J. Biomedical Science and Engineering, 2013, 6, 165-174 JBiSE
http://dx.doi.org/10.4236/jbise.2013.62020 Published Online February 2013 (http://www.scirp.org/journal/jbise/)
Novel algorithms for accurate DNA base-calling
Omniyah G. Mohammed1, Khaled T. Assaleh1, Ghaleb A. Husseini2, Amin F. Majdalawieh3,
Scott R. Woodward4
1Department of Electrical Engineering, American University of Sharjah, Sharjah, UAE
2Department of Chemical Engineering, American University of Sharjah, Sharjah, UAE
3Department of Biology, Chemistry and Environmental Sciences, American University of Sharjah, Sharjah, UAE
4Sorenson Molecular Genealogy Foundation, Salt Lake City, USA
Email: kassaleh@aus.edu
Received 5 October 2012; revised 6 November 2012; accepted 17 November 2012
The ability to decipher the genetic code of different
species would lead to significant future scientific achi-
evements in important areas, including medicine and
agriculture. The importance of DNA sequencing ne-
cessitated a need for efficient automation of identi-
fication of base sequences from traces generated by
existing sequencing machines, a process referred to as
DNA base-calling. In this pap er, a pattern recognition
technique was adopted to minimize the inaccuracy in
DNA base-calling. Two new frameworks using Artifi-
cial Neural Networks and Polynomial Classifiers are
proposed to model electropherogram traces belonging
to Homo sapiens, Saccharomyces mikatae and Dro-
sophila melanogaster. De-correlation, de-convolution
and normalization were implemented as part of the
pre-processing stage employed to minimize data im-
perfections attributed to the nature of the chemical
reactions involved in DNA sequencing. Discriminative
features that characterize each chromatogram trace
were subsequently extracted and subjected to the
chosen classifiers to categorize the events to their re-
spective base classes. The models are trained such
that they are not restricted to a specific species or to a
specific chemical procedure of sequencing. The base-
calling accuracy achieved is compared with the exist-
ing standards, PHRED (Phil’s Read Editor) and ABI
(Applied Biosystems, version 2.1.1) KB base-callers in
terms of deletion, insertion and substitution errors.
Experimental evidence indicates that the proposed
models achieve a higher base-calling accuracy when
compared to PHRED and a comparable performance
when compared to ABI. The results obtained demon-
strate the potential of the proposed models for effi-
cient and accurate DNA base-calling.
Keywords: Artificial Neural Network (ANN);
Base-Calling; Electropherogram; Polynomial Classifier
(PC); Sequencing
Until the last decade, the complete human genome se-
quence was not identified. However, a massive research
effort resulted in deciphering nearly three billion con-
stituents of the human genome. The human genome re-
fers to the heredity information encoded in the DNA of
Homo sapiens stored in 23 pairs of chromosomes located
in the cell nucleus. A DNA, or deoxyribonucleic acid,
strand consists of four nucleotide bases: Adenine (A),
Cytosine (C), Thymine (T) and Guanine (G). A DNA
molecule has a double helical structure consisting of two
intertwined chains made up of complementary nucleotide
strands in which A bonds with T and C pairs up with G
[1]. The process of determining the ordered sequence of
these nucleotide bases in a DNA molecule is referred to
as DNA sequencing. Information derived from the ge-
nomic sequence is likely to contribute enormously to
medical advances such as more accurate diagnosis of
genetic diseases, improved drug design to target specific
genes causing certain diseases and gene therapy by re-
placement of defective genes. The ability to decode the
genetic material is also very important to researchers
trying to improve the resistance of crops to parasites,
detect bacteria that may pollute air or water, determine
pedigree for seed or livestock breeds, explore species
origin and ancestry, and determine the cause of migration
of different populations and various other evolutionary
studies. DNA sequencing also has potential benefits in
applied fields such as DNA forensics in which crime
suspects can be identified by matching their DNA with
evidence left at crime scenes, establishing paternity and
identifying crime and catastrophe victims.
One of the first DNA sequencing techniques was de-
veloped in 1976 by Maxam and Gilbert based on chemi-
cal modification of the DNA molecule which breaks a
terminally labeled DNA template partially at each base.
