Large-Scale Data Fusion Tutorial at BC^2, Basel 2015 by Collective - - PowerPoint PPT Presentation

Marinka Žitnik & Blaž Zupan University of Ljubljana, Slovenia

Large-Scale Data Fusion

by Collective Matrix Factorization

Tutorial at BC^2, Basel 2015

Tutorial Overview

❖ Motivation: search for bacterial-response genes, a case study ❖ Warm up: recommender systems ❖ Data fusion: tri-factorization and sharing of latent features ❖ Examples: movies & genes ❖ Hands-on: visual programming and scripting ❖ Applications: case studies in prioritization and classification ❖ Other approaches: related work

BC2 Tutorial on
 Large-scale data fusion by collective matrix factorization

Motivation

Search of bacterial response genes in a social amoeba Dictyostelium discoideum.

Motivation: Bacterial-Response Genes in Dicty

Gad Shaulsky Adam Kuspa Dictyostelium discoideum

Baylor College of Medicine, Houston, USA

Search for Bacterial Response Genes

Dicty is bacterial predator! genetic screen 50,000 clonal mutants genome found workload estimated 12,000 genes 7 genes 5 years ~200 genes

Gram+ defective: swp1, gpi, nagB1 Gram- defective: clkB, spc3, alyL, nip7

Now What?

50% coverage (100 genes) 80% coverage (160 genes) 20 screens required! 65 screens required!

Alternative: A Data-Driven Approach

Genes

spc3 swp1 kif9 alyL nagB1 gpi shkA nip7

Mutant Phenotypes

Gram neg. defective Aberrant spore color Aberrant spore color Decreased chemotaxis Gram pos.defective

So Much More Data …

Genes Publications

spc3 swp1 kif9 alyL nagB1 gpi shkA nip7

MeSH terms Timepoints MeSH terms Mutant Phenotypes MeSH Ontology Phenotype data Phenotype Ontology Pubmed data Expression data MeSH annotations

Gram neg. defective Aberrant spore color Aberrant spore color Decreased chemotaxis Gram pos.defective

Actually, in Biomedicine, Matrices Abound …

Genes Experiments

T1 T2 T3 T4 T5 T6 T7

Timepoints Normalized counts

V1 V2 V3 V4 V5 T1 T2 T3 T4 T5 T6 T7

Gene Expression

Actually, in Biomedicine, Matrices Abound …

gacT xacA racI racJ gemA racM racN rdiA gacT gemA rdiA racN racJ racI xacA racM gacT gemA rdiA racN racJ racI xacA racM

Gene Interactions

Actually, in Biomedicine, Matrices Abound …

Genes Pathways Part of N-Glycan biosynthesis pathway Part of N-Glycan biosynthesis pathway

alg7 alg13 alg14 alg1 alg2 alg11 alg3 alg9 alg12 dpm1 dpm2 dpm3

Fructose and mannose metabolism GPI-anchor biosynthesis

Gene Pathways

Actually, in Biomedicine, Matrices Abound …

Gene Ontology terms Gene Ontology terms

Response to bacterium Response to

• ther organisms

Response to external biotic stimulus Response to external stimulus Response to biotic stimulus

Part of Gene Ontology graph

Defense response Defense response to

• ther organism

Response to stress Defense response to bacterium R e s p

• n

s e t

• t

h e r

• r

g a n i s m s Defense response R e s p

• n

s e t

• s

t r e s s Response to bacterium

Ontologies

Actually, in Biomedicine, Matrices Abound …

Medical Subject Headings Literature

MeSH terms

Cell separation Cytoplasmic vesicles/metabolism Ethidium/metabolism Immunity/innate Mutation Phagocytes/cytology Phagocytes/immunology* Phagocytosis*

Ontologies of Controlled Vocabularies

Actually, in Biomedicine, Matrices Abound …

Pathways Ontology terms

alg7 alg13 alg14 alg1 dpm1 dpm2 dpm3

Fructose and mannose metabolism

Protein N-linked glycosylation (GO:0006487) Dolichol kinase (K00902) Alpha-mannosidase II (K01231) Oligosaccharyltransferase complex (K12668) Orthology Ontology GO:0004168 GO:0004572 GO:0008250

Part of N-Glycan biosynthesis pathway

Cross-Links of Controlled Entities

BC2 Tutorial on
 Large-scale data fusion by collective matrix factorization

Warm-Up

Working with matrices: recommender systems, two- factorization and tri- factorization.

