Vol.2, No.6, 390-399 (2009)
SciRes Copyright © 2009 Openly accessible at http://www.scirp.org/journal/JBISE/
Classification with binary gene expressions
Salih Tuna, Mahesan Niranjan1
1School of Electronics and Computer Science, University of Southampton, Southampton, UK.
Email: mn@ecs.soton.ac.uk
Received 30 March 2008; revised 25 May 2009; accepted 3 June 2009.
Microarray gene expression measurements are
reported, used and archived usually to high
numerical precision. However, properties of
mRNA molecules, such as their low stability and
availability in small copy numbers, and the fact
that measurements correspond to a population
of cells, rather than a single cell, makes high
precision meaningless. Recent work shows that
reducing measurement precision leads to very
little loss of information, right down to binary
levels. In this paper we show how properties of
binary spaces can be useful in making infer-
ences from microarray data. In particular, we
use the Tanimoto similarity metric for binary
vectors, which has been used effectively in the
Chemoinformatics literature for retrieving che-
mical compounds with certain functional prop-
erties. This measure, when incorporated in a
kernel framework, helps recover any informa-
tion lost by quantization. By implementing a
spectral clustering framework, we further show
that a second reason for high performance from
the Tanimoto metric can be traced back to a
hitherto unnoticed systematic variability in ar-
ray data: Probe level uncertainties are system-
atically lower for arrays with large numbers of
expressed genes. While we offer no molecular
level explanation for this systematic variability,
that it could be exploited in a suitable similarity
metric is a useful observation in itself. We fur-
ther show preliminary results that working with
binary data considerably reduces variability in
the results across choice of algorithms in the
pre-processing stage s of microarray analysis.
Keywords: Microarray Gene Expression; Binary
Gene Expressions; High N umerica l Prec ision ; mRN A
It is anecdotally known and has been formally estab-
lished recently that gene expression measurements ar-
chived in microarray repositories are reported to a far
higher numerical precision than is supported by the un-
derlying biology of the measurement environment. Here,
precision refers to the difference between representing
the mRNA abundance, or relative abundance, of a gene
to several decimal places (e.g. 2.4601) and retaining
only the binary information as to whether the gene is
expressed or not. Shmulevich and Zhang [1] recommend
that gene expressions should be quantized to binary pre-
cision and Hamming distance between signatures used
as distance metric in solving class prediction problems.
Their starting point in defining binary expressions is a
“notion of similarity used by biologists when comparing
gene expressions from different samples... counting the
number of genes that show significant differential ex-
pression”. From this premise, th ey give an algorithm for
binarizing gene expressions and show that a multi di-
mensional scaling (MDS) projection of the data sepa-
rates different types of tumors. More recently, Zilliox
and Irizarry [2] introduce the concept of gene expression
“barcodes”, which are essentially binary representations
of transcriptomes, and present impressive results on pre-
dicting tissue types. These authors take a very different
approach in that they scan through a very large number
of archived datasets of a particular array type to con-
struct barcodes. Genes that are frequently expressed
across the whole ensemble are set to be ON and the oth-
ers set OFF. In our own recent work [3], we show ed that
progressive quantization of gene expression measure-
ments, right down to binary levels, loses very little in-
formation as far as the quality of inference is con cerned.
We were able to demonstrate this on a range of different
inference problems including classification, cluster
analysis, determination of genes that are periodically
expressed and the analysis of developmental time course
Why would we be interested in low precision, or bi-
nary, representations? The initial motivation comes from
the underlying biology. mRNA is only available in very
S. T una et al. / J. Biomedical Science and Engineering 2 (2009) 390- 399
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small quantities in cells and are extracted fro m a popula-
tion of cells rather than from a single cell. Further, the
process of microarray hybridization itself is a stochastic
one, the effect of which is pronounced when small
numbers of molecules are involved. All these reasons put
together make one sceptical about high precision repre-
sentations of the transcriptome, i.e. the signal available
may only be reliable to low precision. Critical appraisals
of microarray technology, while recognising good re-
producibility of technical replicates, often identifies
large variations with respect to biological replicates. One
such survey by Draghici et al. [4] concludes:
“...the existence and direction of gene expression
changes can be reliably detected for the majority of
genes. However, accurate measurements of abso-
lute expression levels and the reliable detection of
low abundance genes are currently beyond the
reach of microarray technology.”
