Interpreting self-organizing maps through space--time data models

Applications of Self-Organizing Maps, 2012

2012

The self-organizing map is an unsupervised neural network first described by the Finnish scientist Teuvo Kohonen. By a self-organizing adaptation process this neural network learns to map the input space onto a discretized representation which preserves the topology and reflects the probability distribution of the input. This book is about how the original selforganizing map as well as variants and extensions of it can be applied in different fields. In fourteen chapters, a wide range of applications of the Self-Organizing Map is discussed. To name a few, these applications include the analysis of financial stability, the fault diagnosis of plants, the creation of well-composed heterogeneous teams and the application of the self-organizing map to the atmospheric sciences.

IEEE Transactions on Neural Networks, 1990

Abstmct-The self-organizing maps have a bearing on traditional vector quantization. A characteristic that makes them more resemble certain biological brain maps, however, is the spatial order of their responses, which is formed in the learning process. This paper discusses the basic algorithms and two innovations: dynamic weighting of the input signals at each input of each cell, which improves the ordering when very different input signals are used, and definition of neighborhoods in the learning algorithm by the minimal spanning tree, which provides a far better and faster approximation of prominently structured density functions. Finally, it is cautioned that if the maps are used for pattern recognition and decision processes, it is necessary to fine tune the reference vectors so that they directly define the decision borders.

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.

Menemui Matematik (Discovering Mathematics), 2016

The Self-organizing map is among the most acceptable algorithm in the unsupervised learning technique for cluster analysis. It is an important tool used to map high-dimensional data sets onto a low-dimensional discrete lattice of neurons. This feature is used for clustering and classifying data. Clustering is the process of grouping data elements into classes or clusters so that items in each class or cluster are as similar to each other as possible. In this paper, we present an overview of self organizing map, its architecture, applications and its training algorithm. Computer simulations have been analyzed based on samples of data for clustering problems.

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.

Neural networks : the official journal of the International Neural Network Society, 2018

Kohonen's Self Organizing feature Map (SOM) provides an effective way to project high dimensional input features onto a low dimensional display space while preserving the topological relationships among the input features. Recent advances in algorithms that take advantages of modern computing hardware introduced the concept of high resolution SOMs (HRSOMs). This paper investigates the capabilities and applicability of the HRSOM as a visualization tool for cluster analysis and its suitabilities to serve as a pre-processor in ensemble learning models. The evaluation is conducted on a number of established benchmarks and real-world learning problems, namely, the policeman benchmark, two web spam detection problems, a network intrusion detection problem, and a malware detection problem. It is found that the visualization resulted from an HRSOM provides new insights concerning these learning problems. It is furthermore shown empirically that broad benefits from the use of HRSOMs in b...

2002

IEEE Transactions on Applications and Industry, 2000

Exploration of large and high-dimensional data sets is one of the main problems in data analysis. Self-organizing maps (SOMs) can be used to map large data sets to a simpler, usually two-dimensional, topological structure. This mapping is able to illustrate dependencies in the data in a very intuitive manner and allows fast location of clusters. However, because of the black-box design of neural networks, it is difficult to get qualitative descriptions of the data. In our approach, we identify regions of interest in SOMs by using unsupervised clustering methods. Then we apply inductive learning methods to find fuzzy descriptions of these clusters. Through the combination of these methods, it is possible to use supervised machine learning methods to find simple and accurate linguistic descriptions of previously unknown clusters in the data.

IEEE Transactions on Neural Networks, 2009

The self-organizing map (SOM) is a powerful method for visualization, cluster extraction, and data mining. It has been used successfully for data of high dimensionality and complexity where traditional methods may often be insufficient. In order to analyze data structure and capture cluster boundaries from the SOM, one common approach is to represent the SOM's knowledge by visualization methods. Different aspects of the information learned by the SOM are presented by existing methods, but data topology, which is present in the SOM's knowledge, is greatly underutilized. We show in this paper that data topology can be integrated into the visualization of the SOM and thereby provide a more elaborate view of the cluster structure than existing schemes. We achieve this by introducing a weighted Delaunay triangulation (a connectivity matrix) and draping it over the SOM. This new visualization, CONNvis, also shows both forward and backward topology violations along with the severity of forward ones, which indicate the quality of the SOM learning and the data complexity. CONNvis greatly assists in detailed identification of cluster boundaries. We demonstrate the capabilities on synthetic data sets and on a real 8-D remote sensing spectral image.