The reaction of dimethyl sulphate, piperidine, formic
acid, hydrazine and sodium chloride, individually or in
combinations, causes the cleavage of the four bases. The
O. G. Mohammed et al. / J. Biomedical Science and Engineering 6 (2013) 165-174
lengths of the labeled fragments then identify the posi-
tions of each base. This method allowed the sequencing
of at least 100 bases [2].
Chain Termination Method, also referred to as the
Sanger Method, is currently the most widely used tech-
nique for DNA sequencing [3]. The Sanger Method in-
volves the decomposition of a DNA strand into smaller
fragments using restriction enzymes followed by frag-
ment amplification using the Polymerase Chain Reaction
(PCR) technique generating many copies of the DNA
template. PCR involves denaturation; breaking of the
hydrogen bonds between the complementary DNA strands,
annealing; attachment of the DNA strands with primers,
and primer extension; binding of the polymerase with the
primers resulting in the elongation of the DNA template.
The DNA template to be sequenced is then divided into
four sequencing reactions, each containing a primer to
act as a starting point for DNA replication, deoxynucleo-
tides (dATP, dGTP, dCTP and dTTP) and a DNA poly-
merase. To each sequencing reaction, only one of the
four dideoxynucleotides (ddATP, ddGTP, ddCTP and
ddTTP) is added to serve as a radioactive fluorescent
chain terminator resulting in various DNA fragments of
different lengths. Electrophoresis is then performed on
the synthesized DNA fragments to separate the DNA
fragments based on their length resulting in an electro-
pherogram trace [3]. Figure 1 shows a small portion of a
human DNA electropherogram.
The electropherogram produced as a result of the
Sanger Method undergoes base-calling, a process by
which the ordered sequence of nucleotides in a DNA
strand is identified. DNA base-calling involves translat-
ing Figure 1 to a string of A, T, C and G sequence—e.g.
Several systems were designed in the past couple of
decades to facilitate and automate DNA base-calling.
Giddings et al. [4] proposed an object oriented modular
algorithm for the determination of a DNA sequence. The
system undergoes noise filtering, manual mobility shift
correction, normalization and baseline correction as pre-
Figure 1. Segment of an electropherogram trace.
processing. Identification of peaks in the chromatogram
trace is then performed. A confidence value is assigned
to each peak based on the following features: height,
spacing and width. Post processing is then carried out by
inserting bases in appropriate locations where no bases
were called.
In 1996, a graph theoretic approach was introduced by
Berno for base-calling [5]. The approach involved low
pass-filtering of the data to reduce the noise, followed by
channel separation to eliminate cross-talk between the
four channels. Mobility shift correction, baseline removal
and de-convolution were also carried out prior to assign-
ing a scoring function to assess the confidence of each
peak occurrence. Berno’s method proved to generate less
insertion and mismatch errors compared to the ABI base-
caller. However, it produced double the deletion errors
when compared to ABI.
In 2000, Brady et al. [6] proposed an automated base-
calling algorithm known as the Maximum Likelihood
Base-Caller. Pre-processing involved a soft-caller and a
hard-caller. The soft caller was used to compute a set of
tentative call amplitudes and their locations for each base
producing a set of soft calls. The hard caller combines
the tentative calls for all four bases and produces the
final sequence estimate using a computationally expen-
sive dynamic programming approach. On testing the
method, the base-caller resulted in 40% fewer errors than
ABI and its performance was comparable to that of
PHRED base-caller.
In 2006, Eltoukhy et al. [7] proposed to perform DNA
base-calling by using Sequencing-by-Synthesis methods
such as pyrosequencing. Given a test sequence and the
expected noisy output DNA sequence, system parameters
were proposed to be determined by finding the DNA
sequence that minimizes the probability of decoding er-
rors. The pre-processing stage consisted of baseline cor-
rection and normalization. Iterative partial maximum like-
lihood sequence detection was applied to five pyrose-
quencing datasets. Of the two longest datasets, a total of
170 out of 208 bases, and 205 out of 224 bases were ob-
served to be correctly decoded while the other shorter
datasets resulted in no errors in base-calling.
Another approach to perform DNA base-calling was
proposed by Thornley et al. [8] using Neuro-Fuzzy clas-
sifiers. A Self Adaptive Neuro-Fuzzy Inference System
(SANFIS) classifier was chosen as a Neuro-Fuzzy net-
work due to its immunity to the problem of dimensional-
ity. Using four SANFIS classifiers, bases were attempted
to be recognized. In case of failure to call a base, a Neu-
ral Network was used as a classifier. On testing the
model, an average accuracy rate of approximately 69%
was obtained.
