**Invited Speakers **

** **

**Teuvo Kohonen (Helsinki), **“Is the SOM a biological
model?”

**Jean-Claude
Fort (Toulouse), “ **SOM's mathematics ”

**Barbara Hammer (Clausthal), “** Self Organizing Maps for
Time Series”

**Samuel Kaski (Helsinki), “**Dependency exploration”

**Jose Principe (Univ. de Floride), “ **SOM as general
infrastructure for signal processing and controls”

**Takeshi Yamakawa (Kitakiushu), “**Brain-Inspired
SOR Network with Fuzzy Inference Based Evaluation and Its Application to
Controller Design”

** **

**Teuvo Kohonen (Helsinki), **"Is the SOM a
biological model?"

The SOM
paradigm was originally motivated by an attempt to explain some functional structures
of the brain. Quite surprisingly, however, the SOM turned out to be very
useful in exploratory data analysis and started to live a life of its own: some
6000 scientific articles have been based on it. Contrary to that, it is still
not quite sure to what extent the SOM could be regarded as a biophysical model.
At least there does not exist complete physiological evidence for the
following partial functions: 1. The winner-take-all, in particular since
several activity clusters may occur in brain maps concurrently; 2. Implementation
of the neighborhood function, in particular because some newer biochemical
findings contradict with the older hypotheses; 3. The Hebbian law of synaptic
plasticity, since the conditions for synaptic modification can be very
different; and 4. The biological mechanisms for the temporal control of the
learning laws, where newer findings also contadict with older biochemical
hypotheses.

The topic
of this talk is to survey the status of the biological foundations of the SOM. After
that I suggest how the WTA could be replaced by a concurrent, nonlinear enhancement
process that also leads to the ordering of the connections, especially in the
somatosensory maps. With this revision the implementation of the neighborhood
function becomes very simple, and the Hebbian law takes a biologically more
plausible form. Notwithstanding, the original SOM algorithm has still a
superior organizing power, and may be regarded as an abstract idealization of
the biologically more plausible self-organizing processes.

** **

**Jean-Claude Fort (Toulouse), “ **SOM's mathematics ”

Since the
discovery of the SOMs by T. Kohonen many results have been found in order to
get a better description of their behaviour. Most of them are very convincing
but ona mathematician point of view only a few are actually proved. Let's
mention two wellknow facts that have been obseved a million

times but still
unproved :

- the 8
neighbours square grid Som with uniform stimuli on [0,1]^{2} has the
square grid as (unique?) stable equilibrium.

- it is possible
to choose a slowly decreasing step so as it converge to this equilibrium

In this
talk we will list the results actually established and point out some nice
results which it would be satisfying to prove.

**Barbara Hammer
(Clausthal), “** Self Organizing Maps for Time Series”

The
self-organizing map (SOM) as proposed by Kohonen constitutes one of the most
prominent data mining and visualization tools which has successfully been used
in different application areas such as web-mining, telecommunication, image
processing, or, generally speaking, unsupervised detection of information in
large vectorial data sets.

Many real
life data structures possess an inherent temporal characteristics: speech
signals, biological time series such as EEG data, sensor streams as they occur in robotics etc. Since these data
are nonvectorial, consisting of temporal sequences of possibly different and
priorly unlimited length, a direct application of SOM is not possible. Several
extensions of SOM for time series have been proposed in the literature,
including biologically plausible but restricted models such as the temporal
Kohonen map (TKM) or recurrent SOMs, or recent more complex models such as SOM
for data structures or the recursive SOM.

In this
talk, we present a new extension of SOM for temporal structures which is based
on a very simple and sparse recurrence and which allows efficient training as
well as a combination with arbitrary lattice structures.

We
demonstrate its practical applicability in several examples and discuss its
theoretical properties, in particular the internal representation of sequences
within the model and its principled representation ability. It turns out that
the model can be seen as a more efficient and powerful realization of the
encoding scheme intended by TKM.

Afterwards,
we put the approach into a general framework of recursive unsupervised models
which also covers a variety of alternative approaches including the approaches
mentioned above and standard supervised recurrent networks. Based on this
formulation, mathematical properties, benefits and drawbacks of the models can
be investigated in a uniform way. Interestingly, the formulation can be
generalized from sequences to more general tree structures thus opening

the way to
unsupervised processing of general data structures.

The results
presented in this talk are based on joint work with Marc Strickert (IPK
Gatersleben), Alessandro Sperduti (University of Padova), and Alessio Micheli
(University of Pisa).

** **

**Samuel Kaski (Helsinki), “**Dependency exploration”

We have
recently introduced new kinds of data fusion techniques, where the goal is to
find what is shared by data sets, instead of modeling all variation in data. They
extend our earlier works on learning of distance metrics, discriminative
clustering, and other supervised statistical data mining methods. In the new
methods the supervision is symmetric, which translates to mining of
dependencies. We have introduced methods for associative clustering, for
extracting dependent components which generalize classical canonical
correlations, and for non-parametric dependency mining.

** **

**Jose Principe (Univ. de Floride), « **SOM as general infrastructure for
signal processing and controls”

We will
discuss the SOM as a general infrastructure to extract valuable information
from the data in several relevant tasks in signal modeling. Specificaly, we
will describe how the SOM can be used to create competitive multiple models for
system identification and controls of aircrafts, as well as to create time
saving algorithms for information theoretic distances in biomedical pattern
recognition applications.

** **

**Takeshi Yamakawa (Kitakiushu), “**Brain-Inspired
SOR Network with Fuzzy Inference Based Evaluation and Its Application to
Controller Design”

The
self-organizing relationship (SOR) network has been proposed as a brain-inspired neural
network model. The SOR network realizes an approximation of a desired Input/Output (I/O) relationship of a target system
as a result of learning. The SOR
network is effective in case that a set of learning data (desired I/O
relationship) is unavailable but the input-output data obtained by trial and
error can be evaluated. In learning process, I/O vector
pairs with their evaluations are
used. The structure
of the SOR network and evaluation for the I/O vector pairs are equivalent to
the lower brain function and the higher brain function, respectively. In the
human brain, the lower brain function facilitates the mapping from sensory inputs to
motor outputs, and the higher one controls the overall behavior of the learning process of the
mapping. In fact, the evaluation
criterion becomes the key to whether the desired I/O relationship is
successfully approximated or not. Human beings evaluate the
I/O relationship linguistically as
opposed to mathematically when the target system is
complex.

In this paper, we introduce a new evaluation method for the I/O relationship of the SOR network. In the proposed method, the
evaluations are linguistically described with fuzzy if-then rules. After that, the controller is self-organizingly
established by learning of the SOR network. In these processes, only experts’
commonsense knowledge is required. The proposed method is inspired by the
process in which a human being obtains desirable motions by accumulating trial
and error based on one’s evaluation criterion.

The back-up control of a
trailer-truck is very difficult due to its nonlinear mechanism. The proposed method is successfully applied to the trailer-truck back-up
controls both in computer simulations and in practical experiments with a radio
controlled trailer-truck.

** **