fast algorithms for querying and mining large graphs hanghang tong machine learning department...

Fast Algorithms for Querying and Mining Large Graphs

Hanghang TongMachine Learning Department

Carnegie Mellon [email protected]

http://www.cs.cmu.edu/~htong

1

mailto:[email protected]

http://www.cs.cmu.edu/~htong

-----

Graphs are everywhere!

2

Internet Map [Koren 2009] Food Web [2007]

Protein Network [Salthe 2004]

Social Network [Newman 2005]

Web Graph

Terrorist Network [Krebs 2002]

Why Do

We Care?

Research Theme

Help users to understand and utilize large graph-related data?

3

A1: Social Networks

• Facebook (300m users, $10bn value, $500mn revenue)• MSN (240m users, 4.5pb); Myspace (110m users)• LinkedIn (50m users, $1bn value); Twitter (18m users)

How to help users explore such networks?(e.g., find strange persons, communities, locate common friends, etc)4

A2: Network Forensics [Sun+ 2007]

How to detect abnormal traffic?

5

Port scanning DDoS Normal Traffic

Footnote: Rows are IP sources; Columns are IP destinations.

Adj. Matrix

ibm.com

cmu.edu

Graph

6

2005

NY Time

Forbes

Reuters Hardware

Service

IBM

2006

NY Time

Forbes

Reuters Hardware

Service

IBM

2007

NY Time

Forbes

Reuters Hardware

Service

IBM

A3: Business Intelligence

….….

Year

Rank of IBM in Global Service(higher is better)

What is IBM’s rank in global service business over years?

Footnote: nodes are business reviews and keywords; edges means ‘reporting’

A4: Financial Fraud Detection[Tong+ 2007]

7

7.5% of U.S. adults lost money for financial fraud 50%+ US corporations lost >= $500,000 [Albrecht+ 2001]

e.g., Enron ($70bn) Total cost of financial fraud: $1trillion [Ansari 2006]

How to detect abnormal transaction patterns?(e.g., money-laundry ring)

: Anonymous accounts

: Anonymous banks

Legends:

A5: Immunization

How to select k `best’ nodes for immunization?8

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Footnote: SARS costs 700+ lives; $40+ Bn

http://images.google.com/imgres?imgurl=http://newscoma.com/wp-content/uploads/2009/04/whooping-cough.jpg&imgrefurl=http://newscoma.com/2009/04/&usg=__m-D-1VIbVwVRhQsNlJZ1gw52pSY=&h=350&w=315&sz=68&hl=en&start=3&um=1&tbnid=DvSaKUuCMp_swM:&tbnh=120&tbnw=108&prev=/images?q=cough&hl=en&sa=N&um=1












http://www.clker.com/cliparts/3/a/0/7/1194984764384665883shield_matt_todd_01.svg.med.png






This Talk

• Querying [Goal: query complex relationship]– Q.1. Find complex user-specific patterns;– Q.2. Proximity tracking;– Q.3. Answer all the above questions quickly.

• Mining [Goal: find interesting patterns]– M.1. Immunization;– M.2. Spot anomalies.

9

Tasks vs. Applications App.sTasks

A1 A2 A3 A4 A5

Q1Q2Q3M1M2

10

A1: Social Networks A2: Network Forensics A3: Business IntelligenceA4: Financial FraudA5: Immunization

Q1: Complex User-Specific PatternsQ2: Proximity Tracking Q3: Fast Proximity ComputingM1: Immunization M2: Anomaly Detection

Overview

Q1

Q3

Q2

Q3

M1

M2 M2

Overview

CePS, iPoG (KDD06, ICDM08, CIKM09)

Q1

FastProx (ICDM06, KAIS07, KDD07 b, ICDM08)Q3

pTrack/cTrack (SDM08, SAM08)Q2

FastProx(SDM08, SAM08)Q3

NetShield

M1

Colibri-S (KDD08)

M2 Colibri-D (KDD08)

M2

Proximity Measurement

13Q: How close is A to B?