Heuristic base-callers [4,5] are not built on a strong
theoretical basis. They depend on a large number of pa-
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O. G. Mohammed et al. / J. Biomedical Science and Engineering 6 (2013) 165-174
Copyright © 2013 SciRes.
rameters that needs to be optimized to a specific type of
chemistry or to a certain type of sequencing technology.
Statistical base-callers [6] are either poorly tested or slow,
due to the high computational complexity of the imple-
mented algorithms. In this paper, a well-established pat-
tern recognition framework is used to build our base-
caller. Artificial Neural Networks (ANN) and Polynomial
Classifiers (PC) are proposed as base-calling classifiers
such that the base-caller designed is not restricted to a
specific chemistry or sequencing machine. Success achie-
ved in our approach indicates the potential of our models.
The rest of the paper is organized as follows. In section II,
we briefly describe the method adopted for data acquisi-
tion, pre-processing and feature extraction. In section III,
we describe the proposed system models: Artificial Neu-
ral Network (ANN) and Polynomial Classifier (PC), fol-
lowed by a brief description of the testing results ob-
tained using the trained models in Section 4. Finally,
Section 5 summarizes our conclusions.
The approach adopted in this paper to solve the problem
of base-calling is based on designing a pattern recogni-
tion classifier. The data to be classified are acquired from
sequencing machines; hence a pre-processing stage is
needed to achieve noise removal prior to feature extrac-
tion. The success in the implementation of any approach
depends on the effectiveness of the features extracted to
represent a DNA pattern. In this section, the main com-
ponents of any pattern recognition model are: data ac-
quisition (or sensing), pre-processing and feature extrac-
tion, are discussed.
2.1. Data Acquisition/Sensing
One of the main considerations in designing a pattern
recognition classifier is the presence of an adequate size
of data to train and test the model. Performance of the
classifier model increases as the amount of data used
increases. The training data are chosen such that every
possible case scenario is seen and learnt by the model.
However, over-fitting needs to be prevented so that the
generalization of the classifier model to novel data is not
The needed chromatogram traces for training and test-
ing the classifier models were obtained from the Sorenson
Molecular Genealogy Foundation (SMGF) along with
their respective consensus sequences, i.e. DNA sequences
obtained from the sequencing of overlapping fragments
of a gene several times. Moreover, data obtained from the
National Center for Biotechnology Information (NCBI)
trace archive [9] were labeled using commercially avail-
able PHRED base-calling software, CodonCode Aligner.
PHRED is used since it demonstrates high accuracy
when tested over a wide variety of sequencing methods
and has proven to have a higher system performance
compared to other existing base-callers [10]. The NCBI
Basic Local Alignment Search Tool (BLAST) is then run
on each PHRED generated sequence to locate the corre-
sponding consensus sequence for each DNA fragment
being tested. The determined consensus sequences were
used to label the chromatogram traces for accurate train-
ing of the classifier.
To evaluate the performance of the designed classifier
models based on noise contamination, chromatogram
source and read length of the electropherograms, the
traces obtained from the SMGF and from the NCBI trace
archive were categorized into three main data sets as
shown in Table 1.
For the analysis of classifier performance, the DNA
sequence obtained using PHRED and ABI base-callers
on the above three data sets are needed. CodonCode
Aligner and Bioedit were used to obtain the DNA se-
quence called by PHRED and ABI base-callers.
2.2. Pre-Processing
Electropherograms obtained after the implementation of
electrophoresis may be contaminated by noise introduced
at various stages of DNA sequencing. Noise contamina-
tion occurs as a result of the imperfections in the chemis-
try involved and the electronics of electrophoresis. Noise
superimposed on a DNA trace may appear in the form of
overlapping spectra, presence of one or more large peaks
at the beginning of the trace, a drift in the DC value of
the signal, variations in the dynamic range, or low peak
resolution. The data chosen for both training and testing
the designed models are hence subjected to several stages
Table 1. Distribution of data acquired into three data sets.
