The self-organizing map (SOM) is an excellent tool in exploratory phase of data mining. It projects input space on prototypes of a low-dimensional regular grid that can be effectively utilized to visualize and explore properties of the data. When the number of SOM units is large, to facilitate quantitative analysis of the map and the data, similar units need to be grouped, i.e., clustered. In this paper, different approaches to clustering of the SOM are considered. In particular, the use of hierarchical agglomerative clustering and partitive clustering using k-means are investigated. The two-stage procedure--first using SOM to produce the prototypes that are then clustered in the second stage--is found to perform well when compared with direct clustering of the data and to reduce the computation time.

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.

In this paper, we introduce a modeling approach called independent variable group analysis (IVGA) which can be used for finding an efficient structural representation for a given data set. The basic idea is to determine such a grouping for the variables of the data set that mutually dependent variables are grouped together whereas mutually independent or weakly dependent variables end up in separate groups. Computation of an IVGA model requires a combinatorial algorithm for grouping of the variables and a modeling algorithm for the groups. In order to be able to compare different groupings, a cost function which reflects the quality of a grouping is also required. Such a cost function can be derived, for example, using the variational Bayesian approach, which is employed in our study. This approach is also shown to be approximately equivalent to minimizing the mutual information between the groups. The modeling task is computationally demanding. We describe an efficient heuristic grouping algorithm for the variables and derive a computationally light nonlinear mixture model for modeling of the dependencies within the groups. Finally, we carry out a set of experiments which indicate that IVGA may turn out to be beneficial in many different applications.Index Terms-Compact modeling, independent variable group analysis (IVGA), mutual information, variable grouping, variational Bayesian learning.

The Self-Organizing Map (SOM) is one of the most popular neural network methods. It is a powerful tool in visualization and analysis of high-dimensional data in various engineering applications. The SOM maps the data on a two-dimensional grid which may be used as a base for various kinds of visual approaches for clustering, correlation and novelty detection. In this chapter, we present novel methods that enhance the SOM based visualization in correlation hunting and novelty detection. These methods are applied to two industrial case studies: analysis of hot rolling of steel and continuous pulp process. A research software for fast development of SOM based tools is brie y described.

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In this paper, a neural network based analysis method for monitoring and modeling the dynamic behavior of complex industrial processes is considered. The method is based on the unsupervised learning property of the Self-Organizing Map (SOM) algorithm. The time series produced by s e v eral sensors measuring the process parameters as well as other process data are used in mapping the process behavior and dynamics into the network.

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