagation of viruses Predicting if two people will become friends Understanding what are the important nodes Showing how the network will evolve Helping the visualization of complex structures Finding roles, positive and negative influence prediction 27

28 What is involved in graph mining? Basic graph algorithms (shortest paths, BFS, DFS, isomorphisms, traversals, random walks ) Storage and indexing Smart representations for compactness Modeling of problems as graphs Distance metrics and similarity measures Exact, Approximate, and heuristic algorithms Evolving structures Interactivity and online updates Complexity (most of the problems are not polynomially solvable) 28

29 Practical applications of graph mining 29

30 Finding substructures 30

31 Community detection 31

32 Influence propagation 32

33 Link prediction 33

34 Graph evolution 34

35 Detecting frauds 35

36 Visualization Several visualization tools: General: Gephi, GraphViz, Biological: Cytoscape, Network Workbench Social: EgoNet, NodeXL,... Relational: Tulip 36

37 Lost in the graph? Hopefully not after this course ;) 37

38 Current: Query languages SELECT?name? WHERE {?person a foaf:person.?person foaf:name?name.?person foaf:mbox? . } Query languages ARE: Expressive Powerful Scalable Compact SPARQL g.v().haslabel('movie').as('a','b'). where(ine('rated').count().is(gt(10))). select('a','b'). by('name'). by(ine('rated').values('stars').mean()). order(). by(select('b'),decr). limit(10 GREMLIN MATCH (node1:label1)-->(node2:label2) WHERE node1.propertya = {value} RETURN node2.propertya, node2.propertyb but Not user friendly Not interactive CYPHER 38

39 Lecture road Course Information Introduction to graph mining Graphs: models and basic concepts 39

40 Network or graphs? Network refers to real systems Web, Social, Biological, Terminology: Network, node, link/relationship Graph is an abstract mathematical model of a network Web graph, Social graph Terminology: Graph, vertex/node, edge BUT we often use both without distinction 40

41 Graphs a a 0.2b c0.2 a b c b G = (V, E,p) E) l) Verteces Edges Labeling Probability function l: V E Σ E V V Undirected Graphs Co-authorship, Roads, Biological Directed graphs Follows, Labeled (or colored) Graphs Knowledge graphs, Probabilistic graphs Causal graphs 41

42 Graph databases (set of graphs) a a b a a c c b d a b a a c b b G 1 G 2 G 3 D = G -, G /,, G 1, G 2 = V 2, E 2, l 2, l 2 : E 2 V 2 Σ Set of small labeled graphs Chemical compounds, Business models, 3D objects 42

43 An example? Give me an example of network you know. What are the nodes? What are the edges? What shape? 43

44 Important Terminology Degree of a node: Number of neighbors of a node In directed graphs In-degree: number of inbound links Out-degree: number of outgoing links Adjacent node: A node u is adjacent to a node v if there is an edge between u and v, i.e. u, v E Path: Sequence of adjacent, non-repeating nodes in a graph Length of a path = number of edges Diameter of a graph: Size of the longest shortest path a v a Degree of v: 3 In-degree: 1 Out-degree: 2 44

45 Graph representation Adjacency matrix A = a 27 = 8 1 i, j E 0 otherwise 1 => {2} 2 => {4} 3 => {1,2,4,6} Adjacency list What are the advantages/disadvantages of one or another representation? 45

46 Static vs Evolving graph t n A 1 A 1 A1 A 1 A 1 t 1 Static graph Adjacency matrix A Dynamic, temporal graph 3D Matrix (tensor) 46

47 Graph Isomorphism G 1 G 2 f Given two graphs,g - : V -, E -, l -, G / : V /, E /, l / G - is isomorphic G / iff exists a bijective function f: V - V / s.t.: 1. For each v - V -, l v - = l(f v - ) 2. v -, u - E - iff f v -, f u - E / 47

48 Subgraph Isomorphism Q G G A graph,q: V M, E M, l M is subgraph isomorphic to a graph G: V, E, l if exists a subgraph G N G, isomorphic to Q 48

49 Frequent Subgraph Mining a a c c Problem Find all subgraphs of G that appear at least σ times b a c Suppose σ = 2, the frequent subgraphs are (only edge labels) a, b, c a-a, a-c, b-c, c-c a-c-a b Exponential number of patterns!!! G 49

50 Questions? 50