A BH1 1

D1 1

E

F

G1 11

I J1

1 1

a.k.a Relevance, Closeness, ‘Similarity’…

Background

Random Walk with Restart [Tong+ ICDM 2006]

Node 4

Node 1Node 2Node 3Node 4Node 5Node 6Node 7Node 8Node 9Node 10Node 11Node 12

0.130.100.130.220.130.050.050.080.040.030.040.02

1

4

3

2

56

7

910

811

120.13

0.10

0.13

0.13

0.05

0.05

0.08

0.04

0.02

0.04

0.03

Ranking vector More red, more relevant

Nearby nodes, higher scores

4r

Background

Intuitions: Why RWR is Good Score?

15

54

2

3

1513

1412

10 116 7 8 9

1 20

TargetSource

Score (Red Path) = (1-c) c6 x W(1,3) x W(3,4) x …. x W(14,20)

Penalty of length of path Prob of traversing the path

Footnote: (1-c) is restart probability in RWR; W is normalized adjacency matrix of the graph.

Background

Prox (1, 20) = Score (Red Path) + Score (Green Path) + Score (Yellow Path) +

Score (Purple Path) + …

A high proximity means many short/high weighted paths

54

2

3

1513

1412

10 116 7 8 9

1 20

TargetSource

Intuitions: Why RWR is Good Score?

Background

Overview


Q1




NetShield

M1

Colibri-S (KDD08)


M2

Q1: Find Complex User-Specific Patterns

• Q1.1. Center-Piece Subgraph Discovery,– e.g., master-mind criminal given some

suspects X, Y and Z?

• Q1.2 Interactive Querying (e.g. Negation)– e.g., find most similar conferences wrt KDD,

but not like ICML?

18

Footnote: Our algorithms for both Q1.1 and Q1.2 are to be deployed in a real system (Cyano) in IBM

Overview


Q1




NetShield

M1

Colibri-S (KDD08)


M2

Q1.1 Center-Piece Subgraph Discovery [Tong+ KDD 06]

A C

B

A C

B

Original GraphCePS

Q: How to find hub for the black nodes?

CePS Node

Input Output

Red: Max (Prox(A, Red) x Prox(B, Red) x Prox(C, Red))

CePS: Example (AND Query)

21

DBLP co-authorship network: - 400,000 authors, 2,000,000 edges

?

CePS: Example (AND Query)

R. Agrawal Jiawei Han

V. Vapnik M. Jordan

H.V. Jagadish

Laks V.S. Lakshmanan

Heikki Mannila

Christos Faloutsos

Padhraic Smyth

Corinna Cortes

15 1013

1 1

6

1 1

4 Daryl Pregibon

10

2

11

3

16

22

DBLP co-authorship network: - 400,000 authors, 2,000,000 edges

K_SoftAND: Relaxation of AND

Asking AND query? No Answer!

Disconnected Communities

Noise

23

details

R. Agrawal Jiawei Han

V. Vapnik M. Jordan

H.V. Jagadish

Laks V.S. Lakshmanan

Umeshwar Dayal

Bernhard Scholkopf

Peter L. Bartlett

Alex J. Smola

1510

13

3 3

5 2 2

327

4

CePS: 2 SoftAND

Stat.

DB

24

details

Overview


Q1




NetShield

M1

Colibri-S (KDD08)


M2

Q1.2: Interactive Querying

26

User Feedback

User Feedback

User Feedback

User Feedback

Initial Results No to `ICML’ Yes to `SIGIR’

'ICDM' 'ICML' 'SDM' 'VLDB' 'ICDE'

'SIGMOD' 'NIPS''PKDD''IJCAI'

'PAKDD'

'ICDM' 'SDM''PKDD''ICDE''VLDB'

'SIGMOD''PAKDD''CIKM''SIGIR'

'WWW'

'SIGIR''TREC''CIKM''ECIR''CLEF''ICDM''JCDL''VLDB''ACL''ICDE'

two main sub-communities in KDD: DBs (green) vs. Stat (Red)

Negative feedback on ICML will exclude other stats confs (NIPS, IJCAI)

Positive feedback on SIGIR will bring more IR (brown) conferences.

what are most related conferences wrt KDD?(DBLP author-conference bipartite graph) 27

Q1.2 iPoG for Interactive Querying [Tong+ ICDM 08, CIKM 09]





'PAKDD'