Artificially inflated precision can potentially hurt. A
plethora of sophisticated inference methods (e.g. Bayes-
ian inference) have been applied to microarray data. Al-
gorithmic complexity of such models is generally de-
rived from how well noise is captured. High precision
gives the illusion of complex noise structures leading to
the use of such algorithms. If the data were far simpler,
one would impose a far higher sense of parsimony in
model selection. Simple classification rules offering
good performance (e.g. the top scoring pairs of genes
approach of Geman et al. [5]) on some problems also
bears testimony to this point. Motivated by the above,
we ask the following research question: If transcriptome
can be represented at low precision, binary for instance,
can we take advantage of properties of high dimensional
binary spaces to achieve increased classification per-
formance? We show that this is indeed the case, by use
of a particular similarity metric between high dimen-
sional binary vectors, the so called Tanimoto metric.
Following experiences seen in the chemoinformatics
literature, we embed this similarity metric in a kernel
discriminant framework (support vector machines-SVM)
and show that very high classification accuracies are
obtainable with binary representation of expression pro-
files. We offer explanations for why such increased per-
formances can be achieved, and attribute this to two
reasons: a) the training of class boundaries that happen
in SVMs, and b) a hitherto unnoticed probe level uncer-
tainty in microarray data.
Finally, the analysis of microarray data goes through a
number of stages of processing steps: background inten-
sity correction, within array normalization, between ar-
ray normalization and algorithms for detecting differen-
tially expressed genes. A user has a choice of several
algorithms at each of these steps and a very large choice
if we consider combinations of available algorithms. A
particular appeal of working with binarized representa-
tions, as shown by preliminary results in this paper, is
that the algorithmic variability in inference is drastically
reduced without compromising the quality o f inference.
2.1. Classification
Table 1 compares classification performances of several
classifiers on six microarray class prediction datasets. In
all cases the accuracies are averaged over 25 random
partitions of the data into training and test sets, and
standard deviations in performance across these parti-
tions is also given. In all the different problems we
checked to ensure that our implementation of the linear
SVM classifier acting on raw data performed as well as
the results quoted in the original publication or some
other publication that used the dataset, thus confirming
the correctness of our implementation. Note that in all
the tasks considered, comparing data represented at raw
and binary precisions and classifying with linear SVMs,
we note that binarising the data has not lost much dis-
crimination. In fact in some of the tasks binarization has
actually improved performance. Secondly, in half the
tasks considered, the use of Tanimoto kernel SVM im-
proves the results of binarized classification. Where
there is not an improvement, the method is at least as
good as a linear SVM on binarized data.
Our simulations also show that in all the tasks consid-
ered the distance to template methods perform signifi-
cantly worse than the corresponding kernel methods.
This is true both for templates set as centroids and for
centroids positioned optimally by genetic search. In two
of the four datasets considered, optimization of tem-
plates quickly led to overtraining, resulting in classifiers
whose performance on test data (entries in Table 1) were
worse than their initial values (which were the perform-
ances with templates at centroids). In the genetic opti-
mization, we also found that the local search by mutation
was the dominant contributor, showing that the solution
to the optimized distance based classifier was in the vi-
cinity of the centroids. Cross-over operations nearly al-
ways produced far worse solutions and were quickly
abandoned. To explore this further, in addition to the
centroids, we included noisy templates into the search
algorithm, but found no improvement.
2.2. Clustering
Figure 1 shows the eigenvector obtained in spectral
clustering for the widely studied ALL/AML problem
[11], computed in three different ways: raw and bi-
narized data with negative exponential of Euclidean dis-
tance as similarity, and binarized data with Tanimoto
similarity. The scatter clearly shows cluster separation
along the components of the eigenvector. This is also
S. T una et al. / J. Biomedical Science and Engineering 2 (2009) 390- 399
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reflected in the Fisher scores between clusters and the
corresponding classification errors which are shown in
Ta b l e 2, (columns 4 and 5), where except in one of the
datasets, there is improvement in the cluster tightness
when Tanimoto similarity is app lied. Similarly, in all but
one of the tasks, the resulting classification error rates
are also lower for the Tanimoto metric.