Data Set No. Data Source No. of Traces Specie Characteristics
1 NCBI 6 Homo sapiens chromosome: 5, 6, 11, 12, 13. Noisy trace, belongs to one species, consists
of 600 - 700 bases.
2 NCBI & SMGF 11 Homo sapiens mitochondrian D-loop,
Saccharomyces mikatae, Drosophila melanogaster.
Noisy trace, belongs to three species,
consists of 675 - 775 bases.
3 SMGF 5 Homo sapiens mitochondrian D-loop. Lower noise level, trace belongs to only one
species, consists of 800 - 900 bases.
O. G. Mohammed et al. / J. Biomedical Science and Engineering 6 (2013) 165-174
of pre-processing to condition the signals without losing
useful information. Therefore, this stage involves three
main processing functions: color correction, peak sharp-
ening, and windowed normalization.
2.2.1. Color Correction
During DNA sequencing, the four-base traces in their
respective channels undergo interference resulting in the
detection of false peaks or peaks with erroneous excita-
tion wavelengths, a process known as cross-talk. This
process causes signal distortion which affects the per-
formance of any base-caller. Hence, de-correlation, also
referred to as color correction, is implemented to reduce
such interference.
Using the noisy raw chromatogram traces (Figure 2
(a)), a 4 × 4 correlation matrix, M, is needed to remove
the cross-talk between the four lanes. Each column of the
cross correlation matrix also referred to as the mixing
matrix, represents the relative signal intensity of each
dye compared to the other three dyes. However, M is not
known initially and needs to be determined. One com-
mon practice uses the manufacturer’s provided mixing
matrix to implement the linear transformation. If the
manufacturer is not known, the components of M can be
determined by identifying a clear known peak in each
lane of the raw data. For each of the identified peaks, the
corresponding relative signal intensities are obtained and
are placed as a single row in the matrix [4,11].
Since the data were acquired mainly from public da-
tabases, the matrix M provided by the respective man-
ufacturers could not be found. Instead, the matrix M was
initially estimated by the identification of four clear peaks
in the chromatogram trace and the relative signal intensi-
ties were obtained. However, it was observed that the
data did not achieve sufficient de-correlation. Hence, M
was re-estimated by taking into consideration the entire
trace, not only four clear peaks. The correlation coeffi-
cients were calculated from a raw input trace, XR, of size
n × 4, whose rows represent the observation samples and
the columns represent the bases (the variables). A linear
transformation, using the matrix M, is then implemented
to obtain the desired color corrected signal, XCC, as fol-
MX. (1)
,,,,RccAcc Ccc Tcc G
Figure 2(b) shows the trace data obtained after the
implementation of the above de-correlation routine. On
comparing Figures 2(a) and (b), it can be clearly ob-
served how the noisy interference represented in the
form of background ripples or overlapping peaks have
Figure 2. Part of an electropherogram trace (a) before and (b)
after color correction.
been either removed or highly reduced as a result of
color correction.
2.2.2. Pe ak Sharpeni ng
In an ideal electropherogram trace, each peak is repre-
sented by a single clear peak. However, this does not
happen in a real trace. During electrophoresis, based on
the length of the DNA fragments, the time needed for a
fragment to reach the photo-detector depends on its
length. Short DNA fragments travel faster than longer
ones and hence, are located in the early segments of a
chromatogram trace. Typically, a certain range of short
fragments arrive at the photo detector at approximately
the same time resulting in sharp and easy-to-distinguish
peaks. But as time passes and the slower “longer” DNA
fragments reach the detector, the resolution of successive
peaks is observed to deteriorate gradually as a result of
electrophoretic diffusion. This occurs due to the variation
in the arrival time of various similar long DNA frag-
ments resulting in wider, flatter and more distorted peaks
[12]. Figure 3 illustrates the initial and final segments of
a DNA trace obtained after the process of electrophoresis.
It is clearly shown in Figure 3(a) that peaks in the first
part of the trace are sharp and of a higher resolution
compared to peaks in the last segments of the chroma-
togram trace (Figure 3(b)) which are of a much lower
resolution and are not easily identifiable.