Back to the Problem: Recommender Systems

Genes

spc3 swp1 kif9 alyL nagB1 gpi shkA nip7

Mutant Phenotypes

Gram neg. defective Aberrant spore color Aberrant spore color Decreased chemotaxis Gram pos.defective

Kate Alex Jerry John Bride Wars Passengers War of the Worlds The Matrix Reloaded Mike Morgan Nick Jenny Pulp fiction The Godfather The Dark Knight Schindler’s List

Users Movies

Recommender Systems

Netflix Prize, 2009

Example: A Small Relation Matrix

Movie User

2 3 5 4 4 5 4 5

Kate Alex Mike John

B r i d e W a r s P a s s e n g e r s W a r

• f

t h e W

• r

l d s T h e M a t r i x R e l

• a

d e d

Matrix Two-Factorization

0.2 0.5 0.5 0.5

Kate Alex Mike John

6.3 0 1.1 8 3.9 10.7 3.3

B r i d e W a r s P a s s e n g e r s W a r

• f

t h e W

• r

l d s T h e M a t r i x R e l

• a

d e d L1 L2 L1 L2

Matrix Two-Factorization

~ ~

2 3 5 4 4 5 4 5

Kate Alex Mike John Bride Wars Passengers War of the Worlds The Matrix Reloaded

0.2 1.6 2 5.4 1.7 3.2 0.6 4 2 5.4 1.7 1.3

Matrix Tri-Factorization

0.2 0.3 0.8 0.2 0.7 1.2 0.8 1.2

Kate Alex Mike John

0.9 0.2 0.2 1 0.6 0.1 0.7 0.8

Bride Wars Passengers War of the Worlds The Matrix Reloaded

• 4.4 9.1

6.7 -5.8

U1 U2 M1 M2 U1 U2 M1 M2

Matrix Tri-Factorization

~ ~

2 3 5 4 4 5 4 5

Kate Alex Mike John Bride Wars Passengers War of the Worlds The Matrix Reloaded

0.3 0.2 1.2 1.7 4.5 0.2 2.1 4.1 0.5 0.9 4.5 1.5 4.8 0.1 1.9 1.1

Hands-On: Matrix Tri-Factorization

BC2 Tutorial on
 Large-scale data fusion by collective matrix factorization

Data Fusion

Collective matrix tri-factorization. Latent factor sharing.

Data Fusion Graph: One Data Matrix

B A

~ ~

x x =

A

Tri-factorization

• f matrix A-B

B

Recipe matrix of A Recipe matrix of B Backbone matrix of A-B Reconstructed matrix A-B

Data Fusion Graph: Two Data Matrices

~ ~

x x =

Collective tri-factorization

• f matrices A-B and A-E

Recipe matrix of A Recipe matrix of B Backbone matrix of A-E Reconstructed matrix A-B

E B A E B A

Backbone matrix of A-E Recipe matrix of E

~ ~

x x =

Reconstructed matrix A-E

Data Fusion Graph: All Together Now

E B D C A F G

Sharing of Latent Matrices

E B D C A F G

R =      ⇤ R12 · · · R1r R21 ⇤ · · · R2r . . . . . . ... . . . Rr1 Rr2 · · · ⇤     

S = 2 6 6 6 4 ⇤ Sk1×k2

12

· · · Sk1×kr

1r

Sk2×k1

21

⇤ · · · Sk2×kr

2r

. . . . . . ... . . . Skr×k1

r1

Skr×k2

r2

· · · ⇤ 3 7 7 7 5

2 { Θ(t) = Diag(Θ(t)

1 , Θ(t) 2 , . . . , Θ(t) r )

G = Diag(Gn1×k1

1

, Gn2×k2

2

, . . . , Gnr×kr

r

),

min

G≥0 J(G; S)

