Self-Organizing Map Convergence

2018 ◽  
Vol 9 (2) ◽  
pp. 61-84 ◽  
Author(s):  
Robert Tatoian ◽  
Lutz Hamel
Keyword(s):  
Quality Measures ◽  
Training Data ◽  
Self Organizing Map ◽  
Self Organizing Maps ◽  
Data Set ◽  
Clustering Problem ◽  
Neighborhood Function ◽  
Real World Datasets ◽  
Clustering Problems ◽  
Self Organizing

Self-organizing maps are artificial neural networks designed for unsupervised machine learning. Here in this article, the authors introduce a new quality measure called the convergence index. The convergence index is a linear combination of map embedding accuracy and estimated topographic accuracy and since it reports a single statistically meaningful number it is perhaps more intuitive to use than other quality measures. The convergence index in the context of clustering problems was proposed by Ultsch as part of his fundamental clustering problem suite as well as real world datasets. First demonstrated is that the convergence index captures the notion that a SOM has learned the multivariate distribution of a training data set by looking at the convergence of the marginals. The convergence index is then used to study the convergence of SOMs with respect to the different parameters that govern self-organizing map learning. One result is that the constant neighborhood function produces better self-organizing map models than the popular Gaussian neighborhood function.

Constraining self-organizing map facies analysis with stratigraphy: An approach to increase the credibility in automatic seismic facies classification

2017 ◽  
Vol 5 (2) ◽  
pp. T163-T171 ◽  
Author(s):  
Tao Zhao ◽  
Fangyu Li ◽  
Kurt J. Marfurt
Keyword(s):  
Facies Analysis ◽  
Vertical Axis ◽  
Training Data ◽  
Seismic Facies ◽  
Self Organizing Map ◽  
Self Organizing Maps ◽  
Data Set ◽  
Statistical Correlations ◽  
Facies Classification ◽  
Self Organizing

Pattern recognition-based seismic facies analysis techniques are commonly used in modern quantitative seismic interpretation. However, interpreters often treat techniques such as artificial neural networks and self-organizing maps (SOMs) as a “black box” that somehow correlates a suite of attributes to a desired geomorphological or geomechanical facies. Even when the statistical correlations are good, the inability to explain such correlations through principles of geology or physics results in suspicion of the results. The most common multiattribute facies analysis begins by correlating a suite of candidate attributes to a desired output, keeping those that correlate best for subsequent analysis. The analysis then takes place in attribute space rather than ([Formula: see text], [Formula: see text], and [Formula: see text]) space, removing spatial trends often observed by interpreters. We add a stratigraphy layering component to a SOM model that attempts to preserve the intersample relation along the vertical axis. Specifically, we use a mode decomposition algorithm to capture the sedimentary cycle pattern as an “attribute.” If we correlate this attribute to the training data, it will favor SOM facies maps that follow stratigraphy. We apply this workflow to a Barnett Shale data set and find that the constrained SOM facies map shows layers that are easily overlooked on traditional unconstrained SOM facies map.

Machine Learning: Automated Knowledge Acquisition Based on Unsupervised Neural Network and Expert System Paradigms

2005 ◽  
Vol 9 (6) ◽  
pp. 693-697 ◽  
Author(s):  
Nazar Elfadil ◽  
Keyword(s):  
Neural Network ◽  
Expert System ◽  
Knowledge Acquisition ◽  
Training Data ◽  
Neural Network Models ◽  
Self Organizing Maps ◽  
Data Set ◽  
Unsupervised Neural Network ◽  
Automated Knowledge ◽  
Self Organizing

Self-organizing maps are unsupervised neural network models that lend themselves to the cluster analysis of high-dimensional input data. Interpreting a trained map is difficult because features responsible for specific cluster assignment are not evident from resulting map representation. This paper presents an approach to automated knowledge acquisition using Kohonen's self-organizing maps and k-means clustering. To demonstrate the architecture and validation, a data set representing animal world has been used as the training data set. The verification of the produced knowledge base is done by using conventional expert system.

scholarly journals Towards model evaluation and identification using Self-Organizing Maps

2008 ◽  
Vol 12 (2) ◽  
pp. 657-667 ◽  
Author(s):  
M. Herbst ◽  
M. C. Casper
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Performance Measures ◽  
Model Identification ◽  
Equivalent Model ◽  
Self Organizing Map ◽  
Watershed Model ◽  
Self Organizing Maps ◽  
Data Set ◽  
Self Organizing

Abstract. The reduction of information contained in model time series through the use of aggregating statistical performance measures is very high compared to the amount of information that one would like to draw from it for model identification and calibration purposes. It has been readily shown that this loss imposes important limitations on model identification and -diagnostics and thus constitutes an element of the overall model uncertainty. In this contribution we present an approach using a Self-Organizing Map (SOM) to circumvent the identifiability problem induced by the low discriminatory power of aggregating performance measures. Instead, a Self-Organizing Map is used to differentiate the spectrum of model realizations, obtained from Monte-Carlo simulations with a distributed conceptual watershed model, based on the recognition of different patterns in time series. Further, the SOM is used instead of a classical optimization algorithm to identify those model realizations among the Monte-Carlo simulation results that most closely approximate the pattern of the measured discharge time series. The results are analyzed and compared with the manually calibrated model as well as with the results of the Shuffled Complex Evolution algorithm (SCE-UA). In our study the latter slightly outperformed the SOM results. The SOM method, however, yields a set of equivalent model parameterizations and therefore also allows for confining the parameter space to a region that closely represents a measured data set. This particular feature renders the SOM potentially useful for future model identification applications.

