J. Biomedical Science and Engineering, 2010, 3, 13-19
doi:10.4236/jbise.2010.31002 Published Online January 2010 (http://www.SciRP.org/journal/jbise/
JBiSE
).
Published Online January 2010 in SciRes. http://www.scirp.org/journal/jbise
A new projection method for biological semantic map
generation
Hoan N. Nguyen, Nicolas Wicker, David Kieffer, Olivier Poch
Laboratoire de bioinformatique et génomique intégratives, Institut de Génétique et de Biologie Moléculaire et Cellulaire, France
University of Strasbourg, Illkirch Cedex, France.
Received 4 September 2009; revised 25 October 2009; accepted 26 October 2009.
ABSTRACT
Low-dimensional representation is a convenient
method of obtaining a synthetic view of complex
datasets and has been used in various domains for a
long time. When the representation is related to words
in a document, this kind of representation is also
called a semantic map. The two most popular meth-
ods are self-organizing maps and generative topog-
raphic mapping. The second approach is statistically
well-founded but far less computationally efficient
than the first. On the other hand, a drawback of
self-organizing maps is that they do not project all
points, but only map nodes. This paper presents a
method of obtaining the projections for all data points
complementary to the self-organizing map nodes. The
idea is to project points so that their initial distances
to some cluster centers are as conserved as possible.
The method is tested on an oil flow dataset and then
applied to a large protein sequence dataset described
by keywords. It has been integrated into an interac-
tive data browser for biological databases.
Keywords: Semantic Map; Dimension Reduction;
Biological Database; SOM
1. INTRODUCTION
Thanks to the availability of the human and other ge-
nomes and the rapid progress of biotechnologies and
information technologies, numerous large biomedical
datasets have been generated. Modern biomedical in-
formation thus corresponds to a high volume of hetero-
geneous data that doubles in size every year and that
covers very different data types, including phenotypic
data, genotypic data as well as standards, processes,
protocols or treatments used to generate information
from raw data. In this context, systemic approaches are
now needed to store, analyze and compare the huge
amount of relevant information.
In addition, the knowledge provided by classical
query services on biological data is often unsatisfactory
(e.g. a list of proteins or sequences) and there is a need
for user-friendly visual representations of the data. Such
a representation exists and is called a feature or semantic
map. It is used to visualize “land maps” in two or three
dimensions that represent, for example, the distribution
(similarity and neighborhood) of protein annotations in
biological databases. When query results are represented
on the map, the repartition of the proteins can be easily
observed, as well as their proximity to clusters labeled
according to their content. In addition, it is straight-for-
ward to superpose the information obtained from addi-
tional requests. Thus, a semantic map can greatly facili-
tate the interpretation of results from large scale data
analyses. To quote a few examples, semantic maps have
already been used in fluid mechanics [1], astronomy [2],
internet data mining [3,4], scientific literature mining [5]
and biology [6].
Many low-dimensional methods have been devised
[5,7,8,9] and two of the most popular are the WEBSOM
method [9] and the Generative Topographic Mapping
(GTM) [1]. These two methods are briefly outlined be-
low.
WEBSOM originates from self-organizing maps [10]
which is a classification algorithm where nodes move
towards cluster centers. In WEBSOM, the nodes are
fixed on a two-dimensional grid and at the same time
live in the space of the dataset, typically a space.
First, a point is picked at random from the dataset.
Next, the closest node in is selected and then
each node moves towards y according to the equa-
tion
Rp
y
j
i
wRp
w
(1) ()t  (t)(ht) ()
jjijj
wy wtwt where
()t

is the learning rate decreasing in time and
is a neighborhood function in the two-dimensional grid.
These steps are then iterated for all data points. The ini-
tialization of the p-dimensional space can be performed
randomly, but a more effective method is to select points
()t
ij
h
The first and second author contribute equally to this paper.

14 H. N. Nguyen et al. / J. Biomedical Science and Engineering 3 (2010) 13-19
SciRes Copyright © 2010 JBiSE
along the two first principal axes of the dataset [4]. Fi-
nally, the dataset is used again by assigning each point to
its closest node in the p-dimensional space using a
Euclidean distance. Then, for each node, the number of
points it has captured is taken as its density up to a given
scaling factor (the size of the dataset).
The generative topographic map (GTM) [1] is a statis-
tical method which is provably (locally) convergent and
which does not require a shrinking neighborhood or a
decreasing step size. It is a generative model: the data is
assumed to arise by probabilistically picking points in a
low-dimensional space and mapping them to the ob-
served high-dimensional input space. The statistical
model can be described in the following way:
2
2
(,,)()exp{.()
22
p
ii
pyxWW xy