The final column in Table 2 shows classification error
rates arising from spectral clustering when the microar-
ray profile consists of a filtered subset of genes. In each
task we ranked the genes according to their Fisher scores
of discriminating power taken one at a time, precisely
the same way as done by Golub et al. [11], and report
best performing subsets. The difference between the
different distance metrics with subsets of genes is shown
in Figure 2 for four of the tasks. We see that the use of
Tanimoto similarity leads to better separated clusters in
general. Further the better separated clusters also lead to
better discrimination. We emphasize that the clustering
here is done without the use of class labels, and it is to
verify how good the clusters are that we use this infor-
mation. Thus as expected note the accuracies much
lower than when the problem is formulated as a classifi-
cation problem in the first place.
Table 1. Comparison of classification with different types of kernels for SVM.
Dataset Data type Method Accuracy
Raw-Binary Linear- S VM 0.83 ± 0.10
Binary Linear- SVM 0.86 ± 0.08
Binary Tanimoto-SVM 0.87 ± 0.08
Binary Distance-to-class mean 0.79 ± 0.08
West et al. [6]
Binary Distance-to-optimized template 0.77 ± 0.11
Raw-Binary Linear- S VM 0.63 ± 0.12
Binary Linear- SVM 0.67 ± 0.08
Binary Tanimoto-SVM 0.67 ± 0.10
Binary Distance-to-class mean 0.60 ± 0.11
Huang et al. [7]
Binary Distance-to-optimized template 0.66 ± 0.11
Raw-Binary Linear- S VM 0.99 ± 0.01
Binary Linear- SVM 0.96 ± 0.03
Binary Tanimoto-SVM 0.99 ± 0.01
Binary Distance-to-class mean 0.88 ± 0.07
Gordon et al. [8]
Binary Distance-to-optim ize d t emplate 0 .90 ± 0.07
Raw-Binary Linear- S VM 0.99 ± 0.01
Binary Linear- SVM 0.98 ± 0.01
Binary Tanimoto-SVM 0.98 ± 0.01
Binary Distance-to-class mean 0.67 ± 0.02
Brown et al. [9]
Binary Distance-to-optim ize d t emplate 0 .75 ± 0.03
Raw-Binary Linear- SVM 0.78 ± 0.11
Binary Linear- SVM 0.82 ± 0.07
Binary Tanimoto-SVM 0.84 ± 0.03
Binary Distance-to-class mean 0.80 ± 0.07
Alon et al. [10]
Binary Distance-to-optim ize d t emplate 0 .72 ± 0.10
Raw-Binary Linear- S VM 0.96 ± 0.05
Binary Linear- SVM 0.95 ± 0.03
Binary Tanimoto-SVM 0.96 ± 0.04
Binary Distance-to-class mean 0.94 ± 0.02
Golub et al [11].
Binary Distance-to-optim ize d t emplate 0 .92 ± 0.09
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(a) (b)
Figure 1. Figures showing spectral clustering results for different type of metr ics. In (a) spe ctral clustering is applied
to continuous data by using Euclidean distance, in (b) binary data is used with Euclidean distance and in (c) binary
data is used with Tanimoto coefficient for spectral clustering. Data from [11].
Table 2. Comparison of spectral clustering results by using Tanimoto and Euclidean distance with Fisher score and error rates.
Dataset Data type Distance metrics Fisher score Error rate Error rate
(best subset of genes)
Raw Euclidean 2.47 ± 0.50 0.14 ± 0.08
Binary Euclidean 0.47 ± 0.49 0.33 ± 0.02
Simulated data
Binary Tanimoto 0.66 ± 0.21 0.21 ± 0.10
Raw Euclidean 0.98 ± 0.41 0.32 ± 0.23 0.05 ± 0.11
Binary Euclidean 1.01 ± 0.43 0.10 ± 0.08 0.02 ± 0.04 Golub et al. [11]
Binary Tanimoto 1.49 ± 0.42 0.05 ± 0.05 0.004 ± 0.02
Raw Euclidean 0.35 ± 0.22 0.21 ± 0.05 0.04 ± 0.05
Binary Euclidean 0.37 ± 0.18 0.22 ± 0.05 0.03 ± 0.05 Huang et al. [7]
Binary Tanimoto 0.33 ± 0.17 0.21 ± 0.05 0.02 ± 0.04
Raw Euclidean 0.35 ± 0.04 0.45 ± 0.06 0.45 ± 0.06
Binary Euclidean 0.30 ± 0.18 0.33 ± 0.08 0.21 ± 0.15
West et al. [6]
Binary Tanimoto 0.35 ± 0.24 0.28 ± 0.09 0.11 ± 0.07
Raw Euclidean 0.21 ± 0.07 0.17 ± 0.03 0.16 ± 0.03
Binary Euclidean 0.41 ± 0.19 0.13 ± 0.02 0.09 ± 0.03 Gordon et al. [8]
Binary Tanimoto 0.52 ± 0.19 0.12 ± 0.02 0.08 ± 0.02
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(a) (b)
(c) ) (d)
Figure 2. Comparison of spectral clustering results for four different datasets at various number of genes
selected with Fisher Ratio. (a) is for [11], (b) is for [7], (c) is for [6] and (d) is for [8].