= X

Rij∈R

||Rij GiSijGT

j ||2 +

+

maxi ti

X

t=1

tr(GT Θ(t)G),

(8)

Input: A set R of relation matrices Rij; constraint matrices Θ(t) for t 2 {1, 2, . . . , maxi ti}; ranks k1, k2, . . . , kr (i, j 2 [r]). Output: Matrix factors S and G. 1) Initialize Gi for i = 1, 2, . . . , r. 2) Repeat until convergence:

• Construct R and G using their definitions in Eq. (1) and
• Eq. (3).
• Update S using:

S (GT G)−1GT RG(GT G)−1.

• Set G(e)

i

0 for i = 1, 2, . . . , r.

• Set G(d)

i

0 for i = 1, 2, . . . , r.

• For Rij 2 R:

G(e)

i

+= (RijGjST

ij)+ + Gi(SijGT j GjST ij)−

G(d)

i

+= (RijGjST

ij)− + Gi(SijGT j GjST ij)+

G(e)

j

+= (RT

ijGiSij)+ + Gj(ST ijGT i GiSij)−

G(d)

j

+= (RT

ijGiSij)− + Gj(ST ijGT i GiSij)+ (10)

• For t = 1, 2, . . . , maxi ti:

G(e)

i

+= [Θ(t)

i

]−Gi for i = 1, 2, . . . , r G(d)

i

+= [Θ(t)

i

]+Gi for i = 1, 2, . . . , r (11)

• Construct G as:

G G Diag( v u u t G(e)

1

G(d)

1

, v u u t G(e)

2

G(d)

2

, . . . , v u u t G(e)

r

G(d)

r

), (12) where denotes the Hadamard product. The p· and

· ·

are entry-wise operations.

Hands-On: Collective Matrix Factorization

BC2 Tutorial on
 Large-scale data fusion by collective matrix factorization

Scoring

Data sampling. Completion scoring.

Data Sampling & Completion

Hands-On: Performance Evaluation

Hands-On: Latent Profiling

BC2 Tutorial on
 Large-scale data fusion by collective matrix factorization

The Yeast Case Study

A large data compendium. Functional genomics.

The Yeast Case Study

Gene

Gene annotation data

Literature Literature Topic Experiment Biochemical pathway Gene Ontology Term

Gene expression data Genetic and physical interactions G e n e l i t e r a t u r e Gene pathway data Literature on functions and processes Ontology structure Topics of yeast biology

Hands-On: The Yeast Case Study

Latent Matrix Chaining

x x

= =

Chain of latent matrices

Gene Literature topic Gene profile matrix Gene Literature Literature Topic

Gene literature Topics of yeast biology

Gene Literature topic

Hands-On: Latent Matrix Chaining

BC2 Tutorial on
 Large-scale data fusion by collective matrix factorization

Case Studies

Dictyostelium bacterial gene hunt. Functional genomics. Drug-induced liver injury. Survival analysis.

Dictyostelium Bacterial Gene Hunt

4 seed genes 14 data sets, only one of which was directly related to bacterial response

R1,10 Θ1

ABC family

Miranda et al. 2013

Gene Gene Ontology term Phenotype Ontology term PubMed identifier MeSH descriptor Development

Parikh et al. 2010

Bacterial RNA-seq

Nasser et al. 2013

KEGG pathway Reactome pathway

1 4 8 2 3 5 6 7 9 10

R1,9 R1,8 R1,7 R1,6 R6,5 R6,4 R1,5 R1,4 R1,2 R2,3 R2,4 R5,4

Gene Hunt: Object Profiling by Latent Chaining

R1,10 Θ1

ABC family

Miranda et al. 2013

Gene Gene Ontology term Phenotype Ontology term PubMed identifier MeSH descriptor Development

Parikh et al. 2010

Bacterial RNA-seq

Nasser et al. 2013

KEGG pathway Reactome pathway

1 4 8 2 3 5 6 7 9 10

R1,9 R1,8 R1,7 R1,6 R6,5 R6,4 R1,5 R1,4 R1,2 R2,3 R2,4 R5,4

Latent chains

Gene Hunt: Similarity Estimation and Ranking

Seed genes

Similarity estimation Gene ranking

Similarity score aggregation Seed genes Similarity scoring Candidate genes Candidate gene Chains i ix ii iv v vi vii viii iii Scored candidate gene Scored candidate genes Similarity score matrix Similarity scoring Similarity score matrices Similarity score aggregation

