Association Analysis Techniques for Discovering Functional Modules
from Microarray Data
Gaurav Pandey*, Gowtham Atluri, Michael Steinbach and Vipin Kumar
Department of Computer Science and Engineering, University of Minnesota, Twin Cities
*To whom correspondence should be addressed:
1. INTRODUCTION
DNA microarray technology is one of the major recent advances in biotechnology [1]. In particular, their
ability to measure the expression of thousands of genes simultaneously under a certain condition makes
them suitable for several biological applications, such as the functional analysis of genes and identification
of significantly over- or under-expressed genes in complex diseases like cancer. An application of great
interest in microarray data analysis is the identification of a group of genes that show very similar patterns
of expression in a data set, and are expected to represent groups of genes that perform common/similar
functions, also known as functional modules [2]. Although clustering offers a natural solution to this
problem, it suffers from the limitation that it uses all the conditions to compare two genes, whereas only a
subset of them may be relevant.
Association analysis [3] offers an alternative route for finding such groups of genes that may be co-
expressed only over a subset of the experimental conditions used to prepare the data set. The techniques in
this field attempt to find groups of data objects that contain coherent values across a set of attributes, in an
exhaustive and efficient manner. However, a major limitation of these techniques is that they are only able
to analyze data sets that are constituted of binary and/or categorical variables, i.e., attributes whose values
can come only from a finite set, such as {0,1}. Consequently, most of the applications of association
analysis techniques to microarray data [4,5] incorporate a pre-processing step, wherein the expression
values are discretized before groups of genes showing similar patterns of expression are extracted.
In recent work [6], we developed a generalization of association analysis for data sets where all the
attributes are real-valued, such as gene expression datasets. More details of this methodology are provided
in Section 2. This generalization enables us to efficiently extract groups of genes that show coherent
patterns of expression across several experimental conditions, and are thus expected to constitute functional
modules. We evaluate these modules for enrichment with a set of functional classes from the biological
process ontology of GO. These evaluations show that a large number of the modules discovered are indeed
functionally enriched, and thus demonstrate the ability of association analysis techniques to efficiently
discover interesting functional information from microarray and other real-valued biological datasets. More
details of these results are provided in Section 3.
2. METHODS
Several measures for the coherence of the values taken by a set of data objects across a set of cases have
been defined in association analysis, mostly for binary data. One such measure is the support of a group of
objects, also known as a pattern or an itemset, which measures the number of cases where each object in a
group takes a value of 1. Also, much of the work on the design of efficient algorithms for extracting various
types of patterns from data is based on the anti-monotonicity property of these association measures,
particularly support. More specifically, the support of a group of objects I is guaranteed to be greater than
or equal to that of a superset of this set. This property enables the design of algorithms such as Apriori [10],
that are able to discover hundreds of such groups of coherent patterns that have a certain minimum support
from large datasets very efficiently.
In order to generalize such analysis for large real-valued datasets, it is necessary to define a support
measure that captures the coherence of the values of the data objects and is anti-monotonic. In particular,
since our focus is on the use of these techniques for analyzing gene expression data, we took into account
the following two aspects of the expression values to define such a support measure:
a)
Direction: Since we use the log
2
-transformed ratio as the expression value of a gene, an important
consideration for measuring the coherence of values of a group of genes in a given condition is the
sign or parity of the value. Thus, we only allow conditions under which all the genes in a pattern are
either over- or under-expressed to contribute towards the coherence of the pattern.
b)
Magnitude: Another important consideration for measuring the coherence of the expression of a
group of genes is that the magnitude of their expression should be within a certain range. We
incorporate this requirement in an adaptive manner, where this range is computed as a multiple of
the expression value of the least expressed gene in the group under each condition.
Using these two semantic requirements for measuring the coherence of the expression values of a set of
genes across several experimental conditions, we defined an anti-monotonic support measure named
ContSupport, the mathematical details of which can be found in [6]. This measure also enabled the design
of an efficient algorithm for deriving groups of genes from a microarray dataset that are highly co-
expressed across a significant subset of conditions. We would like to note here that other methods of
measuring the coherence of expression values of a set of genes are possible, and our definitions above
represent one such method. In the next section, we discuss the evaluation of the functional enrichment of
the set of gene patterns generated from a standard gene expression dataset.
3. RESULTS
We applied our gene pattern discovery algorithm to Hughes et al [7]'s
popular S. cerevisiae microarray data set. The dimensions of this dataset
are 300 conditions × 6316 genes, and thus, its large scale nature justifies
the use of sophisticated data mining algorithms for extracting useful
knowledge about functions of the constituent genes. The gene patterns
extracted using various thresholds were tested for enrichment by Myers
et al's list [8] of 138 functional classes from the GO biological process
ontology, and significantly enriched patterns were identified after
correcting for multiple hypothesis testing using Bonferroni correction.
Figure 1 shows the annotation of a pattern of ten genes discovered by the
RNA-mediated transposition class in the GO biological process ontology.
The accurate annotation of this large set by a very specific functional
class illustrates the ability of association analysis techniques to derive
reasonably large groups of inter-related genes. The evaluation of a large
set of patterns generated by this technique at different parameter values
also produces similar positive results. For instance, among a set of 26093
patterns derived using certain thresholds, 8347 (31.98%) patterns were
found to be significantly enriched by at least one functional class in the
set considered, after Bonferroni correction. Also, the 500 largest patterns,
which are usually of most interest to practitioners, are all found to be
enriched by at least one of these classes with a p-value smaller than 10
-10
.
More detailed results can be found in [6].
In summary, these results illustrate that association analysis is a useful
technique for deriving functional modules and other types of gene groups
from large microarray gene expression datasets.
4. REFERENCES
1
.
D. J. Duggan et al. Expression profiling using cDNA microarrays. Nature Genetics, 21(1 Suppl):1014, 1999.
2. M. B. Eisen et al. Cluster analysis and display of genome-wide expression patterns. Proc Natl Acad Sci, 95(25):14863-14868, 1998.
3. P.-N. Tan, M. Steinbach, and V. Kumar. Introduction to Data Mining. Pearson Addison-Wesley, 2006.
4. C. Becquet et al. Strong-association-rule mining for large-scale gene-expression data analysis: a case study on human SAGE data.
Genome Biology, 3, 2002.
5. T. McIntosh and S. Chawla. High confidence rule mining for microarray analysis. IEEE/ACM TCBB, 4(4):611623, 2007.
6. G. Pandey et al. Association Analysis for Real-valued Data: Definitions and Application to Microarray Data, TR 08-007,
Department of Computer Science and Engineering, University of Minnesota, Twin Cities, submitted to KDD 2008.
7. T. R. Hughes et al. Functional discovery via a compendium of expression profiles. Cell, 102(1):109126, 2000.
8. C. L. Myers et al. Finding function: evaluation methods for functional genomic data. BMC Genomics, 7:187, 2006.
9. E. I. Boyle et al. Go::termfinder--open source software foraccessing gene ontology information and finding significantly enriched
gene ontology terms associated with a list of genes. Bioinformatics, 20(18):37103715, 2004.
10. R. Agrawal and R. Srikant. Fast algorithms for mining association rules. In Proc. VLDB, pages 487499, 1994.
Figure 1: Enrichment of one of the
continuous patterns in the GO biological
process ontology. Image obtained from
GO:TermFinder [9]. Best seen in color.