(a) (b)
Figure 3. Reduction in variability of results due to preprocessing choice of algorithms. randomly chosen 38 combi-
nations of preprocessing the CEL files produce large variations in classification results (leftmost columns). Working
with discretized data reduces this variation in the inference. (a) data from [6], and (b) data from GSE2665.
2.3. Reduction in Algorithmic Variability
Figure 3 shows reduction in the variability caused by
choice of preprocessing algorithms. Patterns of gene
expression levels change substantially with choice of
algorithms, and this has a substantial effect on the re-
sulting inference. A recent careful study (P. Boutros,
personal communication1) established that this variabil-
ity is significant. The leftmost columns of Figures 3(a)
and (b) show this as box plots on two datasets. We see
1Also presented at the Microarray Gene Expression Society (MGED)
meeting, Riva del Garda, Italy, September 2008.
S. T una et al. / J. Biomedical Science and Engineering 2 (2009) 390- 399
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standard deviations in classifier performances, with out-
liers removed, of 0.032 and 0.134 re spectively, and th ese
reduce to 0.017 and 0.009 when th e ex pr essio n leve ls ar e
binarized. The use of Tanimoto metric (box plots of the
last columns of Figure 3) improves this even further.
3.1. Approach
Our approach was to show that on a sample of classifi-
cation problems published in literature, classification
accuracies reported by the authors do not significantly
degrade when the gene expression data is quantized to
binary precision (i.e. if the gene is expressed or not).
Having achieved this, we implemented a similarity
measure suitable for high dimensional binary spaces in a
kernel framework to show that any loss of performance
is easily recovered. In a number of cases the approach
we took indeed produced better accuracies than working
with the data at raw precision (see Results).
3.2. Tanimoto Similarity
Tanimoto coefficient (
) [12], between two binary vec-
tors, is defined as follow:
a: the number of expressed points for gene x,
b: the number of expressed points in gene y and
c: the number of common expressed points in two
Tanimoto similarity ranges from 0 (no points in com-
mon) to 1 (exact match) [13] and is the rate of the num-
ber of common bits on to the total number of bits on two
vectors. It focuses on the number of common bits that
are on. The denominator of Tanimoto coefficient can be
considered as a normalization factor which helps to re-
duce the bias of the vector size (i.e with larger vectors
Tanimoto coefficients work better [14,15]. For this rea-
son Tanimoto coefficient is the preferred similarity
measure in chemoinformatics as all the vectors are long
and there are only few bits on.
Tanimoto kernel can be defined as [16]:
Tan 
where , and . It follows
from the work of Trotter [16] that this similarity metric
satisfies Mercer conditions to be useful as a valid kernel:
i.e. kernel computations in the space of the given binary
vectors map onto inner products in a higher dimensional
space so that SVM type optimizations for large margin
class boundaries is possible.
xxa T
Alternate ways of classification of binarized data can
be considered. Motivated by the distance to barcode
classifier built by Zilliox and Irizarry [2] we imple-
mented similar classifiers. An obvious choice in these
circumstances is to set two templates, one to represent
each class, and position them at the centroids of the two
class profiles. This is a distance to mean classifier in
standard statistical pattern recognition terminology. A
particular limitation of this strategy is discussed later.
The barcodes designed by Zilliox and Irizarry [2], how-
ever, are not positioned at the centroids because they are
evaluated by analysing a large number of archived ex-
periments. We also built such discriminant templates, by
doing a stochastic search starting from the centroids as
initial condition. Such an optimization achieves tem-
plates that are better positioned in the input space than
centroids for distance-base d di scri mination.