Low resolution peaks result in inaccurate peak detec-
tion and hence, need to be resolved. A non-linear itera-
tive de-convolution algorithm [13] is employed to re-
cover the high resolution base peaks. Chromatogram
traces obtained from electrophoresis ideally represent a
Copyright © 2013 SciRes. OPEN ACCESS
O. G. Mohammed et al. / J. Biomedical Science and Engineering 6 (2013) 165-174 169
Figure 3. (a) High resolution peaks at the initial parts of a trace;
(b) Low resolution peaks at the last part of a trace.
linear system. A high resolution trace, ,
, is assumed
to be a sparse pulse train corresponding to the occurrence
of each base.
 
ak pnk
where, k represents the position of each base peak, p(n)
is a pulse of a narrow width, and a(k) corresponds to the
pulse amplitude. The observed low resolution trace, ,cc i
can be obtained, mathematically, by the convolution of
the high resolution trace, ,
, with a point spread func-
tion, h. That is,
cc iD i
xh (3)
Thus, to reconstruct the high resolution trace, iterative
de-convolution is adopted. The following outlines the
general procedure to obtain the de-convolved DNA trace:
- Color corrected data, ,cc i
, of size n × 1 is treated as
the observed signal. Note that i represents the four bases:
A, C, T and G.
- ,cci
is initially normalized by its maximum obser-
vation to obtain ,CN i
For , , and
max( )
cc i
CN i
cc i
 (4)
- A normalized point spread Gaussian function, h, is
chosen and de-convoluted data, ,
, of size n × 1 is
used to represent the desired signal.
- The first iteration, y = 0, is initialized as follows to
obtain ,y
CN i
- The initial assumption is convoluted with the point
spread function and ,
is updated as follows,
,,, ,
DiDi DiCNiDi
 
where, F is an operator and λ is the relaxation constant.
- When y is sufficiently large, converges to the
underlying pulse train, 1
lim y
 (8)
By performing iterative de-convolution, peak sharp-
ening and enhancement of signal quality are achieved.
Figure 4(a) shows part of a chromatogram trace prior to
de-convolution, while Figure 4(b) shows the same trace
after de-convolution. By comparing the two figures, the
low resolution peaks sharpened to a higher resolution as
a result of de-convolution can be observed.
2.2.3. N ormaliz ation
Peak amplitudes in a chromatogram trace are observed to
decay with time due to several factors including elec-
tropherogram source imperfections and variations in de-
tector sensitivity. Due to the difference in the dynamic
range of a trace, it is vital to normalize the signals before
base-calling is initiated. Normalization can be achieved
using many different techniques. Giddings et al. [11]
proposed segmentation of the observation points into
consecutive windows. A scaling factor was then deter-
mined such that the amplitudes of the segmented data are
normalized to the [0,1] range. Another method adopted
[12] involves also the segmentation of the observation
points into windows. However, for each window the av-
erage peak height is calculated and the segmented data
are normalized according to it.
Figure 4. Chromatogram trace (a) before and (b) after de-
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O. G. Mohammed et al. / J. Biomedical Science and Engineering 6 (2013) 165-174
In this paper, a simple windowed normalization tech-
nique is adopted to obtain a normalized chromatogram
trace. The pre-processed trace obtained from the previous
stage is initially divided into non-overlapping consecu-
tive windows. Each segment is then normalized by its
maximum amplitude. Figure 5(a) illustrates the trace
signal prior to normalization while Figure 5(b) illus-
trates the same trace after normalization. The decay in
the amplitude is evident in Figure 5(a) while the uni-
formity of the signal height after normalization is seen in
Figure 5(b).
2.3. Feature Extraction
Feature extraction is the main stage which has a direct
effect on the performance of a pattern recognition model.
Feature extraction can be thought of as a form of dimen-
sionality reduction. It is the process in which the pre-
processed input data is transformed into a set of repre-
sentative, discriminative and unique set of features to
characterize each chromatogram trace. These features are
then used to train and test the proposed classifier model
in a much more efficient way.
In our approach, the features chosen to represent each
observation point in a chromatogram trace are as fol-
FFFF (9)
for ,, and
gxgiACT G
 (10)
- F1 represents the set of feature vectors of base i. It is
a matrix of size n × 3 where, n is the number of sample
Figure 5. Part of an electropherogram trace (a) before and (b)
after normalization.
points in the chromatogram trace.
