1. Two études on modularity
Ron Shamir
Tel Aviv University
Simons Networks workshop, April

2. Integrated analysis of two biological networks
David Amar
NAR Feb 2014

3. A module map Input: networks H,G with same vertex set
Goal: summarize the key information in both in a module map
Node – module: gene set highly connected in H
Link – two modules highly interconnected in G

4. Generalizes clustering and biclustering

5. The winning alg
Initial solution based on enumeration of maximal bicliques in G
Global refinement based on probabilistic score of the whole map
Successfully tested on
Yeast H: PPI G: GI
Yeast H: PPI+ G: DDR specific GI
Lung cancer patients, H: co-expression, G: differential co-expression
Software available

6. Flexible module discovery in 3-way data
David Amar, Daniel Yekutieli , Adi Maron-Katz, Talma Hendler
Proc. ISMB/ECCB 2015, Bioinformatics July 15

7. Outline Intro: input and goals Probabilistic model Algorithm Results
Simulations
Gene expression
Brain fMRI
Comparison to other approaches

8. Genes\voxels\parcels
Module discovery
A fundamental task
The standard case: a matrix
Cluster: subset of rows
Bicluster: subset row, subset of columns
Subjects
Genes\voxels\parcels
Cluster
Bicluster

9. Genes\voxels\parcels
Three-way data
Time points
A matrix for each subject
Rows: measured objects
Columns: time points
Measured objects:
Gene expression
Activity at voxels / parcels in fMRI …
Subjects
Genes\voxels\parcels
Kim J, Matthews NL, Park S., Via: Wikimedia Commons
Kim J et al. Via: Wikimedia Commons

10. A single subject vs. multiple subjects
Time points
Consistent signal across multiple subjects?
Genes\voxels\parcels
A module (e.g., a bicluster):
Gene set; Time point set
“Interesting signal” within
ISA (Bergmann et al Physical Review E)
Samba (Tanay et al PNAS)
Plaid (Lazzeronni and Owen 2002, Stat. Sinica)
Bimax (Prelic et al. 2006, Bioinformatics)

11. A single subject vs. multiple subjects
Consistent signal across multiple subjects?
Time points
Subjects
Subjects
Only a subset is relevant
Genes\voxels\parcels

12. A single subject vs. multiple subjects
Consistent signal across multiple subjects?
Subject 1
Subject 2 B B
Subjects
Only a subset is relevant
Time points
Subject-specific (asynchronicity)
Gene set
Same set across subjects: too rigid
What if some are missing?
What if subject s has additional activated pathways? A A A A C C
Subject 5 D A D

13. Modules in 3-way data Core module:
A subset of the subjects 
A subset of rows
A (possibly different) subset of time points for every subject in 
Subject-specific part of the module:
A subset of the core module rows
Additional rows per subject 5

14. (v,t,s) in a subject- specific module:
Modules in 3-way data II
Want modules with unusually high / low values
F0: background, F1: distribution within modules
Binary data
Probability of 1 within modules is much higher
Real valued data: distinct normal distributions
(v,t,s) in a subject- specific module:
Zv,t,s ~ F1
Zv,t,s ~ F0

15. The generative model: scheme
Toy example
Core module rows
Relevant subjects
Subjects: 1, 2, 5
Core rows
Rows: core + subject specific
Time points
Subject-specific information
Subject 1
Subject 2
Subject 5
Observed data D B B
Zv,t,s A A A A A C C D

16. The posterior Z HSvs: Row v in the module of subject s?
Subject rows depend on the core and θ
Markov model for the time points
θ: Hyper-parameters
Core rows, subject relevancy
Data likelihood
HSvs: Row v in the module of subject s? Z
PS: Row relevant to subject s?
Cst: Time point t in the module of subject s?
Hv: Row v in the module?
f: current implementation: Bernoulli (binary data) or normal

17. The Algorithm Initialization: Use a biclustering solution (Bimax, ISA)
TWIGS - Three-Way module Inference via Gibbs Sampling
Initialization: Use a biclustering solution (Bimax, ISA)
Improvement: Gibbs sampling
Requires deriving all conditionals
~50 iterations suffice (<10sec)
Local optimum
Our algorithm starts from a solution produced using a standard
biclustering algorithm, and then applies iterative improvement steps.
In each step all parameters are fixed except a single one that is
sampled according to its conditional probability. The order of parameters
matches the subsections below. This order is repeated
cyclically k times. The output of the process is the set of sampled
values for each parameter in all iterations. We then extract the core
modules and the subject-specific modules from this output
Initial solution

18. Finding multiple modules
Algorithm filter
Get a set of biclusters
Run Gibbs on each one – get a set of modules M
Remove redundancies
Select large modules
Algorithm masker
Get the best bicluster
Run Gibbs on it – get a module m
Remove the signal of m from the data Z
Repeat 1-4 until no module is found

19. Simulation results TWIGS = Bimax-Gibbs-masker
V=500, T=50, S=10, 5 core modules, ps=0.9, p0 = 0.01 (+ additional subject-specific rows in each module)
TWIGS = Bimax-Gibbs-masker
improves performance even when no subject-specific information is present

20. Gene Expression analysis
Septic Shock data (Parnel et al. 2013, Shock)
14 subjects, 4 measurements each
Binarized matrix: fold change > 2 compared to time zero, genes
TWIGS found 2 core modules
Module 1: 11 subjects; 53 core genes
Enriched with response to bacteria
Module 2: 7 subjects, 62 core genes
Enriched with T-cell activity

21. Core module 1: non-core enrichments
Red stripes: relevant time points
Highlighted subjects did not survive.

22. Brain fMRI analysis
Rest data: 20 subjects; 464 parcels; 94 time points (Vaisvaser 2013 Frontiers in Human Neuroscience)
TWIGS found 4-5 core modules
Modules partition the brain into functional regions known to be related to rest
Subject-specific enrichments reveal additional connections among regions
4-5 core modules: (depending on the desired intensity; results are robust) 1 2 3 4
4 subjects had additional enrichment for attention  suggests a tendency to be more attentive to sensory stimuli during thought processes.

23. Brain fMRI results Subjects cover a different % of the core module
Subjects have different time points

24. Brain fMRI vs. GE results
Small, highly enriched core module
Subject-specific modules of 100+ additional genes
fMRI:
Large core modules: each subject covers a part
Subject-specific modules are relatively small
Integrated analysis is crucial in both cases
Subject-specific signal found in both
Subject-specific signal less extensive in fMRI

25. Comparison to other methods: subject coverage
> 2-fold improvement in subject coverage

26. Comparison to other methods: Enrichment tests (GE)
Rank summarizes enrichment and redundancy

27. Summary
acgt.cs.tau.ac.il/twigs/
A probabilistic model for analyzing 3-way data: Core + subject-specific modules
Developed a Gibbs sampling algorithm
Outperforms extant methods
Even in “pure” biclustering tasks
2-fold improvement in subject coverage
Successfully applied to gene expression and fMRI; Integrative analysis was crucial
R implementation available
Lots of room to improve

28. w
postdocs available