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Framing analyses by self-organizing network

July 18, 2011

As the systems are becoming more and more complex, it is more and more difficult to identify and separate the behaviour patterns and sub-systems in the complex set of transactions and processes in the network through which, the results flows are being transferred. There is a need to translate the multidimensional characteristics of the systems into a low-dimensional indicator describing representative patterns (tacit knowledge). The neural networks, in particular the self-organizing network, offer solutions in doing this.

A self-organizing Kohonen network means a single layer of neurons (nodes) working in a self-organizing competitive mode [Kohonen T. (1988) Self organization and associative memory, Springer Verlag][ Osowski S. (2000) Sieci neuronowe do przetwarzania informacji, Oficyna Wydawnicza PW, Warszawa]. In a Self-Organizing Map (SOM) [Kohonen T.  (1997) Self-Organizing Maps, 2nd Ed. Berlin, Heidelberg, New York: Springer-Verlag] is defined a layer of Kohonen, structured on nodes k disposed spatially in ordered way.

The typical dimensionality for the layer of Kohonen is of two dimensions and evolves during the learning, specialising the positions of the single node k as indicators of the statistical characteristics important for the input stimulus. SOM is also known in literature as Kohonen Feature Map and realize the feature mapping with a technique of non supervised learning. It is possible to represent in a low-dimensional space, the topologies associated to the input data defined in high dimensional spaces. Thus, a cluster of tacit knowledge representing a sort of behaviour invariants may be ‘extracted’ from a set of many behavioural instances.

Let’s consider X as the input vector introduced during the generic cycle of learning. Then it is calculated which node k, between the general kr of the layer of Kohonen, has a vector of the weights Wr closer to X. Once elected the winning node ks, is carried an update of the weights for the same k and for all those that are physically in its neighbourhood in the layer of Kohonen. Doing this procedure, the topological characteristics of the input during the mapping is preserved. The learning continues till the system is in a meta-stable state.

Once the network has learnt, it can be used to give output answers in correspondence to introduced inputs. The output is extracted from the trained layer of Kohonen and it consists in the elected winner node having the vector of the weights with minimal distance from the input vector. The output value is the position of the winner node indicated with a vector of M components. Thus, the behaviour of a system can be described by a set of indicators that can be elements of a vector. It can be used as input vector in a Kohonen network, at whose output it results a set of patterns that will characterize the respective system. During the utilization of Kohonen network, each input vector received from the operation of the respective system, at different moments, will belongs automatically to a certain type of behaviour gathered at the output of the network. Thus, it is obtained the characterization of the system behaviour in time, i.e. a cluster of tacit knowledge.


From → Science

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