'WWW'


two main sub-communities in KDD: DBs (green) vs. ML/AI (Red)

Negative feedback on ICML will exclude other ML/AI conf.s (NIPS, IJCAI)



Overview


Q1




NetShield

M1

Colibri-S (KDD08)


M2

Q2.2 pTrack: Challenge[Tong+ SDM 08]

• Observations (CePS, iPoG…)– All for static graphs– Proximity: main tool

• Graphs are evolving over time!– New nodes/edges show up; – Existing nodes/edges die out; – Edge weights change…

Q: How close is Philip Yu to DBs over years? A: Track proximity, incrementally! 31

32

Author-Keyword Bipartite Graphs (NIPS)….….

NIP

S 1

995Sejnowski

Jordan

Neural Network

ICA

Bayes

NIP

S 1

994Sejnowski

Jordan

Neural Network

ICA

Bayes

NIP

S 1

993Sejnowski

Jordan

Neural Network

ICA

Bayes

pTrack: Trend analysis on graph level

M. Jordan

G.HintonC. Koch

T. Sejnowski

Year

Rank of Influence

33

pTrack: Problem Definitions

• [Given] – a large, skewed time-evolving bipartite graphs, – the query nodes of interest

• [Track] – (1) top-k most related nodes for each query node

at each time step t; – (2) the proximity score (or rank of proximity)

between any two query nodes at each time step t.

34

pTrack: Philip S. Yu’s Top-5 conferences up to each year

ICDE

ICDCS

SIGMETRICS

PDIS

VLDB

CIKM

ICDCS

ICDE

SIGMETRICS

ICMCS

KDD

SIGMOD

ICDM

CIKM

ICDCS

ICDM

KDD

ICDE

SDM

VLDB

1992 1997 2002 2007

DatabasesPerformanceDistributed Sys.

DatabasesData Mining

DBLP: (Au. x Conf.) - 400k authors, - 3.5k conferences - 20 years

35

Prox. Rank

Year

Data Mining and Databases are getting closer & closer

36

(Closer)

John

KDD

Tom

Bob

Carl

Van

RoyRECOMB

ICML

VLDB

KDD’s Rank wrt. VLDB over years…

….

Q2: pTrack on Bipartite Graphs• Computational Challenges (assuming )

– Iterative method O(m)– Straight-forward update

• Example– NetFlix (2.6m users x 18k movies, 100m ratings)– Both need >1hr

37

Q2: pTrack on Bipartite Graphs• Observation #1

– n1 authors; n2 conferences;

– n1 >> n2

• e.g., 400k authors, 3.5k conf.s in DBLP

• Observation #2– m edges changed, (n1 authors, n2 conf.s)

– rank of update = = update

• Proposed algorithm: Fast-Update

38

Theorem: (Tong+ 2008) (1) Fast-Update has no quality loss (2) Fast-Update is

~ ~ ~

KDD

3939

176x speedup

40x speedup

log(Time) (Seconds)

Data Sets

Our method

Our method

Q2: Speed Comparison

Overview


Q1




NetShield

M1

Colibri-S (KDD08)