Clustering is the most popular tool in the analysis of
microarray data. In order to conform whether the use of
Tanimoto distance metric is useful in clustering, we ap-
plied the method of spectral clustering to the classifica-
tion problems considered above. Without knowledge of
the class labels, we clustered each of the datasets into
two clusters using spectral clustering. Subsequently, us-
ing knowledge of the class labels we looked to see how
well separated the clusters formed were, and how accu-
rately the data was allocated to the right clusters. To
measure cluster compactness we used the Fisher ratio as
performance metric:
Fisher Score = 21
21 )(
Checking if the examples were consistently associated
with the right clusters, we computed percentage classifi-
cation errors. The choice of classification problems to
evaluate cluster compactness offers a far better setting
than clustering genes into functions. This is because
cluster analysis, when the data has large numbers of
clusters in them, is notoriou sly unstable. With data taken
from classification problems, we could expect well de-
fined cluster formations (e.g. cancer versus non-cancer),
in which we can compare the role of different distance
3.3. Datasets
We give a short description of the datasets used in our
Yeast dataset compiled and first used in Brown et
al. [9] for predicting yeast gene functions. cDNA
arrays, in which the task is to classify 121 ribo-
somal genes from the remaining 2346 using 79
features. The features are hybridization conditions
during cell cycle progression under different syn-
chronization methods.
Widely used Leukemia dataset (Golub et al.,
[11]); there are 5000 genes with 38 samples (27
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ALL, 11 AML), being the test subset of the full
Colon da taset (Alon et al., [10]), 2000 genes with
62 samples (20 normal and 42 tumour samples).
Two Breast cancer datasets, first one from (West
et al., [6]) 7129 genes and 49 samples, (25 ER+
and 24 ER-) and the other Huang et al. [7] 12625
genes with 89 samples (depending on LN status).
Lung cancer dataset, (Gordon et al., [8]), 12533
genes and 181 samples (31 malignant pleural
mesothelioma (MPM) and 150 adenocarcinoma
53 randomly selected datasets from ArrayExpress
(http://www.ebi.ac .uk/ar rayexpress/) and Gene
Expression Omnibus (GEO)
(http://www.ncbi.nlm.nih.gov/geo/) for probe level
uncertainty analysis analysis. Accession numbers
of these datasets are:
GEO: GSE5666, GSE7041, GSE8000, GSE8505,
GSE6487, GSE6850, GSE8238, GSE2665
Array Express: E-GEOD-6783, E-GEOD-6784},
E-MEXP-1403, E-ATMX-30,
E-GEOD-6647, E-GEOD-6620 ,
E-ATMX-13, E-MEXP-1443,
E-GEOD-2450, E-GEOD-2535 ,
E-MEXP-914, E-MEXP-268,
E-GEOD-2848, E-GEOD-2847 ,
E-MEXP-430, E-GEOD-6321,
E-MEXP-70, E-GEOD-1588,
E-MEXP-727, E-TABM-291,
E-GEOD-3076, E-GEOD-1938 ,
E-GEOD-7763, E-GEOD-3854 ,
E-GEOD-1639, E-TABM-169,
E-MAXD-6, E-MEX P-526,
E-GEOD-2343, E-GEOD-3846 ,
E-MEXP-26, E-GEOD-1723,
E-GEOD-1934, E-MAXD-6,
E-MEXP-879, E-GEOD-10262,
E-GEOD-10422, E-MEXP-998,
E-MEXP-580, E-GEOD-10072,
Web Pages:
http://yeast.swmed.edu/cg i-b in/dlo ad. cgi,
Synthetic data was produced following Dettling
[17], using R code made available by the au-
thors. Data is produced to follow the statistics
(mean and correlation structure) of the leukae-
mia data [11]. We generated several realizations
of 200 samples in 250 dimensions. We explored
varying these values over a range, and results
reported in this paper correspond to the above
3.4. Spectral Clustering
Spectral clustering uses eigenvectors of the pairwise
similarity matrix to partition the data. The most widely
used distance metric to calculate the similarity matrix is
the negative exponential of a scaled Euclidean distance.
 2
),( exp
where the scale parameter
is a free tuning parameter.
The steps involved in spectral clustering, in which we
replace the similarity measure by Tanimoto similarity
between binary strings, are summarized as follows:
Pairwise similarity matrix ji
A, between the
genes i and j is calculated by us ing Tanimoto coef-
Following Brewer [18] an exponential is applied:
exp 
Compute the normalized Laplacian matrix.
2/12/1 
Compute the eigenvalue decomposition of L.
iii DyyLD
Select the eigenvector corresponding to the second
smallest eigenvalue.
were tuned by searching over a
range of feasible values: –5.05.0.