 }
where i
x
is a two-dimensional grid node,

is a scal-
ing parameter, .( )
i
Wx

a generalized regression model,
a W
p
m() matrix and the elements of
x

consist of
basic functions m()
j
x

W
typically equal to radially
symmetric Gaussians centered on the nodes of a
two-dimensional grid. The parameters and

of the
model are estimated through the expectation-maximiz-
ation (EM) algorithm [11]. This model can be considered
to be the probabilistic counterpart of SOM/WEBSOM.
However, the WEBSOM method is quicker than GTM
when large amounts of data must be dealt with, especially
if the winner selection is optimized so that millions of
documents and nodes can be treated [4].
An alternative choice is to follow Flexer's approach [12]
which first clusters the points in the data space and then
projects cluster centers using Sammon's multidimensional
scaling method [13]. However this means that only a sub-
set of points are effectively projected. In this paper, we
present a complementary method that projects all points
using their distances to the cluster centers.
First this new projection method is presented, then it is
evaluated on a benchmark data set and compared to other
methods. Finally, it is used in the results section to gener-
ate a semantic map in the context of a new integrative
navigator for biological databases.
2. METHODS
The principle of the presented method is to project points
after they have been clustered and the cluster centers have
been projected onto a two-dimensional map. This is done
by conserving as much as possible the original distances
between the points and the cluster centers. Basically, for
each point indexed by , the two- dimensional coordi-
nates are search such as to minimize the difference be-
tween the distances computed in the -dimensional data
space with those computed on the map.
i
n
This comes down to finding the point i
x
in two di-
mensions minimizing the following function : ()
i
Ex
2
2
22
,
11
()( )
G
ikgk
gk
Exx cd






 g
with
g
d denoting the distance between point and
cluster
i
g
and ,
g
k
c
)
the projection of the cluster
center. The Newton-Raphson algorithm was used to
minimize . At each step,
th
k
tt
ii
(
i
Ex 11 .
x
xH E

with
H
the Hessian and the gradient of . EE
22
2
1112
xx
22
2
212 2
,
E
EE
xx
EEE
xxx x
EH




 

 

 

 
 
The optimizing function is not convex as the Hessian
is not always semi-definite positive. To show this, it is
sufficient to find a point
X
verifying '0XHX

. In
particular, we show that 11
H
can be negative which is
also sufficient. First let us note that
2
22
,,
11
2() 2(
G
kgkg lgl
lgk
E)
x
cdxc
x





 
2
2
22
,,
2
111
8( )4()
GG
lglkgk g
lggk
E2
x
cxc
x

 



d
and then set
11,12,13,1
22
11 1,121,2
22
21 2,122,2
22
31 3,12 3,2
()(
()(
()(
xc cc
dxc xc
dxc xc
dxcxc





 


 

)
)
)
Thus,
 


22
2
111 3,123,23
40Hxcxcd


Consequently, a global optimization process was per-
formed using different initial values. Each cluster center
projection was used as an initial value and the best solu-
tion after convergence was kept.
3. RESULTS AND DISCUSSION
3.1. Validation Using the Oil Flow Dataset
To validate the new points projection method, a previ-
ously established oil flow dataset [14] was used as a
benchmark. This training dataset is available at
http://www.ncrg.aston.ac.uk/GTM/ and contains 1000

