Engineering, 2013, 5, 244-249
http://dx.doi.org/10.4236/eng.2013.510B050 Published Online October 2013 (http://www.scirp.org/journal/eng)
Integrativ e Self-Organizing Map—A Mean Pattern Model
Zihua Yang1, Zhengrong Yang2
1Wolfson Institute of Preventive Medicine, University of Queen Mary, London, UK
2School of Biosciences, University of Exeter, Devon, UK
Received June 2013
ABSTRACT
We propose an integrative self-organizing map (iSOM) for exploring differential expression patterns across multiple
microarray experiments. The algorithm is based on the assumption that observed differential expressions are random
samples of a mean pattern model which is unknown a priori. The learning mechanism of iSOM is similar to the con-
ventional SOM. The mean pattern model which underlies the proposed iSOM models mean differential expressions
using a one-dimension of mean differential expressions for the mean differential expressions. The feature map of an
iSOM model can be used to reveal correlation between multiple medically/biologically related disease types or multiple
platform experiments for one disease. We illustrate applications of iSOM using simulated data and real data.
Keywords: Integrative Study of Microarrays; Pattern Discovery; Differential Expressions; Self-Organizing Map
1. Introduction
The self-organizing map (SOM) is a popular unsuper-
vised artificial neural network algorithm [1] used for
topological pattern recognition. It explores hidden pat-
terns in data and visualizes it in a two -dimensional array.
In this array, each grid or neuron preserves or demon-
strates a loca l pattern of the whole p attern h idden in d ata.
The local patterns smoothly changes across the grids of
the array. Neighboring neurons therefore show similar
local patterns. SOM and its many variants have been
widely used in data analysis/mining.
However, SOM and its variants are designed for dis-
covering topological structure hidden in one data set or
experiment. Thus they cannot be directly used for an
integrative study across multiple data sets for exploring
common patterns.
In cancer research, we may often wish to search for
common cancer signatures [2-17], based on the under-
standing that diseases may have some common gene ex-
pression pattern in spite of diseases heterogeneity. For
instance, it is believed that common gene signature may
exists among various cancers [12] as well as among in-
flammatory diseases [18]. The commonly used method
for detecting a common gene signature is to integrate
multiple microarray data sets into one study. From this,
we can detect a subset of genes whose expressions can be
highly correlated with experimental design for as many
microarray data sets as possible. Various classification
algorithms have been employed to train a classifier to
maximize the prediction power of signatures [19].
In addition to these classification models, it is also
important to determine signatures in terms of their com-
mon or distinct expression differentiation without classi-
fication labels. A simple way is to pool all the data sets
into one data set and then use a clustering algorithm to
partition the pooled data. However this is not possible
when data sets have different number of samples (dimen-
sions). On the other hand, separately analyzing each data
set individually and then integrating the separate results
may be inaccurate and inefficient. One popularly ap-
proach is to use non-negative matrix factorization (NMF)
[20,21]. However it has been noted that NMF is a linear
algorithm which may not be able to explore complex
pattern across multiple data sets [22].
We propose an extension to SOM, integrative SOM
(iSOM), for exploring structural relationships in integra-
tive studies. Based on modern high-resolution microarray
technology, we assume that the differential expression
variance of a gene is relatively low and that most micro-
array expression data demonstrate a high positive corre-
lation among replicates. We therefore propose a mean
pattern model, i.e. all differential expressions are as-
sumed to be random samples drawn from a mean pattern
model. The model can be considered as a library of all
possible mean differential expressions with variances. An
integrative study of multiple microarray data sets then
aims to reveal how the hidden and unknown mean pat-
tern model shapes the observed differential expressions
from multiple data sets. We can thereafter discover how
differentialy expressed genes are common or distinct in
multiple biologically related disease types or in different

Z. H. YANG, Z. R. YANG
245
platforms of the same study.
The proposed iSOM is composed of two major steps.
In the first step, the vector of all differential expression
matrices across multiple data sets is analyzed using SOM
leading to an array in which each neuron represents one
local pattern, i.e., one mean differential expression. In the
second step, we assume this mean pattern model under-
lies the observed differential expressions. The standard
SOM learning rule is thus altered. We show in this paper
how iSOM can be useful for co rrelated pattern discovery
using bot h si mulate d da ta and real da ta.
2. Methods
2.1. Data Pre-Processing and Filtering
Each microarray expression data set is first normalized to
the logarithm scale. After normalization, a significance
analysis is carried out using eBayes [23]. Only those
genes which show sufficient significant differential ex-
pressions are selected for further analysis. This is be-
cause the major aim of integrative study such as common
gene signature discovery will not be interested in genes,
which do not show significant differential expression.
Afterwards, we save the differential expression matrix
for significantly differentially expressed genes for each
data.