Uncertainties in results for cluster analysis were
evaluated by a bootstrap method. For each of the tasks,
100 datasets of the same size as the original data were
created by sampling with replacement before the appli-
cation of the spectral clustering algorithm. Perfor-
mances reported are averages and standard deviations
across these 100 bootstrap samples.
3.5. Optimised Templates
The search to find templates better than class means for
a distance-to-template classifier was implemented as a
stochastic local search by means of a genetic algorithm.
Templates were initialized to class means. At every step
in an iterative search, we randomly changed 20% of the
elements in the two templates, to derive mutated bar-
codes in their vicinity. Throughout the search, we re-
tained ten best template pairs at any iteration. Large
search steps were implemented by crossover operation
between pairs of templates whereby half the bits in the
patterns were swapped between pairs, a standard opera-
tion in genetic algorithms. We evaluated the accuracy of
the resulting classifier and there was an improvement we
retained the mutated templates, and discarded them if
was no improvement.
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that classification by computing distances to a template
is optimal only in the case that the distributions of each
class is Gaussian, isotropic (i.e. variances of each feature
is the same) and these variance s are the same for both [22 ].
3.6. Algorithmic V ariability
We used the EXPRESSO set of algorithms in package
Affy in Bioconductor. For both datasets West et al. [6]
and GSE2665, we worked from the CEL files and app-
lied a total of 38 different preprocessing combinations
from a total of 315 possibilities, randomly chosen.
When any of these assumptions is violated, a distance to
template classifier is no longer optimal. Even under the
mild relaxations of the assumption, that of Gaussian den-
sities with identical but nonisotropic covariance matric-
3.7. Other Details es, the optimal classifier requires computation of second
order statistics in the form of the Mahalanobis distance
to class means. In gene expression data isotropic v ari a tio n
cannot be assumed. Under regulation by combinatorial
transcription factor activity where each transcription fac-
To analyse probe level uncertainties (Milo et al. [19]) we
used the PUMA package (Propagating Uncertainty in
Microarray Analysis), downloaded from the site
(www.bioinf.manch ester.ac.uk/resources/pu ma/).
For quantization of microarray data, we used the method
developed by Zhou et al. [20], which models gene ex- tor may control several genes, correlated expression of
groups of genes should be expected. Indeed, the wide
use of cluster analysis of microarray data is based on the
assumption that correlated expression profiles might su-
pressions as mixture Gaussian densities. For quantiza-
tion to binary levels, two Gaussians are used, resulting in
two means and standard deviations:1
and 2
. ggest co-regulation. Therefore, as uncorrelated features
cannot be assumed, optimal classification is unlikely to
be achieved by distance to template decision rules.
From these a threshold
, is computed as
)( 2121
 . SVM implementations were done Does the same difficulty arise in the barcode method
proposed by Zilliox and Irizarry (2007)? To verify this
we took three datasets, one of which was not included in
their analysis. Prediction accuracies for these three, co m-
in the MATLAB SVM package described in Gunn [21]
4. CONCLUSIONS paring the barcode method to Tanimoto-SVM, are shown
in Table 3. We note that training and testing on the same
database, as we have done with Tanimoto-SVM, achiev-
The results suggest that a binary representation for tran-
scriptomic data is indeed suitable and good classification
accuracies can be obtained in this space using suitable es consistently better prediction accuracies than the bar-
code method. But in fairness to the barcode method we
remark that their intention is to make predictions on a
new dataset based on accumulated historic knowledge,
rather than repeat the training/testing process all over
again. On this point, while there is impressive perform-
similarity metrics cast in a kernel framework. There are
two reasons for the superior performance of Tanimoto-
SVM based approach over the distance to template appr-
oach inspired by the barcode approach.
4.1. Distance to Template Classifier
ance reported on the datasets Zilliox and Irizarry (2007).
worked on, the method can fail badly too, as in the case
of the lung cancer prediction task E-GEOD-10072
shown in Table 3.
Why did the distance to template method not perform
well consistently in classification problems? We suggest
this result is largely to be expected. With continuous data,
it is a well known result of statistical pattern recognition
Table 3. Comparison of Tanimoto-SVM with [2]’s barcode.
