Growing Self-Organizing Maps for Data Analysis

1996

Two methods providing representation of high-dimensional (input) data in a lowerdimensional (target) space are compared. Although multidimensional scaling (MDS) and Kohonen's self-organizing maps (SOM) are dedicated to very di erent applications both methods are based on an iterative process that tends to approximate the topography o f high-dimensional data and both can be used to model self-organization and unsupervised learning. In general it is impossible to nd a lower-dimensional representation that preserves exactly the topography of high-dimensional data. An error function is de ned to measure the quality of representations and is minimized in an iterative process. The minimal error measures the unavoidable distortion of the original topography represented in the target space.

A performance comparison of two self-organizing networks, the Kohonen Feature Map and the recently proposed Growing Cell Structures is made. For this purpose several performance criteria for self-organizing networks are proposed and motivated. The models are tested with three example problems of increasing difficulty. The Kohonen Feature Map demonstrates slightly superior results only for the simplest problem. For the other more difficult and also more realistic problems the Growing Cell Structures exhibit significantly better performance by every criterion. Additional advantages of the new model are that all parameters are constant over time and that size as well as structure of the network are determined automatically.

2007

In this paper, we introduce a new variant of Growing Self-Organizing Maps (GSOM) based on Alahakoon's algorithm for SOM training; so called 2IBGSOM (Interior and Irregular Boundaries Growing Self-Organizing Maps). It's dynamically evolving structure for SOM, which allocates map size and shape during the unsupervised training process. 2IBGSOM starts with a small number of initial nodes and generates new nodes from the boundary and the interior of the network. 2IBGSOM represents the structure of the training data as accurately as possible. Our proposed method was tested on real world databases and showed better performance than the classical SOM and the Growing Grid (GG) algorithms. Three criteria were used to compare the above algorithms with our proposed method; the quantization error; the topological error and the labeling error to have more accuracy on the produced structure. Results report that 2IBGSOM shows a very good capacity of estimation for the training data based on the three tested factors.

Proceedings of the" 4th European Symposium on …, 1996

Self-Organizing Feature-Mapping (SOFM) algorithm is frequently used for visualization of high-dimensional (input) data in a lower-dimensional (target) space. This algorithm is based on adaptation of parameters in local neighborhoods and therefore does not lead to the best global visualization of the input space data clusters. SOFM is compared here with alternative methods of global visualization of multidimensional data, such as the multidimensional scaling (MDS) and Sammon non-linear mapping, methods based on minimization of error function measuring topographical distortions. SOFM is inferior as a visualization method but facilitates faster classification. A combination of global methods with SOFM should be useful for visualization and classification.

En este artículo se presenta una demostración de los mapas auto organizados de Kohonen's también llamados SOM. Así mismo es realizado un estudio del funcionamiento de los mapas de kohonen en una y dos dimensiones y las características de este tipo de redes que trabajan de forma similar al cerebro humano. Finalmente, son detalladas las características necesarias para realizar el entrenamiento de las redes y la forma como son utilizados sus resultados, con

2017

Data min ing and data visual izati ons are becoming essential parts in inform ation techno logy in recent e ra. Wi thout the existence of data minin g techno logy, big data can be near imposs ible to be ex tracted and have to be done manually. With the aid of data mining techn ology, now information can be gathered from data sets at much shorter time. The di scovery of data visua lizati ons a lso aid s in managing data into presen table fom) that can be understood by everyone. B ig dimensions can now be reduced to help data be more understandable . In this thesis, Kohonen se lf-organiz ing map(SOM) technique is di scussed and examined for data mining and data visualizations. SOM is a neural network technique that can performs data mining, data classificat ion and data visua lizati ons. SOM Too lbox was used on MATLAB. All steps in SOM are exp la ined in detail s from weight initi a lization until trai nin g is stopped . Graphical explanations of how SOM works are a lso used to help ...

2012

As a special class of artificial neural networks the Self Organizing Map is used extensively as a clustering and visualization technique in exploratory data analysis. This chapter provides a general introduction to the structure, algorithm and quality of Self Organizing Maps and presents industrial engineering related applications reported in the literature.

In the paper, we discuss the visualization of multidimensional vectors taking into account the learning flow of the self-organizing neural network. A new algorithm realizing a combination of the self-organizing map (SOM) and Sammon's mapping has been proposed. It takes into account the intermediate learning results of the SOM. The experiments have showed that the algorithm gives lower mean projection errors as compared with a consequent application of the SOM and Sammon's mapping. This is the essential advantage of the new algorithm, i.e. we succeed to eliminate the influence of the "magic factor" α ( 1 0 ≤ <α ) on Sammon's mapping results. For larger values of α ( 1 > α ), the mean projection error grows. However, in this case the new algorithm operates more stable and gives smaller values of the mean projection error.

2015

The SOM is an artificial neural network based on an unsupervised learning process that performs a nonlinear mapping of high dimensional input data onto an ordered and structured array of nodes, designated as the SOM output space. Being simultaneously a quantization algorithm and a projection algorithm, the SOM is able to summarize and map the data, allowing its visualization. Because using the most common visualization methods it is very difficult or even impossible to visualize the SOM defined with more than two dimensions, the SOM output space is generally a regular two dimensional grid of nodes. However, there are no theoretical problems in generating SOMs with higher dimensional output spaces. In this thesis we present evidence that the SOM output space defined in up to three dimensions can be used successfully for the exploratory analysis of spatial data, two-way data and three-way data. Although the differences between the methods that are proposed to visualize each group of data, the approach adopted is commonly based in the projection of colour codes, which are obtained from the output space of 3D SOMs, in some specific bi-dimensional surface, where data can be represented according to its own characteristics. This approach is, in some cases, also complemented with the simultaneous use of SOMs defined in one and two dimensions, so that patterns in data can be properly revealed. The results obtained by using this visualization strategy indicates not only the benefits of using the SOM defined in up to three dimensions but also shows the relevance of the combined and simultaneous use of different models of the SOM in exploratory data analysis.

2000

The growing self-organizing map (GSOM) has been presented as an extended version of the self-organizing map (SOM), which has significant advantages for knowledge discovery applications. In this paper, the GSOM algorithm is presented in detail and the effect of a spread factor, which can be used to measure and control the spread of the GSOM, is investigated. The spread factor is independent of the dimensionality of the data and as such can be used as a controlling measure for generating maps with different dimensionality, which can then be compared and analyzed with better accuracy. The spread factor is also presented as a method of achieving hierarchical clustering of a data set with the GSOM. Such hierarchical clustering allows the data analyst to identify significant and interesting clusters at a higher level of the hierarchy, and as such continue with finer clustering of only the interesting clusters. Therefore, only a small map is created in the beginning with a low spread factor, which can be generated for even a very large data set. Further analysis is conducted on selected sections of the data and as such of smaller volume. Therefore, this method facilitates the analysis of even very large data sets.