Fractals everywhere
Neural Networks
Entropic feature for sequence pattern through iterated function systems
Pattern Recognition Letters
Recursive self-organizing maps
Neural Networks - New developments in self-organizing maps
Self-organizing maps with recursive neighborhood adaptation
Neural Networks - New developments in self-organizing maps
Principles and networks for self-organization in space-time
Neural Networks - New developments in self-organizing maps
Architectural bias in recurrent neural networks: fractal analysis
Neural Computation
Recursive self-organizing network models
Neural Networks - 2004 Special issue: New developments in self-organizing systems
Neurocomputing
IEEE Transactions on Neural Networks
ViSOM - a novel method for multivariate data projection and structure visualization
IEEE Transactions on Neural Networks
A self-organizing map for adaptive processing of structured data
IEEE Transactions on Neural Networks
Markovian architectural bias of recurrent neural networks
IEEE Transactions on Neural Networks
Gamma SOM for Temporal Sequence Processing
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
Gamma-filter self-organizing neural networks for time series analysis
WSOM'11 Proceedings of the 8th international conference on Advances in self-organizing maps
Self-organized reservoirs and their hierarchies
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part I
Model-based kernel for efficient time series analysis
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
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Recently there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, there is no general consensus as to how best to process sequences using topographic maps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizing map (SOM) for processing sequential data, recursive SOM(RecSOM) (Voegtlin, 2002), as a nonautonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed-input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data.