- x is a vector of size n × 1. It represents the signal
strength of base i at each observation point,
,, ,
xx x (11)
is a vector of size n × 1. It consists of the gra-
dient values for each observation point calculated using
the signal strength of the prior three sample points for
each observation.
gg g
 
3for 4, 5n3
is a vector of size n × 1. It consists of the gra-
dient values for each observation point calculated using
the signal strength of the subsequent three sample points
for each observation.
gg g
 
3for 4, 5n3
From the chromatogram trace, it is observed that the
positive ascent of a peak to the apex and the negative
descent of a peak to the subsequent valley are defined by
using a minimum of three sample points respectively.
Hence, for the calculation of positive (Eq. 15) and ne-
gative (Eq. 13) gradient values, three samples are adop-
Using features extracted in the previous section, the
DNA base-calling problem can now be tackled. In this
paper, two pattern recognition models are used to solve
the problem of base-calling: Artificial Neural Networks
(ANNs) and Polynomial Classifiers (PCs).
3.1. Artificial Neural Network
Artificial Neural Network (ANN) is a computational
approach conceived as an imitation of the human’s brain
neural network. Based on the training data, ANNs are
capable of adapting its structure accordingly. The basic
building block of an ANN is an information processing
unit, referred to as neuron, consisting mainly of weights
equal to the size of the data set, an adder to sum up the
weighted inputs, and an activation function for limiting
the output of the neuron [14]. ANN’s quality as universal
function estimators renders them attractive as pattern
classifiers. ANN’s ability to model both linear and non-
linear data is another advantage. However, this property
Copyright © 2013 SciRes. OPEN ACCESS
O. G. Mohammed et al. / J. Biomedical Science and Engineering 6 (2013) 165-174 171
makes an ANN prone to over-fitting, the tendency of a
model to adapt itself to the minute details of a training
data set.
Figure 6 illustrates a single hidden layer feed forward
neural network consisting of an input layer, a hidden
layer, and an output layer. Multiple neurons group to-
gether to form a layer and are connected to the neurons
in the preceding and subsequent layers through biases
and weights. The features extracted from the acquired
data, represented as the input layer, constitute the input
signals applied to the neurons comprised in the first hid-
den layer. Hence, the number of neurons in the input
layer is equal to the dimensionality of the input feature
vector, i.e. 12 (three features for each of the four bases).
As a rule of thumb, a neural network with one hidden
layer has the same expressive power as a network built
from several hidden layers. Moreover, as a practice, the
number of neurons in a hidden layer is twice that of the
input layer [15]. The outputs of the hidden layer are then
used as inputs to the output layer. The number of neurons
in the output layer represents the number of classes the
input data can be classified into [16]. For the proposed
base-calling problem, classification involves recognition
of the four bases, A, C, T and G, referred to as classes.
Hence, five neurons are used to form the output layer:
four of which represent the presence of each of the four
nucleotides, while the fifth neuron represents the absence
of all the four bases, represented as N.
In the learning stage, a target matrix, T, is needed for
labeling the ANN input data classes.
1,1,1,1, 1,
2,2,2,2, 2,
nAnCnTnG nN
Input La
er d
features Hidden Layer Output Layer M
Figure 6. A single hidden layer feedforward neural network.
The values assigned to the elements of T are as fol-
zi BzN
0 for sample point
z and
,,,CTBAG, if base i has a positive feature
, indicating a positive slope for the three sample
points prior to z, and a negative feature
, indicating a
negative slope for the three sample points subsequent to
t while
t for sample point z
G,,,BACT if the above condition is not satis-
The prior probabilities indicating presence and ab-
sence of a base are imbalanced due to the large availabil-
ity of class N in a chromatogram trace compared to the
other bases. Since it is difficult to balance the amount of
data belonging to each class, the weight given for class N
is reduced by assigning it a target value of 0.05 [17].
Using the MATLAB R2009b Neural Network toolbox,
the neural network model was trained and tested using a
single hidden layer, an output layer consisting of five
neurons to represent each of the five previously men-
tioned classes, and hyperbolic tangent sigmoid transfer
functions. To avoid the problem of over-fitting, a valida-
tion data set is used in addition to the training and testing
data sets. The validation data ensures that the training
process is terminated prior to over-fitting the training
data to the model.
