**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
(**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),**

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
(

** **

**Samuel
Kaski (**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.