M2

41

RWR: Think of it as Wine Spill

1. Spill a drop of wine on cloth 2. Spread/diffuse to the neighborhood

Background

42

RWR: Wine Spill on a Graph

wine spill on cloth RWR on a graph

Query

Background

1

4

3

2

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910

8

11

12

Random Walk with Restart

43

Background

44

Computing RWR

1

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2

5 6

7

9 10

811

12

0.13 0 1/3 1/3 1/3 0 0 0 0 0 0 0 0

0.10 1/3 0 1/3 0 0 0 0 1/4 0 0 0

0.13

0.22

0.13

0.050.9

0.05

0.08

0.04

0.03

0.04

0.02

0

1/3 1/3 0 1/3 0 0 0 0 0 0 0 0

1/3 0 1/3 0 1/4 0 0 0 0 0 0 0

0 0 0 1/3 0 1/2 1/2 1/4 0 0 0 0

0 0 0 0 1/4 0 1/2 0 0 0 0 0

0 0 0 0 1/4 1/2 0 0 0 0 0 0

0 1/3 0 0 1/4 0 0 0 1/2 0 1/3 0

0 0 0 0 0 0 0 1/4 0 1/3 0 0

0 0 0 0 0 0 0 0 1/2 0 1/3 1/2

0 0 0 0 0 0 0 1/4 0 1/3 0 1/2

0 0 0 0 0 0 0 0 0 1/3 1/3 0

0.13 0

0.10 0

0.13 0

0.22

0.13 0

0.05 00.1

0.05 0

0.08 0

0.04 0

0.03 0

0.04 0

2 0

1

0.0

n x n n x 1n x 1

Ranking vector Starting vector(Normalized) Adjacency matrix

1

(1 )i i ir cWr c e

Restart p

Footnote: Maxwell Equation for Web [Chakrabarti]

Computing RWR

45Footnote: 1-c restart prob; W normalized adjacency matrix

Q

How to get (elements) of Q?

-1

= - - c x WIQ

1

4

3

2

5 6

7

9 10

811

12

4r

Computing RWR• OntheFly

– No Pre-Computation; – Light Storage Cost (W)– Slow On-Line Response: O(m x Iter)

• Pre-Compute– Fast On-Line Response – Prohibitive Pre-Compute Cost: O(n3)– Prohibitive Storage Cost: O(n2)

46

Q: How to Balance?

On-line Off-line

47

Goal: Efficiently get (elements) of

B_Lin: Basic Idea[Tong+ ICDM 2006]

1

43

2

5 6

7

9 10

811

120.130.10

0.13

0.13

0.05

0.05

0.08

0.04

0.02

0.04

0.03

1

4

3

2

56

7

910

811

12

Find Community

Fix the remaining

Combine1

43

2

5 6

7

9 10

811

12

56

7

910

811

12

1

43

2

1

4

3

2

5 6

7

910

811

12

1

4

3

2

48

1

43

2

B_Lin: Basic Idea[Tong+ ICDM 2006]

• Pre-Compute Stage– Find Communities– Pre-compute within-community scores

• On-Line Stage– Fix the influence of the bridges (cross-community links)

49

+~~

B_Lin: details

W1: within community Cross community

details

50

+W =

B_Lin: details

WI – c ~~ I – c – cUSVW1

-1 -1

Easy to be inverted LRA difference

Sherman–Morrison Lemma!

details

51If Then

B_Lin: Pre-Compute Stage

• Q: Efficiently compute and store Q• A: A few small, instead of ONE BIG, matrices inversions

52Footnote: Q1=(I-cW1)-1

B_Lin: On-Line Stage

• Q: Efficiently recover one column of Q• A: A few, instead of MANY, matrix-vector

multiplications

53

Query Time vs. Pre-Compute Time

Log Query Time

Log Pre-compute Time

•Quality: 90%+ •On-line:

•Up to 150x speedup•Pre-computation:

•Two orders saving

54

Our Results

More on Scalability Issues for Querying(the spectrum of ``FastProx’’)

• B_Lin: one large linear system – [Tong+ ICDM06, KAIS08]

• BB_Lin: the intrinsic complexity is small – [Tong+ KAIS08]

• FastUpdate: time-evolving linear system – [Tong+ SDM08, SAM08]

• FastAllDAP: multiple linear systems – [Tong+ KDD07 a]

• Fast-iPoG: dealing w/ on-line feedback– [Tong+ ICDM 2008, Tong+ CIKM09]

55

Overview


Q1




NetShield

M1

Colibri-S (KDD08)


M2

A5: Immunization

How to select k `best’ nodes for immunization?57

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2











M1: SIS Virus Model [Chakrabarti+ 2008]

• ‘Flu’ like: Susceptible-Infectious-Susceptible

• If virus ‘strength’ s < 1/ λ1,A , an epidemic can not happen

58Footnote: Think of s as # of sneeze before heal.

Background

M1: Optimal Method• Select k nodes, whose absence creates the

largest drop in λ1,A

59

1

9

10

3

4

5

7

8

6

2

9

1

11

10

3

4

56

7

8

2

9

Original Graph: λ1,A Without {2, 6}: λ1,A~

M1: Optimal Method

• Select k nodes, whose absence creates the largest drop in λ1,A

• But, we need in time– Example:

• 1,000 nodes, with 10,000 edges • It takes 0.01 seconds to compute λ• It takes 2,615 years to find best-5 nodes !

