A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps

The Self-OrganizingMap (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topologypreservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topologypreservation, particularly using Kohonen's model. In this work, two methods for measuring the topologypreservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving ma

Growing Self-Organizing Maps for Data Analysis

Currently, there exist many research areas that produce large multivariable datasets that are difficult to visualize in order to extract useful information. Kohonen self organizing maps have been used successfully in the visualization and analysis of multidimensional data. In this work, a projection technique that compresses multidimensional datasets into two dimensional space using growing self-organizing maps is described. With this embedding scheme, traditional Kohonen visualization methods have been implemented using growing cell structures networks. New graphical map display have been compared with Kohonen graphs using two groups of simulated data and one group of real multidimensional data selected from a satellite scene

Nonlinear principal component analysis

We study the extraction of nonlinear data models in high-dimensional spaces with modified self-organizing maps. We present a general algorithm which maps low-dimensional lattices into high-dimensional data manifolds without violation of topology. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. Moreover we present a second algorithm for the extraction of generalized principal curves comprising disconnected and branching manifolds. The performance of the algorithm is demonstrated for both one- and two-dimensional principal manifolds and also for the case of sparse data sets. As an application we reveal cluster structures in a set of real world data from the domain of ecotoxicology

Visualization of clusters in geo-referenced data using three-dimensional self-organizing maps

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de InformaçãoThe Self-Organizing Map (SOM) is an artificial neural network that performs simultaneously vector quantization and vector projection. Due to this characteristic, the SOM is an effective method for clustering analysis via visualization. The SOM can be visualized through the output space, generally a regular two-dimensional grid of nodes, and through the input space, emphasizing the vector quantization process. Among all the strategies for visualizing the SOM, we are particularly interested in those that allow dealing with spatial dependency, linking the SOM to the geographic visualization with color. One possible approach, commonly used, is the cartographic representation of data with label colors defined from the output space of a two-dimensional SOM. However, in the particular case of geo-referenced data, it is possible to consider the use of a three-dimensional SOM for this purpose, thus adding one more dimension in the analysis. In this dissertation is presented a method for clustering geo-referenced data that integrates the visualization of both perspectives of a three dimensional SOM: linking its output space to the cartographic representation through a ordered set of colors; and exploring the use of frontiers among geo-referenced elements, computed according to the distances in the input space between their Best Matching Units

Self organizing maps for outlier detection

In this paper we address the problem of multivariate outlier detection using the (unsupervised) self-organizing map (SOM) algorithm introduced by Kohonen. We examine a number of techniques, based on summary statistics and graphics derived from the trained SOM, and conclude that they work well in cooperation with each other. Useful tools include the median interneuron distance matrix and the projection ofthe trained map (via Sammon's projection). SOM quantization errors provide an important complementary source of information for certain type of outlying behavior. Empirical results are reported on both artificial and real data

Vowel recognition using Kohonen\u27s self-organizing feature maps

An important organizing principle observed in the sensory pathways in the brain is the orderly placement of neurons. Although the neurons are structurally identical, the specialized role played by each unit is determined by its internal parameters that are made to change during early learning processes. In the human auditory system, the nerve cells and fibres are arranged in a manner that would elicit maximum response from the neurons when they are activated. Although most of this organization is genetically determined, some of the high level organization is created due to algorithms that promote self-organization. Kohonen\u27s self-organizing feature map is a neural net model that produces feature maps similar to the ones produced in the brain. These maps are capable of describing topological relationships of input signals using a one or two dimensional representation. This technique uses unlabeled data and requires no training as in supervised learning algorithms. It is hence immensely useful in speech and vision applications. This neutral net has been implemented for the recognition of vowels in the American English language. The net has been trained and tested with vowel data. The formation of internal clusters or categories has been observed and closely reflects the tonotopic relationships between the vowels. An analysis of the results has been carried out and the performance has been compared to other classification techniques. A graphical user interface has also been developed using Xview to help visualize the formation of the maps during the training and testing processes

Fusion of Visualization Induced SOM

In this study ensemble techniques have been applied in the frame of topology preserving mappings with visualization purposes. A novel extension of the ViSOM (Visualization Induced SOM) is obtained by the use of the ensemble meta-algorithm and a later fusion process. This main fusion algorithm has two different variants, considering two different criteria for the similarity of nodes. These criteria are Euclidean distance and similarity on Voronoi polygons. The goal of this upgrade is to improve the quality and robustness of the single model. Some experiments performed over different datasets applying the two variants of the fusion and other simpler models are included for comparison purposes

The Induced topology of local minima with applications to artificial neural networks.

by Yun Chung Chu.Thesis (M.Phil.)--Chinese University of Hong Kong, 1992.Includes bibliographical references (leaves 163-[165]).Chapter 1 --- Background --- p.1Chapter 1.1 --- Introduction --- p.1Chapter 1.2 --- Basic notations --- p.4Chapter 1.3 --- Object of study --- p.6Chapter 2 --- Review of Kohonen's algorithm --- p.22Chapter 2.1 --- General form of Kohonen's algorithm --- p.22Chapter 2.2 --- r-neighborhood by matrix --- p.25Chapter 2.3 --- Examples --- p.28Chapter 3 --- Local minima --- p.34Chapter 3.1 --- Theory of local minima --- p.35Chapter 3.2 --- Minimizing the number of local minima --- p.40Chapter 3.3 --- Detecting the success or failure of Kohonen's algorithm --- p.48Chapter 3.4 --- Local minima for different graph structures --- p.59Chapter 3.5 --- Formulation by geodesic distance --- p.65Chapter 3.6 --- Local minima and Voronoi regions --- p.67Chapter 4 --- Induced graph --- p.70Chapter 4.1 --- Formalism --- p.71Chapter 4.2 --- Practical way to find the induced graph --- p.88Chapter 4.3 --- Some examples --- p.95Chapter 5 --- Given mapping vs induced mapping --- p.102Chapter 5.1 --- Comparison between given mapping and induced mapping --- p.102Chapter 5.2 --- Matching the induced mapping to given mapping --- p.115Chapter 6 --- A special topic: application to determination of dimension --- p.131Chapter 6.1 --- Theory --- p.133Chapter 6.2 --- Advanced examples --- p.151Chapter 6.3 --- Special applications --- p.156Chapter 7 --- Conclusion --- p.159Bibliography --- p.16