3.2. Polynomial Classifier
Polynomial Classifiers (PCs) [18] represent non-linear
system identifications providing an efficient method to
describe non-linear input/output relationships. PCs are a
single layer neural network that adopts the polynomial
terms of the pattern features as inputs. A PC uses
k:d-dimensional feature vectors, X, which can be catego-
rized into non-linearly separable classes. A mapping
function between each input and its respective class then
needs to be determined. A Kth order polynomial classifier
uses a Kth order polynomial expansion function to map a
d-dimensional feature vector, x, to a higher dimensional
vector space, p(x) For example, if x is a 2-dimensional
feature vector represented as
xx, the mapping of
x to a higher dimensional space of K = 2 produces,
Similarly, the sequence of N:d-dimensional feature
,, ,
xx x is expanded into their Kth
order polynomial expansion, M, where,
12 N
Mpxpx px
Using the expanded feature vectors, M, the polynomial
classifier is trained to determine the optimum set of
weights, , that minimizes the difference between the
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O. G. Mohammed et al. / J. Biomedical Science and Engineering 6 (2013) 165-174
Copyright © 2013 SciRes.
model output and the desired targets, tx such that, itself k times.
The trained models were tested by comparing the re-
sults obtained in terms of bases called to the consensus
sequence of each chromatogram trace and to the DNA
sequences obtained from ABI and PHRED base-callers.
The performance of the neural network model and the
polynomial classifier model in terms of correct bases
obtained was measured based upon three types of errors
that can occur in DNA base-calling: deletion errors, in-
sertion errors, and substitution errors. A deletion error
represents the loss of one or more bases by the base-
caller. For example, when the base sequence of a DNA
template is TACGGT and the base-caller calls TCGGT, a
deletion error has occurred. An insertion error, on the
other hand, involves the addition of one or more bases by
the base-caller. For example, when the base sequence of
a DNA template is TACGGT and the base-caller calls
TATCGGT, an insertion error has occurred. A substitu-
tion error occurs when the base-called replaces the actual
base. For example, when the base sequence of a DNA
template is TACGGT and the base-caller calls TACCGT,
a substitution error has occurred.
arg min
opt x
opt X
MwM t (20)
Using the parameters obtained from the training stage,
an unknown feature vector, z, is expanded to its polyno-
mial terms, p(z), to test the trained model. The target
vector, tz, is obtained as follows,
z opt
twpz (21)
On employing a 2nd order polynomial expansion on the
features extracted from the data acquired, the data are
still observed to be non-linearly separable. Hence, a 3rd
order polynomial classifier using a 3rd order polynomial
expansion function is implemented in this work to train
the PC. The trained model is then tested using novel data
from the three data sets and a set of scores are obtained,
followed by post-processing to attain the final DNA se-
The performance of the trained model is shown in Ta-
bles 2-4 for the three data sets. In the three cases shown,
an overall base-calling average of 98.4% and 98.64% are
achieved by ANN and PC, respectively, indicating the
flexibility of the designed topologies [19,20]. Moreover,
in comparison to ABI and PHRED, the currently most
widely used base-calling software, in terms of deletion,
insertion and substitution errors, both proposed models
achieved a higher accuracy than PHRED and a compara-
ble performance to that of ABI. However, ABI and
PHRED base-callers were designed using thousands of
chromatogram traces while the models designed in this
paper used a discrete number of traces for its training and
testing. This indicates the high potential of the proposed
classifiers as more efficient alternative base-callers.
Data acquired were divided into three sets based on the
extent of noise contamination, source of the data, the
organism the trace belongs to, and the read length. In
light of the limitation in the number of bases, round robin
strategy is used in training and testing the proposed
models to increase the statistical significance of the
results. The available traces are divided into k disjoint sets,
such that k models are trained using the data in the (k 1)
sets and tested on the remaining non-trained data set. In
the case where k is equal to the number of traces in the
data set, i.e. k = 6, leave-one-out method is implemented,
i.e. out of the six available traces, traces 2 to 6 are used
for training while the first trace is used for testing. The
next round uses traces 1, 3 to 6 for training and the
second trace is spared for testing, and the cycle repeats
Table 2. Performance measure of trained ANN and PC compared to PHRED and ABI for data set 1.
