Juha Vesanto

Clustering of the self-organizing map

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.

SOM-based data visualization methods

The self-organizing map SOM is an efficient tool for visualization of multidimensional numerical data. In this paper, an overview and categorization of both old and new methods for the visualization of SOM is presented. The purpose is to give an idea of what kind of information can be acquired from different presentations and how the SOM can best be utilized in exploratory data visualization. Most of the presented methods can also be applied in the more general case of first making a vector quantization e.g. k-means and then a vector projection e.g. Sammons mapping.

An approach to automated interpretation of SOM

The objective of this work was to develop automatic tools for post-processing of SOMs, especially in the context of hierarchical data — data where each higher level object consists of a varying number of lower level objects. Both low and high level data is available and needs to be utilized. The information from lower levels is transferred to higher level using data histograms of lower level clusters. The clusters are formed and interpreted automatically so as to summarize the information given by the SOM, and to produce meaningful indicators that are useful also to problem domain experts. The results show that the approach works well at least in the case study of pulp and paper mills technology data.

Distance Matrix Based Clustering of the Self-Organizing Map

Clustering of data is one of the main applications of the Self-Organizing Map (SOM). U-matrixis a commonly used technique to cluster the SOM visually. However, in order to be really useful, clustering needs to be an automated process. There are several techniques which can be used to cluster the SOM autonomously, but the results they provide do not follow the results of U-matrixv ery well. In this paper, a clustering approach based on distance matrices is introduced which produces results which are very similar to the U-matrix. It is compared to other SOMbased clustering approaches.

An Automated Report Generation Tool for the Data Understanding Phase

To successfully prepare and model data, the data miner needs to be aware of the properties of the data manifold. In this chapter, the outline of a tool for automatically generating data survey reports for this purpose is described. Such a report is used as a starting point for data understanding, acts as documentation of the data, and can easily be redone if necessary. The main focus is on describing the cluster structure and the contents of the clusters. The described system combines linguistic descriptions (rules) and statistical measures with visualizations. Whereas rules and mathematical measures give quantitative information, the visualizations give qualitative information on the data sets, and help the user to form a mental model of the data based on the suggested rules and other characterizations.

Monitoring And Modeling Of Complex Processes Using Hierarchical Self-organizing Maps

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 several sensors measuring the process parameters as well as other process data are used in mapping the process behavior and dynamics into the network.

Self-Organizing map in analysis of large-scale industrial systems

Publisher Summary This chapter discusses the characterization of industrial processes that is traditionally done based on analytic system models. The models may be constructed using knowledge based on physical phenomena and on assumptions of the system behavior. The measurement data and other types of information are typically stored in databases. In many practical situations, even minor knowledge about the characteristic behavior of the system might be useful. The chapter explores the self-organizing map (SOM), which is a powerful tool in visualization and analysis of high-dimensional data in 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 like clustering, correlation, and novelty detection. In this chapter, the methods are discussed and applied to the analysis of hot rolling of steel, continuous pulping process, and technical data from worlds pulp and paper mills.

Importance of Individual Variables in the k -Means Algorithm

In this paper, quantization errors of individual variables in k-means quantization algorithm are investigated with respect to scaling factors, variable dependency, and distribution characteristics. It is observed that Z-norm standardation limits average quantization errors per variable to unit range. Two measures, quantization quality and effective number of quantization points are proposed for evaluating the goodness of quantization of individual variables. Both measures are invariant with respect to scaling/variances of variables. By comparing these measures between variables, a sense of the relative importance of variables is gained.

Analysis of industrial systems using the self-organizing map

The self-organizing map (SOM) is a neural network algorithm which is especially suitable for the analysis and visualization of high-dimensional data. It maps nonlinear statistical relationships between high-dimensional input data into simple geometric relationships, usually on a two-dimensional 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 occurs in various engineering applications, in the analysis of complex processes or systems. In addition, SOM allows easy data fusion enabling visualization and analysis of large databases of industrial systems. As a case study, the SOM has been used to cluster the pulp and paper mills of the world.