Gene Hunt: Validation of Predictions

cf50-1 smlA acbA pirA rps10 abpC tirA DDB_G0272184 pikB vps46 pikA swp1 ggtA DDB_G0288519 pten DDB_G0288551 tra2 DDB_G0286429 dscA-1 cinC udpB sfbA modA DDB_G0287399 prmt5 sh DDB pt cf ac sm DDB DDB tr si rb DDB pi DDB DG1 ad DDB DD_ ds gdt pi DDB DDB ab

abpC– modA– cf50-1– tirA– Day 2 # of D. d cells AX4 acbA– smlA– pikA–/pikB– pten– 104 103 102 10 104 103 102 10 Day 3

Gene

PMID

R14

Experimental Condition

R13 1

GO Term

R 12

KEGG Pathway

R16 2

MeSH Descriptor

R45 R42 5 6 R62

1 2 3 4 5 6

Functional Genomics

Prediction task DFMF MKL RF F1 AUC F1 AUC F1 AUC 100 D. discoideum genes 0.799 0.801 0.781 0.788 0.761 0.785 1000 D. discoideum genes 0.826 0.823 0.787 0.798 0.767 0.788 Whole D. discoideum genome 0.831 0.849 0.800 0.821 0.782 0.801 Pharmacologic actions 0.663 0.834 0.639 0.811 0.643 0.819

Chemical

Θ1

Pharmacologic Action

R12

PMID

R13

Depositor

R14

Substructure Fingerprint

R15

Depositor Category

R46

1 2 3 4 5 6

Drug Toxicity Prediction

GO term

Θ13,13

Drug DILI potential Drug type

Θ10,10 R10;11

Sample metadata Sample from rat in vivo single dose study

R5;9 R5;12 R6;12

Sample from rat in vivo repeated dose study Sample from rat in vitro study

R7;9

Sample from human in vitro study

R8;9

Hematology, biochemistry, liver weight

R 10;14

Gene from rat in vivo single dose study

R1,5 R1,10 Θ1,1 R1,13 R5,10

Gene from rat in vivo repeated dose study

R2,6 R2,10 Θ2,2 R2,13 R6;9 R6,10

Gene from rat in vitro study

R3,7 R3,10 Θ3,3 R3,13 R7,10

Gene from human in vitro study

R4,8 R4,10 Θ4,4 R4,13 R8,10

1 2 3 4 5 6 7 8 9 10 11 12 13

14

Data fusion studies! AUC! In vivo studies! 0.819! In vitro studies! 0.790! Human in vitro study! 0.793! Animal in vitro study! 0.799! Animal studies! 0.811! Human studies! 0.792! All studies! 0.810!

Survival Analysis

R14 Copy number somatic mutation

Sample Gene miRNA Protein 1 5 2 3 4

R13 R15 R12

Gene Ontology term 6

Θ6 R56 R36 R46

Methylation

7

R17 R76

Survival data

I[n]

Survival Analysis

Time (months) Baseline cumulative hazard

3 6 9 12 15 18 21 24 0.4 0.2 0.0 0.6 0.8 1.0 1.2

Time (months) Cumulative hazard

3 6 9 12 15 18 21 24 0.0

• 0.2
• 0.4

0.2 0.4 0.6 0.8

Latent factor 1 Latent factor 2

Disease-Disease Association Discovery

A Data fusion schema Gene GO term DO term Drug

R13 R12 R14 Θ3 Θ2 Θ4

Θ(1)

1

Θ(2)

1

Θ(3)

1

Θ(4)

1

Θ(5)

1

crescentic glomerulonephritis acute proliferative glomerulonephritis glomerulonephritis nephritis interstitial nephritis kidney disease kidney failure urinary system disease

Example of an identified disease class

Disease-Disease Association Discovery

. . .