60

Leading eigenvalue w/o subset of nodes S

M1: Netshield to Rescue

61

Theorem: (Tong+ 2009)(1)

A u = λ1,AX

u(i): eigen-score 1

2

3 4

9

10

11 12

5

6

7 8

13

14

15 16

10

1010

1

11

1

1

11

1

1

11

1

u

Think of u(i) as PageRank or in-degree

M1: Netshield to Rescue (Intuition)

• find a set of nodes S, which– (1) each has high eigen-scores– (2) diverse among themselves

1

2

3 4

9

10

11 12

5

6

7 8

13

14

15 16

10

1010

1

11

1

1

11

1

1

11

1

1

2

3 4

9

10

11 12

5

6

7 8

13

14

15 16

10

1010

1

11

1

1

11

1

1

11

1

1

2

3 4

9

10

11 12

5

6

7 8

13

14

15 16

10

1010

1

11

1

1

11

1

1

11

1


M1: Netshield to Rescue

• Example: – 1,000 nodes, with 10,000 edges – Netshield takes < 0.1 seconds to find best-5 nodes !– … as opposed to 2,615 years

63


(2) Br(S) is sub-modular(3) Netshield is near-optimal (wrt max Br(S))(4) Netshield is O(nk2+m)

Footnote: near-optimal means Br(S Netshield) >= (1-1/e) Br(S Opt)

Why Netshield is Near-Optimal?

64

1

310

8 7

4

6

5

2

9

B

B

1

310

8 7

4

6

5

2

9

Blue Bar: Marginal benefit of deleting blues nodesGreen Bar: Benefit of deleting green nodes

A

A

A Sub-Modular (i.e., Diminishing Returns) >=

B

Theorem: k-step greedy alg. to maximize a sub-modular function guarantees (1-1/e) optimal [Nemhauster+ 78]

M1: Why Br(S) is sub-modular?

65

1

310

8 7

4

6

5

2

9

Marginal Benefit

Pure from Blue Interaction between Blue and Green

Only purple term depends on {1, 2}!

Footnote: greens {1, 2} are nodes already deleted; blue {5,6} nodes are the nodes to be deleted

=

-

details

66

1

310

8 7

4

6

5

2

9

Marginal Benefit = Blue –Purple

More Green

Footnote: greens are nodes already deleted; blue {5,6} nodes are the nodes to be deleted

1

310

8 7

4

6

5

2

9

More Purple Less Red

Marginal Benefit of Left >= Marginal Benefit of Right

M1: Why Br(S) is sub-modular? details

M2: Quality of Netshield

67

Eig

-Dro

p

k

Netshield

Optimal

(1-1/e) x Optimal

(better)

M1: Speed of Netshield

68

Tim

e

k

> 10 days

0.1 secondsNetshield

NIPS co-authorship Network

(better)

Scalability of NetshieldT

ime

# of edges

(better)

X 108

Overview


Q1




NetShield

M1

Colibri-S (KDD08)


M2

Motivation [Tong+ KDD 08 b]

• Q: How to find patterns from a large graph?– e.g., communities, anomalies, etc.

71Author Conference

John

KDD

Tom

Bob

Carl

Van

RoyRECOMB

ISMB

ICDM

Motivation [Tong+ KDD 08 b]

• Q: How to find patterns from a large graph?– e.g., communities, anomalies, etc.

• A: Low-Rank Approximation (LRA) for adjacency matrix of the graph.

72

A L

M RX X

~~

1 1 0 0

1 1 0 0

1 1 0 0

0 1 1 1

0 0 1 1

0 0 1 1

LRA for Graph Mining

John

KDD

Tom

Bob

Carl

Van

RoyRECOMB

ISMB

ICDM

Author Conference Adjacency matrix: A

73

Conference

Au

tho

r

LRA for Graph Mining: Communities

John

KDD

Tom

Bob

Carl

Van

RoyRECOMB

ISMB

ICDM

Author Conf.