H. N. Nguyen et al. / J. Biomedical Science and Engineering 3 (2010) 13-19
SciRes Copyright © 2010
15
First, the dataset was clustered into 15 clusters and the
cluster centers projected according to Sammon's multi-
dimensional scaling method [13]. Then the 1000 points
were projected in two dimensions using the method de-
scribed above. The results are shown on Figure 1, where
it be seen that three different groups are rather well line-
arly separated. The groups obtained with the GTM and
principal component analysis (PCA) methods are shown
on Figures 2 and 3 respectively. In order to objectively
measure the quality of these results, we computed the
ratio of the between-class inertia and the total inertia for
each method. For our method, GTM and the PCA, we
obtained a ratio of 0.83, 0.25 and 0.23 respectively, thus
confirming the visual impression. Nevertheless, it should
be stated that, if only separation is desired and not spe-
cifically linear separation, GTM performs better, even
though it has the drawback of making the underlying
grid very visible.
Figure 1. New projection of the dataset. Results of the pre-
sented projection on the oil flow dataset. Crosses, circles and
plus-signs represent stratified, annular and homogeneous
multi-phase configurations respectively. The three group
separations are clearly identified.
3.2. Semantic Map Generation for Biological
Database
The Laboratory of Genomics and Integrative Bioinfor-
matics (LGBI) at the IGBMC Strasbourg, has developed
a new high-performance biomedical information system,
called the BIRD System [15,16]. BIRD is able to inte-
grate very quickly heterogeneous data either from the
large generalist databases (sequence, structure, function
and evolution, etc.) or from specialized databases dedi-
cated to high throughput biology (transcriptomics, inter-
actomic, etc.) in a relational database (IBM DB2). Thus,
it allows to organize massive sets of biomedical data
according to real world requirements. An original bio-
logical query engine, called BIRDQL, has been designed
to facilitate access to the heterogeneous databases and to
allow pertinent information extraction via a web server.
This system has been used in the Decrypthon computing
grid [17] in order to provide data to the runtime applica-
tions.
Figure 2. Oil flow dataset after GTM. After projection of the
oil flow dataset using the Generative Topographic Mapping,
the three group separations are clearly separated, but in a com-
plex way that is far from linear.
To complete the visualization and analyze functional-
ities of the BIRD System, the new method described
above to build semantic maps was integrated in the
BIRD query engine (BIRDQL). The maps can be used to
explore the data using a combination of high level que-
ries and area selections (Figure 4). The method was
tested by building a semantic map of the Uniprot data-
base [18] using the keyword descriptions for each pro-
tein. After removal of redundant vectors, we obtained
60,000 vectors in a 914-dimensional space
corresponding to the 914 keywords extracted from about
6 million proteins. In the following lines, to avoid fo-
cusing on the numerical details, we will consider
proteins described by keywords where and
16000
,...zz
p
0
n
pn
Figure 3. Oil flow dataset after PCA projection. After projec-
tion of the oil flow dataset using principal component analysis,
the separation of the three groups is not clearly identified. In
particular, the crosses are very scattered.
points in 12 dimensions corresponding to 12 measure-
ments on the mixture of oil, water and gas passing
through a pipeline. The three phases in the pipe can be-
long to three different configurations corresponding to
laminar, homogeneous and annular flows.
stand for 60000 and 914 respectively.
Before projecting the points, some preliminary steps
were necessary:
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16 H. N. Nguyen et al. / J. Biomedical Science and Engineering 3 (2010) 13-19
SciRes Copyright © 2010 JBiSE
Figure 4. Semantic map with density colours and most frequent keyword labels.
Step 1: dimension reduction
The proteins were described by keywords and
were thus represented by points in
dimensions. As in the preprocessing step of WEBSOM
[3,4], an initial dimension reduction was performed to
reduce coordinates to using random projection
directions. More specifically, random vectors
n
p
p
n
*
p
1,..., n
zz p
j
v were
generated on the -dimensional unit-sphere and then
new coordinates were obtained by computing the scalar
product
*
p
,iij j
y
vz on each document i. Thus, the
proteins were described by points . nn 1... n yy
Step 2: mixture models clustering
In a second step, these points were clustered using
mixture models. Mixture models are a powerful method
to cluster datasets of points described by coordinates.
The points are assumed to be independent realizations
from a mixture of several distributions. Here the mix-
ture is only briefly described for components
1
G
,..., G
f
f


with parameters 1..., G


G
. A general pres-
entation of this method and its applications can be found
in [19,20,21,22]. If 1,...,

 indicate the different
weights of the components, the likelihood of the model
for points is expressed as:
n1,..., n
yy
11
, ,...1
1 1
,...,,...,)( )
nG
(
M
GG

*
G
c
()mx
n gg
g i
Lyy

 
 

i
fy
The estimation of the different coefficients of the mix-
ture model is commonly performed via the EM (Expec-
tation-Maximization) algorithm of Dempster [11]. Here,
in order to simplify the estimation, a variant of the EM
algorithm called CEM was used [22]. In this application
was chosen to be equal to 30.
G
Step 3: cluster centers projection
Once clusters were obtained, the centers of grav-
ity were computed in the p-dimensional space.
Then, multidimensional scaling (MDS) [23] was applied
on the cluster centers to produce two-dimensional coor-
dinates . MDS was used because Sammon's
method [13] failed on this dataset, since it produced
G
*
.., G
1,c
1,.cc
...,
many points with the same coordinates.
After these three preliminary steps, the points were
projected on the map using the new projection method.
The density for each point
x
of the map is
given using a kernel method [24]:

H. N. Nguyen et al. / J. Biomedical Science and Engineering 3 (2010) 13-19
SciRes Copyright © 2010 JBiSE
17
Figure 5. The global architecture of the Semantic Map Discovery prototype coupled with the BIRD System using
the BirdQL query engine.
Figure 6. Semantic map with selected proteins. The labels represent the most frequent keywords present inside the
cluster points which are not shared between different clusters.

