PROGRESS REVIEW

Mike Langston’s Research Team

Department of Computer ScienceUniversity of Tennessee

with collaborative efforts at

Oak Ridge National Laboratory

June 27, 2005

Team Members in Attendance

Bhavesh Borate, Suman Duvvuru, John Eblen, Mike Langston, Xinxia Peng, Andy Perkins, Jon S

charff, Henry Suters, Yun Zhang

Team Members Absent

Josh Steadmon

Mike Langston’s Progress ReportSummer, 2005

• Team Changes– Graduating Soon: Xinxia Peng, Jon Scharff– New Member: Andy Perkins

• Team Foci– FPT Tools and Applications– Computational Biology

• Recent Conference Talks– AICCSA-05 (Egypt), RTST-05 (Lebanon), DIMACS (New Jersey)

• Recent Visits– Cold Spring Harbor Lab (New York)

• Upcoming Conference Talks– ACiD-05 (England), Dagstuhl-05 (Germany), COCOON-05 (China)

• Upcoming Major Program Committee Service– AICCSA-06 (Program Chair), IWPEC-06 (Program Co-Chair)

John EblenDr. Ivan Gerling’s Data

• Details– Leukocyte data - 2 ages, 3 strands– Islet data – 3 ages, 4 strands

• Current Project – Adding Proteins– Add 60 proteins to leukocyte data of 22690

probe sets– How can we improve correlation?– What other types of analysis are possible?

General Clique Problem

• Specific Approaches– “Biographs” or graphs created from correlation values– Brock graphs– Approach for keller graphs?

• Information Gathering– Markov chains– General graph properties

• Combining Algorithms

Additional Projects

• Fast Direct Clique Codes– Currently testing on DIMACS challenge

graphs– Work continues

• Common Neighbor Preprocessing

Jon ScharffDifferential Expression

• Student’s t-test, in two normally distributed populations:– Mean assumed to be equal– Variance assumed to be equal

• Gene by gene basis

Differential Correlation

Differential Cliquification

• Cliques that appear in one graph but not the comparison graph

Nucleus Cliques/Clique Nuclei

Yun ZhangClique Enumeration Problem (1)

• Proposed a new maximal clique enumeration algorithm– Inspired by Kose et al algorithm– Enumerates cliques in non-decreasing order of sizes– Uses bitwise operations to speedup and reduce spac

e requirements– Sequential algorithm is parallelizable– Serial code is almost 400 times faster than Kose RAM

on the 0.85 threshold MAS5.0 graph (size 12,422)

Clique Enumeration Problem (2)

• Space required to hold the cliques is enormous

Memory Usage on a graph with 2895 vertices

0

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3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Clique Size

Mem

ory

usage (

GB

yte

s)

On 0.7 threshold MAS5.0 graph, it used up to almost 1 terabyte memory after 12 hours running

Clique Enumeration Problem (3)

• Parallelism on shared-memory machine– SGI Altix, 256 processors, 2 Terabytes shared

memory, 8GB per CPU– Use a dynamic task scheduler to

• Synchronize multiple threads• Make load balancing decisions

– Achieves a super-linear speedup on up to 64 processors

Clique Enumeration Problem (4)

Run times with/ without load balancing using up to 64processors on a graph with 2895 vertices

0.00

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0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68

Number of processors (threads)

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n t

ime (

secon

ds)

no load balancing with load balancing

Maximum Common Subgraph

• Clique branch algorithm by Henry (Cocoon05)– Takes advantage of the special structure of

association graph built from two graphs

• Finished serial implementation• Preliminary performance testing on small graphs• Next step:

– Benchmarking– Parallel implementation

Andy Perkins

• Working with Jon on Brynn Voy's low dose IR mouse data

• Finding and examining paracliques in the low dose data

• Thresholding via spectral graph theory

• Clique on MPSS mouse data

Ways of getting to the threshold

• Graph features/characteristics

• Using confidence intervals with Bayesian statistics

• Random: 0.5% edges in graph

• Gene Ontology

• Utilization of info from pathway databases

Graph & Statistical Analysis Utilizing Biological Info

Bravesh BorateThresholding in High-Throughput data

Normal distribution of No. of edges

-200000

0

200000

400000

600000

800000

1000000

1200000

0 0.2 0.4 0.6 0.8 1 1.2

Series1

Spleen data

-50000

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50000

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350000

400000

0 0.2 0.4 0.6 0.8 1 1.2

Series1

Skin data

-500000

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1000000

1500000

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0 0.2 0.4 0.6 0.8 1 1.2

Series1

MAS5 data

-200000

0

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400000

600000

800000

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1400000

0 0.2 0.4 0.6 0.8 1 1.2

Series1

RMA data

-200000

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Series1PDNN data

Comparison with other datasets

Data No of edges

Maximum Degree

Size of Maximum

Clique

Avg. size of Maximal Cliques

Spleen Data (0.85)

34753 349 39 20.03229

Skin data

(0.87)

32384 606 66 48.009

MAS5 data

(0.84)

3704 134 19 10.35285

RMA data (0.92)

34814 698 116 --

PDNN data

(0.87)

34225 678 88 68.1974

Gene Ontology

1 0.8 0.6 0.4 0.2 0

1

0.8

0.6

0.4

0.2

0

Scores from GO

Correlation Scores

Limitations

•GO data: helpful but blind reliability questionable

• Only applicable to genes with GO annotation

•For Elissa’s data: Bing got inexplicable results (a more so flat curve)

Info from Pathway Databases

• What graphs mean in biological context• Extrapolate info from what is “known” to the “unknown”.• Expression data from House-keeping genes invaluable.

Limitations

• Info in Pathway databases not arranged in tissue-specific or condition-specific manner.

A Combinatorial Strategy

• Get info & develop algo to make sense of it all and suggest a threshold to the user.

• Also suggest the biologist ideal thresholds with each method !!!!

• Provide facility for displaying the graph at each threshold• Better so, if it is interactive and dynamic (perhaps too am

bitious ???)• User discretion in the end, determines the right threshold.

Comparison of clustering algorithms

-Suman Duvvuru

What is clustering

• Clustering:– Partitioning into dissimilar groups of similar objects (in

our case objects refer to genes).– Cluster analysis is used to identify genes that show si

milar expression patterns over a wide range of experimental conditions.

• Traditional definition of a “good” clustering:– Points assigned to same cluster should be highly

similar.– Points assigned to different clusters should be highly

dissimilar.

Overview of clustering algorithms

• K-cores (Implemented):– A k-core of a graph is a largest subgraph wit

h minimum degree at least k – The k-cores of a graph can be generated by

• deleting the vertices from the graph whose degree is less than k and

• Performing a DFS on the resulting graph to find all the cores.

– The edge connectivity or simply the connectivity k(G) of a graph G is the minimum number k of edges whose removal results in a disconnected graph.

– A minimum cut abbreviated mincut is a cut with a minimum number of edges.

– A graph G with n vertices is called highly connected if k(G) > n/2.

– A highly connected subgraph HCS is an induced subgraph H such that H is highly connected.

– This algorithm identifies highly connected subgraphs as clusters.

HCS (Highly connected graph):

HCS Algorithm

• Using Dinics algorithm to compute mincut. The complexity of this computation is O(nm2/3).

• Edge density half as compared to our clique method.

HCS: An example

Other clustering methods

Using cluster 3.0 software:

• K-means

• Hierarchical clustering

Disadvantages:

• None of these methods allow a single gene to be present in multiple clusters.

Quality assessing

• Different measures for the quality of a clustering solution are applicable in different situations.

• It depends on the data and on the availability of the true solution.

• In case the true solution is known, and we wish to compare it to another solution, we can use the Minkowski measure or the Jaccard coefficient.

• When the true solution is not known, edge density, Homogeneity and separation, Average silhouette are used as criteria for evaluation.