2.2. Self-Organizing Map Algorithm
The conventional self-organizing map (SOM) is a two
layer neural network in which the first layer is composed
of input neurons for input variables (
x
n
, n stands for the
nth input vector) while the second layer is composed of
an array of output neurons. Each output neuron has a
weight vector acting as a parameter vector,
w
k
, wher e k
represents the kth neuron. Note that
w
k
and
x
n
have
the same dimensionality. The competitive learning of
SOM is to update
w
k
based on the distance between
w
k
and
x
n
∆w
k
t +1=
ηtαn (x
n
−w
k
t
)
where
0< ηt <1
is called a learning rate at time t and
αn
is the neighborhood constrain associated with
x
n
.
Note that SOM employs an online learning strategy, i.e.
model parameters are undated once one input vector is
fed.
2.3. iSOM
We assume that each output neuron has a scalar weight
functioning as a mean differential expression. This
means that the feature map of iSOM is an array of mean
differential expressions. We denote
µ
k
as the weight
(mean differential expression) of the kth output neuron.
Suppose we have two data sets, X and Y (it is easy to
generalize the analysis of two data sets to multiple data
sets), we denote the nth input of X as
x
n
and the mth
input of Y as
y
m
. We assume that each vector of diffe-
rential expression samples is a random sample drawn
from a hidden signal, i.e. mean differential expression
expressed by
µk
. Using the standard SOM learning rule,
the learning rules for iSOM are
∆ µk = ηtαn (x
n
− µk i)
t
i
∆ µ
k
= η
t
α
m
(y
m
− µ
k
i)
t
i
where i is a vector of ones. These learning rules are used
in building an iSOM model.
2.4. Random Selection of Expressions in
Training
We wish to train an iSOM in such a way as to ensure the
successful discovery of differential expression pattern
between multiple data sets. Suppose we have two data
sets, X and Y, their relationship may be one of the fol-
lowing: 1)
X⊃Y
; 2)
Y⊃X
; 3)
X≡Y
; 4)
(X \Y)≠ φ
and
φ ≠X)\(Y
. When
X≡Y
, any train-
ing procedure will do well. For the remaining cases, the
order of data selection of a training process is crucial. For
instance, if
X⊃Y
and we use Y to train an iSOM first,
the iSOM will have fully learnt differential expression
patterns from Y and leave no space for extra differential
expression pattern in X. Consequently, the data structure
learned from Y will then be lost during the learning
process using X. This will then lead to biased pattern
discovery. The same problem occurs also in the other
two scenarios. To avoid this, we propose a random sam-
pling strategy for iSOM training which randomly selects
one microarray data set and one differential expression
vector (corresponding to a gene) at every step of the
training process. This ensures unbiased pattern discovery
across multiple microarray data sets.
3. Results
3.1. Simulated Scenarios
We design three simulated scenarios. The first satisfies
the condition
X≡Y
. Here we design a mean pattern
model with ten differential expression means (
ϑ
) as −5,
−4, −3, −2, −1, 1, 2, 3, 4, and 5. The X space is of two
dimensions and the Y space is of three dimensions. Both
X and Y spaces are composed of random vectors drawn
from the mean pattern model. Each mean differential
expression value is used to draw 100 vectors randomly
for both X and Y spaces. In total, there are 2000 data
points. Each vector is drawn from the mean pattern model,
z
n
~G( µ
k
, σ
2
)
, where H means the number of output
neurons,
µk ∈ ϑ
,
n
z
is either
n
x
or
n
y
and
σ ∈
(0.1, 0.2, 0.3, 0.4, 0.5). Each vector is labeled indi-

Z. H. YANG, Z. R. YANG
246
cating which mean differential expression value the vec-
tor is drawn from. We then measure whether this topo-
logical structure is maintained during iSOM modeling.
For two data sets, iSOM generates two output maps
named as
),,,( 21 x
H
xx
x
φφφ =Φ
and
),,,(21y
H
yy
y
φφφ =Φ
for two (or more) data sets,
where
φ
h
x
and
φ
h
y
are assumed to be multivariate mean
diffe- rential expression patterns drawn from the same
mean differential expression
E (x
n
|∀x
n
∈ φ
h
x
)= E (y
n
|∀y
n
∈ φ
h
y
)∈{ µ
k
}
(1)
We therefore compare
Φ
x
against
Φ
y
for each
neuron to examine whether Equation (1) is satisfied. Ta-
ble 1 shows this evaluation for five variance values. It
can be seen that the relationship (the designed topologi-
cal structure) is well maintained during iSOM modeling.
The maximum error rate is about 5.6% (=113/2000) for
simulation with a relatively large s.d. of
5.0= σ
. This
data set revealed no distinct genes. Therefore there is no
measurement for checking if distinct genes can be well
revealed.
The second simulated scenario satisfies the condition
X⊃Y
. The mean differential expression structure is the
same as above. The X space is composed of all ten diffe-
rential expression patterns while the Y space is com-
posed of eight of them (−3, −2, −1, 1, 2, 3, 4, 5). This
means that the X space has 2 00 genes which are distinct -
only occurring in the X space not the Y space. There are
therefore 180 0 data points . In Table 1 , we also found the
error to be small. The maximum error rate is 8.6%. In
addition to error, we also examined how the distinct
genes from the X data set can be revealed. Suppose the X
data set contains some distinct differential expression
patterns, which are not found from the Y data set. This
means that some neurons
φ
h
x
contain vectors drawn
from the mean pattern model, which cannot be found
Table 1. Evaluation on three simulated data sets. “Sigma”
means standard deviation. “Error” means the number of
times that Equation (1) is violated. “Distinct” is the per-
centage of distinct genes of one mean differential expression
from one data set are identified. In the second simulated
scenario, only one data set has distinct genes, therefore two
measurements are used. In the third simulated scenario,
both data sets have distinct genes, therefore we use four
measurements.