~~X X

Adj. matrix: AR: Conf. Group

M: Group-Group Interaction

L: author group

74

LRA for Graph Mining: Anomalies

John

KDD

Tom

Bob

Carl

Van

RoyRECOMB

ISMB

ICDM

Author Conf.

Adj. matrix: A

Recon. error is high ‘Carl’ is abnormal

75

Reconstructed A~

Challenges: How to Get (L, M, R)?

• Efficiently • both time and space

• Intuitively• easy for interpretation

• Dynamically • track patterns over time

76

None of existing methods fully meets our wish list!

Why Not SVD and CUR/CMD?

• SVD (Optimal in L2 and LF )

– Efficiency• Time:• Space: (L, R) are dense

– Interpretation• Linear Combination of

many columns

– Dynamic: Not Easy

77

2 2(min( , ))O n m nm

• CUR/CMD (Example-based)

– Efficiency• Better than SVD• Redundancy in L

– Interpretation• Actual Columns from A

xxxx

– Dynamic: Not Easy

Solutions: Colibri [Tong+ KDD 08 b]

• Colibri-S: for static graphs– Basic idea: remove linear redundancy

• Colibri-D: for dynamic graphs– Basic idea: leverage smoothness over time

78

Theorem: (Tong+ 2008)(1) Colibri = CUR/CMD in accuracy

(2) Colibri <= CUR/CMD in time(3) Colibri <= CUR/CMD in space

Comparison SVD, CUR vs. Colibri

s

Wish List SVD [Golub+ 1989]

CUR[Drineas+ 2005]

Colibri[Tong+ 2008]

Efficiency

Interpretation

Dynamics79

details

Performance of Colibri-S

Time SpaceOurs

CUR CUR

CMDCMD

80

SVD SVD

• Accuracy• Same 91%+

• Time• 12x of CMD• 28x of CUR

• Space• ~1/3 of CMD• ~10% of CUR Ours

Performance of Colibri-D

Time

# of changed cols

CMD

Colibri-S

Colibri-D achieves up to 112x speedup

Colibri-D

81

Network traffic

- 21,837 nodes

- 1,220 hours

- 22,800 edge/hr

(Prior Best Method)

Accuracy

- Same 93%+

Overview


Q1




NetShield

M1

Colibri-S (KDD08)


M2

Some of my other work• #1: FastDAP (in KDD07 a)– Predict Link Direction

• #2: Graph X-Ray (in KDD 07 b)– Best Effort Pattern Match in Attributed Graphs.

• #3: GhostEdge (in KDD 08 a)– Classification in Sparsely Labeled Network

• #4: TANGENT (in KDD09)– ``surprise-me’’ recommendation

• #5: GMine (in VLDB 06)– Interactive Graph Visualization and Mining

• #6: Graphite (in ICDM 08)– Visual Query System for Attributed Graphs

• # 7: T3/MT3: (in CIKM 08)– Mine Complex Time-stamped Events

• #8: BlurDetect (in ICME 04)– Determine whether or not, and how, an image is blurred

• #9: MRBIR (in MM 04, TIP06)– Manifold-Ranking based Image Retrieval

• #10: GBMML (in CVPR05, ACM/Multimedia 05)– Graph-based Multiple Modality Learning

83

Tasks Static Graphs Dynamic Graphs Images

84

Overview(this talk + others)

Queryin

gM

ining

CePS, iPoG, Basset, DAP, G-Ray, Grahite, TANGENT, FastRWR(KDD06, CDM06, KDD07a, KDD07b, IICDM08, KAIS08,

CIKM09, KDD09)

pTrack, cTrack, Fast-Update

(SDM08, SAM08)

Netshield, Colibri-S, GhostEdge, Gmine,

Pack, Shiftr(VLDB06, KDD08a, KDD08b,

SDM-LinkAnalysis 09, )

T3/MT3, Colibri-D (KDD08a, CIKM08)

MRBIR, UOLIR(MM04, CVPR05)

BlurDetect, GBMML, iQuality,

iExpertise(ICDE04, ICIP04,

MMM05, PCM05, MM05)

Plans

Goals

Step 1 (this talk)

Step 2 (medium term)

Step 3 (long term)

G1 Querying

CePS, iPoG, pTrack

Recommendation Interpretable Q

Querying rich data

G2Mining

Netshield, Colibri

Immunization Interpretable M

Mining rich data

G3 Scalability

All above O(m) or better (single machine)

Scalable by parallel Scalable on rich data

What is Next?

