big data analytics - universität hildesheimbig data analytics outline 1. graphlab application...

Big Data Analytics

Big Data Analytics

Lucas Rego Drumond

Information Systems and Machine Learning Lab (ISMLL)Institute of Computer Science

University of Hildesheim, Germany

GraphLab On Practice

Lucas Rego Drumond, Information Systems and Machine Learning Lab (ISMLL), University of Hildesheim, Germany

GraphLab On Practice 1 / 15

Big Data Analytics

Outline

1. GraphLab Application Deployment

2. Relational Classification Example

3. Factorization Models on GraphLab



Big Data Analytics 1. GraphLab Application Deployment

Outline







Steps

1. Install GraphLab into a specific directory

I Example: cd /home/user/

I git clone https://github.com/dato-code/PowerGraph.git

2. Create a directory for your application under/home/user/graphlab/apps

3. Create a CMakeLists.txt file into your application directory

4. Add the source files for your program under your application directory

5. Run ./configure under /home/user/graphlab

6. Go to /home/user/graphlab/release/apps/your application

and type make




CMakeLists.txt

p r o j e c t (MyProjectName )

a dd g r a p h l a b e x e c u t a b l e ( execu tab l e name imp l ementa t i on . cpp )




Hello World

#i n c l u d e <g raph l ab . hpp>

i n t main ( i n t argc , char ∗∗ argv ) {

graphlab : : mpi_tools : : init ( argc , argv ) ;graphlab : : distributed_control dc ;

dc . cout ( ) << ” He l l o World !\ n” ;

graphlab : : mpi_tools : : finalize ( ) ;

}



Big Data Analytics 2. Relational Classification Example

Outline







Relational Classification

v1

y(v1) : 1

v2

y(v2) : 3

v3

y(v3) :?

v4

y(v4) : 2

1

1 1 1

1

Given a graph G := (V ,E ) and a set oflabels L

I Some nodes have labels y : V → L

I Edges v , u have weights wv ,u

I Task: estimate a function y : V → L




Weighted voted Relational Neighbor

v1

y(v1) : 1

v2

y(v2) : 3

v3

y(v3) :?

v4

y(v4) : 2

1

1 1 1

1

Probability that a vertex v ∈ V has labelc ∈ L

P(c |v) =1

Zv

∑u∈{u|u∈Nv∧y(u)=c}

w(u,v)

Where:

Zv =∑u∈Nv

w(u,v)

I Nv denotes the neighbors of v

y(v) := arg maxc∈L

P(c |v)




wvRN Vertex Program:

1: procedurewvRNGatherinput: vertex v , scopeSv , ingoing edge (u → v)

2: return (w(u,v), y(u))

3: end procedure

1: procedure wvRNApplyinput: vertex v , scope Sv , gatherresult(Zv ,

(∑{u|u∈Nv∧y(u)=c} wu,v

)c∈L

),

2: y(v) :=

arg maxc∈L

(∑{u|u∈Nv∧y(u)=c} wu,v

)3: end procedure




wvRN Code

I Code and toy data:I http://www.ismll.uni-hildesheim.de/lehre/bd-14s/script/

gl_ex/wvRN_example.zip



http://www.ismll.uni-hildesheim.de/lehre/bd-14s/script/gl_ex/wvRN_example.zip

http://www.ismll.uni-hildesheim.de/lehre/bd-14s/script/gl_ex/wvRN_example.zip

Big Data Analytics 3. Factorization Models on GraphLab

Outline







Factorization modelsI Each item i ∈ I is associated with a latent feature vector qi ∈ Rk

I Each user u ∈ U is associated with a latent feature vector pu ∈ Rk

I Each entry in the original matrix can be estimated by

r(u, i) = p>u qi =k∑

f =1

pu,f qi ,f




Example

Titanic (t) Matrix (m) The Godfather (g) Once (o)

Alice (a) 4 2 5Bob (b) 4 3John (j) 4 3

a≈b xx

RR QQTTPP

TT

AliceAlice

BobBob

JohnJohn

4

4

4

2

3

5

3

MM GG OO

AliceAlice

BobBob

JohnJohn

TT MM GG OO




Learning a factorization model - Objective Function

Task:arg min

P,Q

∑(u,i ,rui )∈Dtrain

(rui − r(u, i))2 + λ(||P||2 + ||Q||2)

Where:

I r(u, i) := p>u qiI Dtrain is the training data

I λ is a regularization constant




Stochastic Gradient Descent Algorithm

1: procedure LearnLatentFactorsinput: DTrain, λ, α

2: (pu)u∈U ∼ N(0, σI)3: (qi )i∈I ∼ N(0, σI)4: repeat5: for (u, i , ru,i ) ∈ DTrain do . In a random order6: pu ← pu − α (−2(ru,i − r(u, i))qi + 2λpu)7: qi ← qi − α (−2(ru,i − r(u, i))pu + 2λqi )8: end for9: until convergence

10: return P,Q11: end procedure




Recommender System Graph

l

n

o

c

prnp = 4

rlp = 2

roc = 5

I Nodes:I Users UI Items I

I EdgesI Ratings rui




Factorization Models on GraphLab

l

n

o

c

prnp = 4

rlp = 2

roc = 5

I Node data:I user node: puI item node: qi

I Edge data:I Rating rui




Factorization Models on Graphlab

l

n

o

c

prnp = 4

rlp = 2

roc = 5

User Nodes:I Gather

I Compute the error andaccumulate the updateon each item

I ApplyI Update latent feature

vectors and computeupdates for eachneighboring item

I ScatterI Send message to items

with updates andaccumulated error

I Signal neighboringitems to execute




Factorization Models on Graphlab

l

n

o

c

prnp = 4

rlp = 2

roc = 5

Item Nodes:I Gather

I Gather messages fromusers

I ApplyI Update latent feature

vectors

I ScatterI Signal neighboring

users to execute



big data analytics - universität hildesheimbig data analytics outline 1. graphlab application...

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