Recognition (%)
Errors (%)
Errors (%)
Errors (%)
Trace 1—639 Bases97.65 98.6 61.19 99.21 1.560.6318.47 0.160.160 0.78 0.63 0.63 0.78 19.560
Trace 2—623 Bases96.15 95.83 71.43 97.75 1.120.644.01 0.161.611.120.32 0.16 1.12 2.41 24.241.93
Trace 3—632 Bases97.63 98.1 97.63 99.68 0.790.790.16 0 0.950.320.16 0 0.63 0.79 2.060.32
Trace 4—632 Bases97.47 98.26 98.73 99.37 1.110.470 0.32 1.27 0.95 1.270.16
Trace 5—722 Bases97.23 98.06 97.51 98.75 0.830.830.14 0.550.830.420.69 0.14 1.11 0.69 1.660.55
Trace 6—722 Bases98.20 98.34 88.92 99.45 0.140.830.550.69 0.28 0.69 0.83 1.660.14
O. G. Mohammed et al. / J. Biomedical Science and Engineering 6 (2013) 165-174 173
Table 3. Performance measure of trained ANN and PC compared to PHRED and ABI for data set 2.
Recognition (%)
Errors (%)
Errors (%)
Errors (%)
sapiens—639 Bases 97.81 98.12 61.19 99.21 0.470.6318.470.160.940.940.780.63 0.78 0.31 19.560
mikatae—674 Bases 99.41 98.81 99.41 99.41 0.590.590.150.150 0.590.150.15 0 0 0.300.30
melanogaster—744 Bases 97.58 98.66 99.33 97.45 2.150.810.671.750 0.270 0.27 0.27 0.27 0 0.54
Table 4. Performance measure of trained ANN and PC compared to PHRED and ABI for data set 3.
Recognition (%)
Errors (%)
Errors (%)
Errors (%)
Trace 1—759
Bases 99.87 99.74 100100 0.13 0.130 0 0 0.130 0 0 0 0 0
Trace 2—882
Bases 99.66 99.55 99.89 100 0.23 0.230 0 0 0.110 0 0.11 0.11 0.11 0
Trace 3—866
Bases 99.31 99.53 99.53 100 0.46 0.350.120 0.230.120 0 0 0 0.35 0
Trace 4—740
Bases 99.19 98.78 99.73 99.86 0.68 0.680. 0 0 0.27 0 0
Trace 5—710
Bases 99.72 99.86 100100 0.14 0.140 0 0 0 0 0 0.14 0 0 0
Efficiently deciphering the human genome through DNA
sequencing has been anticipated widely for the contribu-
tion it is bound to make in a range of applications such as
understanding the causation of genetic diseases and hu-
man evolution. However, the relatively high cost of the
chemistry involved in DNA sequencing results in high
operational cost in genome research centers. This fact
has triggered research initiatives to improve the accuracy
of base reads in noisy electropherograms so that re-se-
quencing of the required DNA fragment is not needed,
thereby, reducing sequencing expenses.
A simple neural network and a polynomial classifier
model that matches the performance of existing base-
callers was proposed in this paper. An average accuracy
of 98.4% and 98.64% is achieved by ANN and PC, re-
spectively, and the ability of the classifiers to result in
negligible substitution errors compared to ABI and PHRED
was proven. PHRED is currently the most widely used
base-caller software due to its high base-calling accuracy
which exceeds that of ABI [21]. The ABI base-calling
software was improved by developing the KB base-caller
which incorporates base-specific quality scores similar to
PHRED. ABI KB was calibrated using more than 20
million base-calls and tested on more than 10 million
bases [22]. Hence, justifying the high accuracy of ABI
compared to the proposed models and PHRED. However,
it should be noted that PHRED results in high error rates
in some traces which already have their quality scores
assigned. In such cases, PHRED makes obvious errors in
perfectly clear sequences.
The proposed models do not depend on the spacing
between adjacent peaks that varies dynamically as we
progress through the trace. In addition, the models were
designed not to assign an “N” to a peak. The base with
the highest score is assigned to a peak irrespective of the
noise. Moreover, the ANN and PC models have not been
trained and tested in this paper using thousands of chro-
matogram traces. In fact, discrete number of traces were
utilized and a performance that exceeds the accuracy of
PHRED and comparable to ABI was obtained. Therefore,
the potential and suitability of a neural network and
polynomial classifier model as a base-calling tool were
demonstrated. Yet, further research is needed to improve
the recognition rate.
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