85

Research Theme: Help users to understand and utilize large graph-related data

Current Recommendation (Focus on Relevance)

86

1001

1

Sci. fiction

comedy

horror

Footnote: Nodes are movies; Edge is similarity between movies

adventure

Red nodes: by (most of) existing algorithms

``Broad Spectrum Recommendation’’(focus on completeness = relevance + diversity + novelty)

87

1001

1

adventureS

ci. fictioncom

edy

horror

Footnote: Nodes are movies; Edge = similarity between movies


Plans

Goals

Step 1 (this talk)


Step 3 (long term)

G1 Querying

CePS, iPoG, pTrack


Querying rich data

G2Mining

Netshield, Colibri


Mining rich data

G3 Scalability



What is Next?

88

Interpretable Recommendation

• Amazon.com recommends

• (based on items you purchased or told us your own)

Current Recommendation 89

Interpretable Recommendation

• Amazon.com recommends

• (based on items you purchased or told us your own)

• Amazing.com recommends

• Because it has the topics • You are interested

• Graph mining• Linear algebra

• You might be interested• Hadoop• Submodularity

Current Recommendation Interpretable Recommendation

Plans

Goals

Step 1 (this talk)


Step 3 (long term)

G1 Querying

CePS, iPoG, pTrack


Querying rich data

G2Mining

Netshield, Colibri


Mining rich data

G3 Scalability



What is Next?

91


Immunization

• This Talk: SIS (e.g., flu)• In the Future

– Immunize for SIR (e.g., chicken pox)– Immunize in Dynamic Settings

Dynamics of Graphs, e.g., edges/nodes are changing

Dynamics of Virus, e.g., the infection/healing rates are changing

92Footnote: SIR stands for susceptible-infectious-recovered.

Plans

Goals

Step 1 (this talk)


Step 3 (long term)

G1 Querying

CePS, iPoG, pTrack


Querying rich data

G2Mining

Netshield, Colibri


Mining rich data

G3 Scalability



What is Next?

93


Interpretable Mining

94

Find CommunitiesFind a few nodes/edges to describe

each community relationship between 2 communities

Footnote: Nodes are actors; edges indicate co-play in a movie.

Plans

Goals

Step 1 (this talk)


Step 3 (long term)

G1 Querying

CePS, iPoG, pTrack


Querying rich data

G2Mining

Netshield, Colibri


Mining rich data

G3 Scalability



What is Next?

95

Research Theme: Help users to understandand utilize large graph-related data

Querying Rich Graphs(e.g., geo-coded, attributed)

96

What is difference between North America and Asia?

Teenage

Adult

Phone

MSN

Mining Rich Graphs(e.g., geo-coded, attributed)

97

Teenager

Adult

Phone

MSN

How to find patterns? (e.g., communities, anomalies)

telemarketer

Plans

Goals

Step 1 (this talk)


Step 3 (long term)

G1 Querying

CePS, iPoG, pTrack


Querying rich data

G2Mining

Netshield, Colibri


Mining rich data

G3 Scalability



What is Next?

98


Scalability• Two orthogonal efforts

–E1: O(m) or better on a single machine–E2: Parallelism (e.g., hadoop)

• (implementation, decouple, analysis)

99


100

Real Data

User

Scalability

CePSiPoGBasset

pTrack

BLin

BBLin

FastUpdate

Fast-iPoG

Colibri

GhostEdge

Graphite

Pack

TANGENT

GMine

T3

Min

ingQ1

Q2

Q3

M3M2

M1

My Collaboration Graph (During Ph.D Study)

Legends:Green: QueryingYellow: MiningPurple: Others

G-Ray

DAP

NBLin

cTrack

Basset

MT3

NetShield

Q & A

Thank you!

102

fast algorithms for querying and mining large graphs hanghang tong machine learning department...

Documents

bn slide

anomaly detection slide

similarity background

immunization m2

higher scores background

immunization q1

proximity tracking q3

users linkedin