Dataset Data type Method Accuracy
E-GEOD-10072 Binary Barcode 0.50
Lung Binary Tanimoto-SVM 0.89 ± 0.03
Lung tumor vs. normal Binary Tanimoto-SVM 0.99 ± 0.03
GSE2665 Binary Barcode 0.95
Lymph node/tonsil Binary Tanimoto-SVM 0.99 ± 0.02
lymph node vs. tonsil Binary Tanimoto-SVM 1.0 ± 0.0
GSE2603 Binary Barcode 0.90
Breast Tumor Binary Tanimoto-SVM 0.99 ± 0.01
Breast Tumor vs. normal Binary Tanimoto-SVM 0.99 ± 0.01
Openly accessible at
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(a) (b)
Figure 4. A systematic variation in probe level uncertainty of Affymetrix microarray data. (a) On 53 randomly
chosen arrays we plot the average uncertainty of determining expression levels against the number of genes de-
tected as present. Only liner regression lines are shown for clarity. (b) Scatter plots of uncertainties against number
of expressed genes, and the linear regression lines, for the three datasets analysed in this paper.
4.2. Probe Level Uncertainty
The Tanimoto similarity metric attaches higher scores to
profiles with large numbers of expressed genes. For
example if we consider two pairs of vectors with
[1 0 0 0 0 0 0 0] [1 1 0 0 0 0 0 0],
[1 1 0 0 0 0 0 0] [1 1 1 0 0 0 0 0]
In both cases Hamming distance, thus Euclidean dis-
tance, is one. The Tanimoto similarities between these
pairs, however, are different: 0.5 for the first pair and
0.66 for the seco nd. We suggest that a reason why such a
weighting on the similarity scores translates to improve
clustering and class prediction performance comes from
the uncertainties associated with microarray measure-
ments. We found a systematic variation in uncertainties
in expression levels as function of the numbers of ex-
pressed genes in an array. To illustrate this we used a
probabilistic model of encapsulating probe level uncer-
tainties introduced in Milo et al. (2003) [19], and plotted
the average uncertainty in expressed genes as a function
of the number of genes marked as expressed under our
quantization scheme for several arbitrarily chosen data-
Figure 4 shows the variation in uncertainty with
numbers of expressed genes, for three of the datasets on
which we report classification results, and for 50 arbi-
trarily taken datasets from archives. We see that there is
a systematic reduction in probe level uncertainty as the
number of expressed genes in an array gets larger2. We
offer no molecular level explanation for this, but the
effect is systematic and its impact on the Tanimoto-SVM
is clear. Arrays with larger numbers of expressed genes
are being measured with higher levels of confidence.
Hence if we were to increase the weighting given to
similarities between such profiles we would expect in-
creased performance. Such probe level uncertainty has
been of interest to other researchers, too. Rattray et al.
[23] and Sanguinetti et al. [24] show how cluster analy-
sis and visualization in a subspace by principal compo-
nent projections can be carried out incorporating probe
level uncertainty. In general these are errors-in-variables
type models. We believe accounting for probe level (and
other low level) uncertainties in microarray analysis is
an important topic, and the systematic variability we
have noted here may well be an aspect that other re-
searchers can exploit in microarray inference.
[1] I. Shmulevich and W. Zhang, (2002) Binary analysis and
optimization-based normalization of gene expression
data, Bioinformatics, 18(4), 555–565.
[2] M. J. Zilliox and R. A. Irizarry, (2007) A gene expre-
ssion bar code for microarray data, Nature Methods,
4(11), 911–913.
[3] S. Tuna and M. Niranjan, (2009) Inference from low
precision transcriptome data representation, Journal of
Signal Processing Systems, [Online, 22 April 2009], doi:
[4] S. Draghici, P. Khatri, A. C. Eklund, and Z. Szallasi,
(2006) Reliability and reproducibility issues in DNA mi-
croarray measurements, Trends in Genetics, 22(2), 101–
[5] D. Geman, C. d’Avignon, D. Q. Naiman, and R. L.
Winslow, (2004) Classifying gene expression profiles
from pairwise mRNA comparisons, Statistical Applica-
tions in Genetics and Molecular Biology, 3.
[6] M. West, C. Blanchette, H. Dressman, E. Huang, S.
Ishida, R. Spang, H. Zuza n, J. A. Olson, J. R. Marks, a nd
2We stress that this variation is not a consequence of amplifying noise
in the data of normalised poor quality arrays; i.e. for an array
scanned at low intensity, normalization amplifies noise; the effect o
such noise would be to increase the average uncertainty when more
and more genes are taken as expressed. This is precisely the opposite
of what we see in Figure 4.