Sigma Error Distinct
Toy 1 Toy 2 Toy 3 Toy 2 Toy 3
0.1 0 0 0 100/100 100/100/100/100
0.2 0 0 0 100/100 100/100/100/100
0.3 0 24 2 100/100 100/100/100/99
0.4 23 61 29 100/99 100/98/99/100
0.5 113 155 35 100/94 100/98/98/100
from the corresponding neuron from
Φ
y
, i.e.
φ
h
y
. Table
1 shows the percentages of distinct differential expres-
sion patterns which were uniquely preserved during
iSOM learning. It can be seen that iSOM is well adapted
for this kind of patterns.
The third simulated scenario satisfies the conditions
(X \Y)≠
φ
and
φ ≠X)\(Y
. The mean differential ex-
pression pattern structure is the same as above. The X
space is composed of eight differential expression pat-
terns centered at (−5, −4, −3, −2, −1, 1, 2, 3) while for Y
the patterns are centered around (−3, −2, −1, 1, 2, 3, 4, 5).
In this case, we have distinct differential expression pat-
terns from both data spaces. In this case, iSOM can still
discover this kind of dual distinct differential expression
patterns—Table 1. In addition, the error is still very
small. Figure 1 shows the distribution of data points of
the first simulated scenario mapped to the iSOM model.
A single number in a grid representing the number of
data points falling into the grid in a grid indicates that the
neuron is composed of data points as random samples of
a single mean differential expression value. When there
are more than one numbers, it means that data points of
multiple mean differential expression values are mapped
to the same neuron. Figure 2 shows the distribution of
data points of the second simulated scenario mapped to
the iSOM model. We can see that some neurons are uni-
quely occupied by a single data set.
3.2. Real Data
We use two data sets downloa ded from Gene Expression
Omnibus (GEO), GSE12630, of breast cancer metastasis
and liver cancer metastasis. Both data sets contain four
replicates. Using eBayes with a critical p value of 0.05,
2359 differentially expressed genes were found for the
Figure 1. The distribution of data points of the first data set
of the third simulated scenario.

Z. H. YANG, Z. R. YANG
247
Figure 2. The distribution of data points of the second data
set of the third simulated scenario.
breast cancer data set and 19029 differentially expressed
genes for the liver cancer data set. The two data sets are
then used for the integrative analysis using iSOM. The
neuron array is set to be ten by ten (100 neurons).
Using iSOM, we found seven common differentially
expressed genes between the breast cancer metastasis and
liver cancer metastasis datasets. Among them, SRSF1
(probe set ID 201741_x_at) was an up-regulated gene
while the six others were down-regulated—Table 2. The
gene SRSF1 has been studied in relation to breast cancer
[24] and liver cancer [25]. Some of the down-regulated
genes have been studied in the context of both breast and
liver cancer metastasis—Table 2. The number of unique
differentially expressed genes for breast cancer metasta-
sis is 773 while the number of unique differentially ex-
pressed genes for liver cancer metastasis is 297. Figu re s
3 and 4 show the differential expression patterns (de-
rived using iSOM) for the breast cancer metastasis data
and liver cancer metastasis data respectively. Compar-
ing these two maps, it can be seen that both the number
of common differentially expressed genes and the num-
ber of distinct differentially expressed genes are quite
small.
4. Conclusion
We have presented a novel extension to SOM for inte-
grative studies of microarray expression data sets. The
proposed integrative SOM (iSOM) is based on the as-
sumption that the microarray expression data under con-
sideration has small variance across replicates. This as-
sumption is reasonable considering recent technology
improvement in the microarray experimental precision.
We assume th at differen tial express ions across mu ltiple mi-
croarray expression data sets with medical or biological
relevance are random samples from a mean pattern model.
This mean pattern model is a one-dimension structure of
Table 2. Six common down-regulated genes between the
breast and liver cancer metastasis datasets. Relevant refer-
ences indices are given under ‘breast’ and ‘liver’.
Probe set ID Gene symbol Breast Liver
200736_s_at GPX1 [26] [27]
200872_at S100A10 [28] [29]
201868_s_at TBL1X [30] n.a.
202069_s_at IDH3A [31] n.a.
201150_s_at TIMP3 [32] [33]
202430_s_at PLSCR1 n.a. [34]
Figure 3. Differential expression pattern for breast cancer
metastasis.
Figure 4. Differential expression pattern for liver cancer
metastasis.

Z. H. YANG, Z. R. YANG
248
mean differential expressions. It is this linear structure
that shapes the observed differential expressions from
multiple data sets in a multivariate model. The iSOM
approach can also be used in cross-omics and cross-spe-
cies studies.
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