6

abetalipoproteinemia, lung metastasis dysgerminoma serous cystadenoma factor XIII defjciency Plasmodium falciparum malaria

Level 3

immune system diseases cognitive disorders acquired metabolic diseases metabolic diseases cancer

18

pulpitis periodontitis

Level 2

cancer inherited metabolic disorders nervous system diseases respiratory system diseases cardiovascular system disease

51

bile duct disease hemolytic-uremic syndrome

Level 1

Largest disease class

146

Hodgkin’s lymphoma Cushing’s syndrome gastric lymphoma crescentic glomerulonephritis

. . . . . .

Root layer

a single disease two diseases three or more diseases eighteen diseases

18

Disease class size:

BC2 Tutorial on
 Large-scale data fusion by collective matrix factorization

Related Approaches

Network-based methods. Kernel-based methods. Probabilistic graphical models. Collective latent factor models.

Data Integration Strategies

D1 D2

1 2 3 4 5 6 7 8

Dint D1 D2

1 2 3 4 5 6 7 8

D1 D2

1 2 3 4 5 6 7 8

Early integration Intermediate integration Late integration

Network-Based Approaches

Mostafavi et al., Genom Biol (2008); Mostafavi and Morris, Proteomics (2012).

Network-Based Approaches

Wang et al., Nat Methods 2014; Greene et al., Nat Genet 2015.

Original data

a b c d e

Patients Patients Patients Patients Patients Patient similarity matrices Patient similarity networks Fusion iterations Fused patient similarity network Patients mRNA expression DNA methylation Patient similarity: Patients mRNA-based DNA methylation–based Supported by all data

Multiple Kernel Learning

M2 M1

M K2 K1 µ1K1+ µ2K2=K w2 w1 w x x

f (x) f (x) f (x)

x

Lanckriet et al., Bioinformatics 2004; Yu et al., BMC Bioinformatics 2010; Gonen et al., JMLR 2012.

KL =

• K: K =

P

∑

m=1

ηmKm, K 0, tr(K) ≤ c

• maximize ω(K) =

N

∑

i=1

αi − 1 2

N

∑

i=1 N

∑

j=1

αiα jyiyjk(xi,x j) with respect to α ∈ RN

+

subject to

N

∑

i=1

αiyi = 0 C ≥ αi ≥ 0 ∀i.

User-selected seed set entered via a web-accessible interface Gene expression dataset 1 Transcription factor binding sites Gene expression dataset 2 Gene expression dataset N Yeast two-hybrid dataset 1 Co-precipitation dataset 1 Gene expression Physical interactions Genetic interactions Synthetic lethality dataset Synthetic rescue dataset Sequence & text Localization Curated literature Data integration via a Bayesian network weights each evidence type probabilistically based on its accuracy and coverage

1 2 3 g w 4 h14 5 h15

3

(a) (b) (c) (d)

Pathway prediction via a probabilistic algorithm that considers direct and indirect connections of each gene to the seed gene set Results displayed in a dynamic visualization

Probabilistic Graphical Models

Troyanskaya et al. PNAS 2003; Savage et al., Bioinformatics 2010; Badegeley et al. Bioinformatics 2015; Zitnik and Zupan, ISMB 2015.

Collective Latent Factor models

Relation heterogeneity — borrow consistent patterns across many potentially heterogeneous input spaces. Object type heterogeneity — leverage heterogeneous types of features to improve the learning performance in each task. Task heterogeneity — exploit related prediction tasks to transfer knowledge between data views.

Effect relation Target relation

. . .

Target relation Effect relation

• bjects of type
• bjects of type

BC2 Tutorial on
 Large-scale data fusion by collective matrix factorization

Conclusion

Current challenges. Universal data fusion.

Multiple Types of Data Heterogeneity

1 2 3 4

Multislice Data

nodes resolution parameters coupling = 0

nodes resolution parameters coupling = 0.1

nodes resolution parameters coupling = 1

Multiscale Data Multiplex & Multirelational Data

E B D C A F G Mucha et al. Science 2010.

Data Fusion of Everything!

Thanks to Bioinformatics Laboratory