18 H. N. Nguyen et al. / J. Biomedical Science and Engineering 3 (2010) 13-19
SciRes Copyright © 2010 JBiSE
1
12
1
11
() exp{()()
2
n
ii
i
mxx xx x
n





} 
Then, a color scale ranging from purple to white, with
intermediary colors red, orange and yellow was assigned
to each point according to its density. The map is repre-
sented in Figure 4.
Then, a color scale ranging from purple to white, with
intermediary colors red, orange and yellow was assigned
to each point according to its density. The map is repre-
sented in Figure 4.
This visual representation allows a global comprehen-
sion of the whole database, which is easier to understand
than numerical or textual data. Some important key-
words shared by many proteins are visible on this map,
such as kinase, ligase and protease. At the same time,
frequent keywords, such as “complete proteome”, that
are non-informative, are avoided because they are shared
by several clusters. Another observation is that the den-
sity is far from being homogeneous, the map being more
crowded in the bottom-left corner than elsewhere.
This visual representation allows a global comprehen-
sion of the whole database, which is easier to understand
than numerical or textual data. Some important key-
words shared by many proteins are visible on this map,
such as kinase, ligase and protease. At the same time,
frequent keywords, such as “complete proteome”, that
are non-informative, are avoided because they are shared
by several clusters. Another observation is that the den-
sity is far from being homogeneous, the map being more
crowded in the bottom-left corner than elsewhere.
When using the integrated biological query engine
BIRD-QL of the BIRD System via a web service or http
protocol, as shown in Figure 5, the selected proteins are
represented on the maps by a plus sign of a given color.
If different selections have been performed, different
colors are used. An example is shown in Figure 6, where
proteins selected by a query with the keyword “apop-
tosis” are shown by blue plus signs. Some of these pro-
teins were selected by the user and are surrounded by a
white square. One of the proteins, DNJA3, belongs to
the small cluster labeled “disease mutation” but does not
possess the “disease mutation” keyword. Interestingly its
deficiency implies dilated cardiomyopathy [25] (MIM-
608382).
When using the integrated biological query engine
BIRD-QL of the BIRD System via a web service or http
protocol, as shown in Figure 5, the selected proteins are
represented on the maps by a plus sign of a given color.
If different selections have been performed, different
colors are used. An example is shown in Figure 6, where
proteins selected by a query with the keyword “apop-
tosis” are shown by blue plus signs. Some of these pro-
teins were selected by the user and are surrounded by a
white square. One of the proteins, DNJA3, belongs to
the small cluster labeled “disease mutation” but does not
possess the “disease mutation” keyword. Interestingly its
deficiency implies dilated cardiomyopathy [25] (MIM-
608382).
There is still room for improvement in the construc-
tion of semantic maps both at the algorithmic level and
at the software functionality level. The point’s projection
is formalized as a global optimization problem and cur-
rently, it is resolved simply using different starting points
with the Newton-Raphson method. However global op-
timization methods could also be tested [26,27]. From a
practical point of view it would also be useful to deter-
mine how many clusters or nodes are necessary to
achieve a good projection of the data points.
There is still room for improvement in the construc-
tion of semantic maps both at the algorithmic level and
at the software functionality level. The point’s projection
is formalized as a global optimization problem and cur-
rently, it is resolved simply using different starting points
with the Newton-Raphson method. However global op-
timization methods could also be tested [26,27]. From a
practical point of view it would also be useful to deter-
mine how many clusters or nodes are necessary to
achieve a good projection of the data points.
4. CONCLUSIONS 4. CONCLUSIONS
The main contribution of this work is a new computa-
tional solution to the construction of semantic maps. The
idea is to project points by locating them according to
cluster centers. This method can thus be coupled with
other methods such as self-organizing maps or Flexer's
approach.
The main contribution of this work is a new computa-
tional solution to the construction of semantic maps. The
idea is to project points by locating them according to
cluster centers. This method can thus be coupled with
other methods such as self-organizing maps or Flexer's
approach.
5. ACKNOWLEDGEMENTS 5. ACKNOWLEDGEMENTS
This work was supported by the CNRS, the University of Strasbourg
and the Décrypthon program initiated by the Association Française
contre les Myopathies, IBM and the CNRS. We are grateful to all
internship students who participated in this work by programming some
parts of it, namely Xavier Brotel, Jérémy Némo Trouslard and Julien
Cadet. The authors would like to thank Anne Friedrich, Laurent Philippe
Albou and Julie Thompson for helpful suggestions.
This work was supported by the CNRS, the University of Strasbourg
and the Décrypthon program initiated by the Association Française
contre les Myopathies, IBM and the CNRS. We are grateful to all
internship students who participated in this work by programming some
parts of it, namely Xavier Brotel, Jérémy Némo Trouslard and Julien
Cadet. The authors would like to thank Anne Friedrich, Laurent Philippe
Albou and Julie Thompson for helpful suggestions.
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