. Several measures have been proposed for comparing nonlinear projection methods but so far no comparisons have taken into account one of their most important properties, the trustworthiness of the resulting neighborhood or proximity relationships. One of the main uses of nonlinear mapping methods is to visualize multivariate data, and in such visualizations it is crucial that the visualized proximities can be trusted upon: If two data samples are close to each other on the display they should be close-by in the original space as well. A local measure of trustworthiness is proposed and it is shown for three data sets that neighborhood relationships visualized by the Self-Organizing Map and its variant, the Generative Topographic Mapping, are more trustworthy than visualizations produced by traditional multidimensional scalingbased nonlinear projection methods. 1

The Self-Organizing Map (SOM) is a powerful neural network method for analysis and visualization of high-dimensional data. It maps nonlinear statistical dependencies between high-dimensional measurement data into simple geometric relationships on a usually twodimensional grid. The mapping roughly preserves the most important topological and metric relationships of the original data elements and, thus, inherently clusters the data. The need for visualization and clustering occur, for instance, in the analysis of various engineering problems. In this paper, the SOM has been applied in monitoring and modeling of complex industrial processes. Case studies, including pulp process, steel production, and paper industry are described.

Abstract. Self-Organizing Maps have a wide range of beneficial properties for data mining, like vector quantization and projection. Several measures exist that quantify the quality of either of these properties. The scope of this work is to describe and compare some of the most well-known measures. This is done by conducting a series of experiments for different map topologies with several well-known data sets. The measures are examined whether they are suited to determine hyperparameters like the optimal map size, how well the measure itself is suited to compare different maps, and if they allow comparison to other algorithms similar to the SOM (e.g. Sammons Mapping). 1

The S-Map is a network with a simple learning algorithm that combines the self-organization capability of the Self-Organizing Map (SOM) and the probabilistic interpretability of the Generative Topographic Mapping (GTM). The simulations suggest that the SMap algorithm has a stronger tendency to self-organize from random initial configuration than the GTM. The S-Map algorithm can be further simplified to employ pure Hebbian learning, without changing the qualitative behaviour of the network. 1 Introduction The self-organizing map (SOM; for a review, see [1]) forms a topographic mapping from the data space onto a (usually two-dimensional) output space. The SOM has been succesfully used in a large number of applications [2]; nevertheless, there are some open theoretical questions, as discussed in [1, 3]. Most of these questions arise because of the following two facts: the SOM is not a generative model, i.e. it does not generate a density in the data space, and it does not have a well-def...

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Introduction The clever handling of control parameters plays an essential role in most learning algorithms. Manipulating the parameters in a convenient way not only may speed up the learning procedure itself but often is responsible for the success of the learning as such. In many learning procedures of practical interest finding the correct learning parameters or cooling strategies is done by trial and error. In a few cases, strong theorems are known which formulate the parameter strategy in an explicit way an example being the Robins-Monroe theorem for the case of stochastic gradient descent. Other examples may be found in [13]. Since these theorems refer to the asymptotic time behavior they are of limited value for practical applications. There an initial learning period is often decisive on whether a meaningful solution is approached during the convergence phase or not. For this reason a variety of empirical parameter-learning procedures has been invented. The self-learning of th

Abstract The Self-Organizing Map (SOM) is a powerful neural network for analysis and visualization of high-dimensional data. It maps nonlinear statistical relationships between high-dimensional input data into simple geometric relationships on a usually twodimensional grid. The mapping roughly preserves the most important topological and metric relationships of the original data elements and, thus, inherently clusters the data. The need for e cient data visualization and clustering is often faced in various engineering problems. In this chapter, SOM based methods are applied in analysis, monitoring and modeling of complex systems. 1.

Abstract. Intrusion Detection Systems (IDS’s) monitor the traffic in computer networks for detecting suspect activities. Connectionist techniques can support the development of IDS’s by modeling ‘normal ’ traffic. This paper presents the application of some unsupervised neural methods to a packet dataset for the first time. This work considers three unsupervised neural methods, namely, Vector Quantization (VQ), Self-Organizing Maps (SOM) and Auto-Associative Back-Propagation (AABP) networks. The former paradigm proves quite powerful in supporting the basic space-spanning mechanism to sift normal traffic from anomalous traffic. The SOM attains quite acceptable results in dealing with some anomalies while it fails in dealing with some others. The AABP model effectively drives a nonlinear compression paradigm and eventually yields a compact visualization of the network traffic progression.

Abstract: The Self-Organizing Map (SOM) is a popular unsupervised neural network able to provide effective clustering and data visualization for data represented in multidimensional input spaces. In this paper we describe Fast Learning SOM (FLSOM) which adopts a learning algorithm that improves the performance of the standard SOM with respect to the convergence time in the training phase. We show that FLSOM also improves the quality of the map by providing better clustering quality and topology preservation of multidimensional input data. Several tests have been carried out on different multidimensional datasets, which demonstrate better performances of the algorithm in comparison with the original SOM.

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