S. T una et al. / J. Biomedical Science and Engineering 2 (2009) 390- 399
SciRes Copyright © 2009 Openly accessible at http://www.scirp.org/journal/JBISE/
J. R. Nevins, (2001) Predicting the clinical status of hu-
man breast cancer by using gene expression profiles
Proceedings of National Academy of Sciences, 98(20),
[7] E. Huang, S. H. Cheng, H. Dressman, J. Pittman, M.
Tsou, C. Horng, A. Bild, E. S. Iversen, M. Liao, C. Chen,
M. West, J. R. Nevins, and A. T. Huang, (2003) Gene ex-
pression predictors of breast cancer outcomes Lancet,
361, 1590–1596.
[8] G. J. Gordon, R. V. Jensen, L. Hsiao, S. R. Gullans, J. E.
Blumenstock, S. Ramaswamy, W. G. Richards, D. J.
Sugarbaker, and R. Bueno, (2002) Translation of micro-
array data into clinically relevant cancer diagnostic tests
using gene expression ratios in lung cancer and meso-
thelioma, Cancer Research, 62(17), 4963–4967.
[9] M. P. S. Brown, W. N. Grundy, D. Lin, N. Cristianini, C.
W. Sugnet, T. S. Furey, M. Ares, and D. Haussler, (2000)
Knowledge-based analysis of microarray gene expression
data by using support vector machines, Proceedings of
National Academy of Sciences, 97(1), 262–267.
[10] U. Alon, N. Barkai, D. A. Notterman, K. Gish, S. Ybarra,
D. Mack, and A. J. Levine, (1999) Broad patterns of gene
expression revealed by clustering analysis of tumor and
normal colon tissues probed by oligonucleotide arrays,
Proceedings of National Academy of Sciences, 96(12),
[11] T. R. Golub, D. K. Slonim, P. Tamayo, C. Huard, M.
Gaasenbeek, J. P. Mesirov, H. Coller, M. L. Loh, J. R.
Downing, M. A. Caligiuri, C. D. Bloomfield, and E. S.
Lander, (1999) Molecular classification of cancer: Class
discovery and class prediction by gene expression moni-
toring, Science, 286(5439), 531–537.
[12] T. T. Tanimoto, (1958) “An elementary mathematical
theory of classification and prediction,” IBM Internal
[13] P. Willett, (2006) Similarity-based virtual screening using
2d fingerprints, Drug Discovery Today, 11(23/24), 1046–
[14] P. Willett, J. M. Barnard, and G. M. Downs, (1998)
Chemical similarity searching, Journal of Chemical In-
formation and Computer Sciences, 38(6), 983–996.
[15] J. D. Holliday, N. Salim, M. Whittle, and P. Willett,
(2003) Analysis and display of the size dependence of
chemical similarity coefficients, Journal of Chemical In-
formation and Computer Sciences, 43(3), 819–828.
[16] M. Trotter, (2006) Support vector machines for drug
discovery. PhD thesis, University College London, UK.
[17] M. Dettling, (2004) BagBoosting for tumor classification
with gene expression data, Bioinformatics, 20(18), 3583–
[18] M. Brewer, (2007) Development of a spectral clustering
method for the analysis of molecular data sets, Journal of
Chemical Information and Modeling, 47(5), 1727–1733.
[19] M. Milo, A. Fazeli, M. Niranjan, and N. D. Lawrence,
(2003) A probabilistic model for the extraction of expres-
sion levels from oligonucleotide arrays, Biochemical So-
ciety Transactions, 31(6), 1510–1512.
[20] X. Zhou, X. Wang, and E. R. Dougherty, (2003) Binari-
zation of microarray data on the basis of a mixture model,
Molecular Cancer the Rapeutics, 2(7), 679–684.
[21] S. Gunn, (1998) Support vector machines for classifica-
tion and regression, Tech. Rep., University of South-
[22] R. O. Duda, P. E. Hart, and D. G. Stork, (2001) Pattern
Classification, John Wiley & Sons, USA, ISBN 0-41-
[23] M. Rattray, X. Liu, G. Sanguinetti, M. Milo, and N.
Lawrence, (2006) Propagating uncertainty in microarray
data analysis, Briefings in Bioinformatics, 7(1), 37–47.
[24] G. Sanguinetti, M. Milo, M. Rattray, and N. D. Lawrence,
(2005) Accounting for probe-level noise in principal
component analysis of microarray data, Bioinformatics,
21(19), 3748–3754.