1. Subspace Clustering for Microarray Data Analysis:
Multiple Criteria and Significance Assessment
Biotechnology Center
at the University of Illinois at Urbana-Champaign
Hui Fang, ChengXiang Zhai and Lei Liu
University of Illinois at Urbana Champaign
Introduction 1
Microarray Data :
Microarray is a powerful tool for monitoring the expression patterns of thousands of genes simultaneously.
GO based Measure 4
GO based Measure:
The quality of a cluster is defined as the depth of the common parent nodes on GO hierarchy shared by the genes in the cluster.
The more specific the node, the better the cluster.
For example, given the following cluster of genes { YBL028C, YCR100C, YFL044C, YHR143W-A, YIL069C, YIL131C, YJR133W, YKL173W, YKR056W, YLL028W, YLL056C, YLR361C, YNL159C, YNL166C, YNR038W, YOL092W}. The GO-based measure is 5.
Experiment Results 6
Importance of multiple criteria (GO-based measure)
Effectiveness of Confidence-based Measure
Our idea:
Use synthetic data set to show that the noisy clusters are always ranked lower than other clusters.
Correlation between Two Types of Measures
There is strong correlation between GO-based measure and confidence-based measure
the mean of several replicates
Biological Process
(GO: )
Physiological Processes
(GO: )
Cellular Process
(GO: )
Common Parent Node with Single criteria
Common Parent Node with Multiple criteria
22 genes
14 genes
Metabolism
(GO: )
Cell
Communication
Cell Growth
and/or
Maintenance
expression level
genes g1 … gn
0.9 …
-0.2
-0.1
0.5
Repeated several times
conditions c1 … cm
Goal:
Find gene clusters that are truly meaningful biologically
Challenges:
How to explore multiple criteria in clustering?
How to access the significance and quality of clusters?
Gene Ontology
(GO: )
Cellular Component
(GO: ) … …
Cell
(GO: ) …
Objectives 2
(1) Perform subspace clustering
Intracellular
(GO: ) … …
Nucleus
(GO: ) a b c d e f g h i j
Expression Level
Conditions
Raw Data
Subspace Clusters
Nucleolus
(GO: )
Nucleoplasm
(GO: )
DNA-directed RNA
polymerase I complex
(GO: )
True Clusters:
cluster1: {11, 20, 21, 35, 54}
cluster2: {4, 62, 70, 74, 92}
cluster3: {14, 15, 58, 71, 79}
cluster4: {45, 48, 52, 83, 94}
Found Clusters by Methods:
cluster1: {11, 20, 21, 35, 54}
cluster2: {4, 62, 70, 74, 92}
cluster3: {14, 15, 58, 71, 79}
cluster4: {45, 48, 52, 83, 94}
cluster5: {6, 43, 48, 51, 85}
cluster1: {4, 14, 53, 54, 76}
cluster2: {25, 29, 31, 49, 80}
cluster3: {1, 6, 61, 85 , 92}
cluster4: {2, 86, 89, 93, 97}
cluster1: {4, 14, 53, 54, 76}
cluster2: {25, 29, 31, 49, 80}
cluster3: {1, 6, 61, 85, 92}
cluster4: {2, 57, 86, 89, 93, 97} 4
DNA-directed RNA
polymerase III complex
(GO: )
DNA-directed RNA
polymerase II, holoenzyme
(GO: )
(2) Study whether multiple criteria improve the quality of clusters
(3) Design the quality measure of clusters based on
Domain knowledge ( e.g. gene ontology)
Significance (e.g. variance in replicates )
DNA-directed RNA polymerase II
core complex ;(GO: )
Confidence based Measure 5
Motivation
A gene may fall into a cluster purely because of the high variance in the replicates rather than biological relevance.
Goal
Give the priority to the clusters that are not generated by chance
Our idea
measure the quality of each generated cluster based on the original variances of each data point.
Method 1: compute the confidence level by taking the average of the standard deviation for each data point in the cluster
Method 2: compute how likely the cluster satisfies the constraints
The higher variance, the lower confidence.
Our Solution---Multiple Criteria:
Combine fluctuation constraint and trend constraint
Fluctuation Constraint
The difference of expression levels between two genes over every condition needs to be similar.
Trend Constraint
When the expression level of one gene goes up under some condition, the expression level of the correlated genes should also go up accordingly.
Why need both?
Subspace Clustering Model 3
Ranking lists based on confidence-based measure
Conditions
Expression Level g1 g2 c1 c2 g1 g2 c1 c2
Conclusion:
Propose multiple criteria model to help biologists discover meaningful gene clusters
Experiment results show the important of multiple criteria.
Define two ways to measure the quality of clusters
based on statistical significance
based on their biological meaning
Synthetic data sets shows the effectiveness of the confidence-based measure.
Future Work:
Approximation algorithm to discover subspace clusters
Employ multiple types of genomic data
Conclusions 7
true distribution
sample mean of replicates
Expression Level
Expression Level
The work is supported in part by the NIH grant No. 2 P30 AR to Lei Liu.
Acknowledgement 8
Conditions
Conditions
Trend Constraint satisfied
Fluctuation Constraint unsatisfied
Trend Constraint unsatisfied,
Fluctuation Constraint satisfied