Self-organizing maps and symbolic data

International audienceIn data analysis new forms of complex data have to be considered like for example (symbolic data, functional data, web data, trees, SQL query and multimedia data, ...). In this context classical data analysis for knowledge discovery based on calculating the center of gravity can not be used because input are not $\mathbb{R}^p$ vectors. In this paper, we present an application on real world symbolic data using the self-organizing map. To this end, we propose an extension of the self-organizing map that can handle symbolic data

String Measure Applied to String Self-Organizing Maps and Networks of Evolutionary Processors

* Supported by projects CCG08-UAM TIC-4425-2009 and TEC2007-68065-C03-02This paper shows some ideas about how to incorporate a string learning stage in self-organizing algorithms. T. Kohonen and P. Somervuo have shown that self-organizing maps (SOM) are not restricted to numerical data. This paper proposes a symbolic measure that is used to implement a string self-organizing map based on SOM algorithm. Such measure between two strings is a new string. Computation over strings is performed using a priority relationship among symbols; in this case, symbolic measure is able to generate new symbols. A complementary operation is defined in order to apply such measure to DNA strands. Finally, an algorithm is proposed in order to be able to implement a string self-organizing map

Integrating Symbolic and Neural Processing in a Self-Organizing Architechture for Pattern Recognition and Prediction

British Petroleum (89A-1204); Defense Advanced Research Projects Agency (N00014-92-J-4015); National Science Foundation (IRI-90-00530); Office of Naval Research (N00014-91-J-4100); Air Force Office of Scientific Research (F49620-92-J-0225

How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?

In numerous applicative contexts, data are too rich and too complex to be represented by numerical vectors. A general approach to extend machine learning and data mining techniques to such data is to really on a dissimilarity or on a kernel that measures how different or similar two objects are. This approach has been used to define several variants of the Self Organizing Map (SOM). This paper reviews those variants in using a common set of notations in order to outline differences and similarities between them. It discusses the advantages and drawbacks of the variants, as well as the actual relevance of the dissimilarity/kernel SOM for practical applications

Computational physics of the mind

In the XIX century and earlier such physicists as Newton, Mayer, Hooke, Helmholtz and Mach were actively engaged in the research on psychophysics, trying to relate psychological sensations to intensities of physical stimuli. Computational physics allows to simulate complex neural processes giving a chance to answer not only the original psychophysical questions but also to create models of mind. In this paper several approaches relevant to modeling of mind are outlined. Since direct modeling of the brain functions is rather limited due to the complexity of such models a number of approximations is introduced. The path from the brain, or computational neurosciences, to the mind, or cognitive sciences, is sketched, with emphasis on higher cognitive functions such as memory and consciousness. No fundamental problems in understanding of the mind seem to arise. From computational point of view realistic models require massively parallel architectures

Bring ART into the ACT

ACT is compared with a particular type of connectionist model that cannot handle symbols and use non-biological operations that cannot learn in real time. This focus continues an unfortunate trend of straw man "debates" in cognitive science. Adaptive Resonance Theory, or ART, neural models of cognition can handle both symbols and sub-symbolic representations, and meets the Newell criteria at least as well as these models.Air Force Office of Scientific Research (F49620-01-1-0397); Office of Naval Research (N00014-01-1-0624

Fast Algorithm and Implementation of Dissimilarity Self-Organizing Maps

In many real world applications, data cannot be accurately represented by vectors. In those situations, one possible solution is to rely on dissimilarity measures that enable sensible comparison between observations. Kohonen's Self-Organizing Map (SOM) has been adapted to data described only through their dissimilarity matrix. This algorithm provides both non linear projection and clustering of non vector data. Unfortunately, the algorithm suffers from a high cost that makes it quite difficult to use with voluminous data sets. In this paper, we propose a new algorithm that provides an important reduction of the theoretical cost of the dissimilarity SOM without changing its outcome (the results are exactly the same as the ones obtained with the original algorithm). Moreover, we introduce implementation methods that result in very short running times. Improvements deduced from the theoretical cost model are validated on simulated and real world data (a word list clustering problem). We also demonstrate that the proposed implementation methods reduce by a factor up to 3 the running time of the fast algorithm over a standard implementation

Extracting finite structure from infinite language

This paper presents a novel connectionist memory-rule based model capable of learning the finite-state properties of an input language from a set of positive examples. The model is based upon an unsupervised recurrent self-organizing map [T. McQueen, A. Hopgood, J. Tepper, T. Allen, A recurrent self-organizing map for temporal sequence processing, in: Proceedings of Fourth International Conference in Recent Advances in Soft Computing (RASC2002), Nottingham, 2002] with laterally interconnected neurons. A derivation of functionalequivalence theory [J. Hopcroft, J. Ullman, Introduction to Automata Theory, Languages and Computation, vol. 1, Addison-Wesley, Reading, MA, 1979] is used that allows the model to exploit similarities between the future context of previously memorized sequences and the future context of the current input sequence. This bottom-up learning algorithm binds functionally related neurons together to form states. Results show that the model is able to learn the Reber grammar [A. Cleeremans, D. Schreiber, J. McClelland, Finite state automata and simple recurrent networks, Neural Computation, 1 (1989) 372–381] perfectly from a randomly generated training set and to generalize to sequences beyond the length of those found in the training set