Application of Spatial Extraction Model for Soil Environmental Quality Anomaly Regions

2013 ◽  
Vol 316-317 ◽  
pp. 415-418
Author(s):  
Chun Lin Yang ◽  
Rui Ping Guo ◽  
Qing Ling Yue
Keyword(s):  
Heavy Metal ◽  
Environmental Quality ◽  
Assessment Model ◽  
Quality Level ◽  
Self Organizing Map ◽  
Concentration Data ◽  
Self Organizing Maps ◽  
Data Set ◽  
Extraction Model ◽  
Self Organizing

An approach for establishment of soil environmental assessment model to evaluate the environmental quality level for soil environmental quality is proposed, in which the GIS and self-organizing map (SOM) techniques are integrated through investigation of soil environmental quality. In this model, self-organizing maps (SOM) and spatial interpolation were applied to cluster a concentration data set of pollutants of soil environmental quality and mapping anomaly region. An application of heavy metal concentrations in soils were surveyed to indicate the status of heavy metal contents and assess environmental quality of soils basing on spatial extraction model. The concentration of 9 metals (Cu, Pb, Zn, Cd, Ni, Cr, Hg, As and Mn) in topsoil were investigated based on samples. The samples were clustered into 3 classes by SOM. According to the concentration level of the samples, the different environmental quality levels were discriminated. The results indicate that SOM as the spatial extraction model was effective to assess the soil environmental quality.

Visually Exploring a Design Space Through the Use of Multiple Contextual Self-Organizing Maps

2011 ◽  
Author(s):  
Trevor Richardson ◽  
Eliot Winer
Keyword(s):  
Design Space ◽  
Contextual Information ◽  
Visual Methods ◽  
Self Organizing Map ◽  
Self Organizing Maps ◽  
Data Set ◽  
Design Variables ◽  
Time Work ◽  
Formal Optimization ◽  
Self Organizing

Understanding relationships amongst n-dimensional design spaces has long been a problem in the engineering community. Many visual methods previously developed, although useful, are limited to comparing three design variables at a time. Work described in this paper builds off the idea of a self-organizing map in order to visualize n-dimensional data on a two dimensional map. By using the contextual self-organizing map, current work shows that more design space information can be gleaned from map nodes themselves. By breaking the final visualization up into three maps containing separate contextual information, an investigator can quickly obtain information about the overall behavior of a design space. Tests run on well-known optimization functions show that information such as modality and curvature may be quickly suggested by these maps, and that they may provide enough information for a designer to choose a function to proceed with formal optimization of a given data set.

An ensemble algorithm for Kohonen self-organizing map with different sizes

2017 ◽  
Vol 25 (6) ◽  
pp. 1020-1033 ◽  
Author(s):  
Leandro Antonio Pasa ◽  
José Alfredo F. Costa ◽  
Marcial Guerra de Medeiros
Keyword(s):  
Data Clustering ◽  
Synthetic Data ◽  
Self Organizing Map ◽  
Cluster Validity ◽  
Stopping Criteria ◽  
Self Organizing Maps ◽  
Single Output ◽  
Kohonen Map ◽  
Clustering Problems ◽  
Self Organizing

Abstract Data Clustering aims to discover groups within the data based on similarities, with a minimal, if any, knowledge of their structure. Variations in the results may occur due to many factors, including algorithm parameters, initialization and stopping criteria. The usage of different attributes or even different subsets of data usually lead to different results. Self-organizing maps (SOM) has been widely used for a variety of tasks regarding data analysis, including data visualization and clustering. A machine committee, or ensemble, is a set of neural networks working independently with some system that enable the combination of individual results into a single output, with the aim to achieve a better generalization compared to a unique neural network. This article presents a new ensemble method that uses SOM networks. Cluster validity indexes are used to combine neuron weights from different maps with different sizes. Results are shown from simulations with real and synthetic data, from the UCI Repository and Fundamental Clustering Problems Suite. The proposed method presented promising results, with increased performance compared with conventional single Kohonen map.

Programmable, Asynchronous, Triangular Neighborhood Function for Self-Organizing Maps Realized on Transistor Level

2010 ◽  
Vol 56 (4) ◽  
pp. 367-373
Author(s):  
Marta Kolasa ◽  
Rafał Długosz ◽  
Krzysztof Bieliński
Keyword(s):  
Circuit Complexity ◽  
Self Organizing Maps ◽  
Data Set ◽  
Ultra Low Power ◽  
Chip Area ◽  
Software Model ◽  
Neighborhood Function ◽  
The Neural Network ◽  
Data Rates ◽  
Self Organizing

Programmable, Asynchronous, Triangular Neighborhood Function for Self-Organizing Maps Realized on Transistor LevelA new hardware implementation of the triangular neighborhood function (TNF) for ultra-low power, Kohonen self-organizing maps (SOM) realized in the CMOS 0.18μm technology is presented. Simulations carried out by means of the software model of the SOM show that even low signal resolution at the output of the TNF block of 3-6 bits (depending on input data set) does not lead to significant disturbance of the learning process of the neural network. On the other hand, the signal resolution has a dominant influence on the overall circuit complexity i.e. the chip area and the energy consumption. The proposed neighborhood mechanism is very fast. For an example neighborhood range of 15 a delay between the first and the last neighboring neuron does not exceed 20 ns. This in practice means that the adaptation process starts in all neighboring neurons almost at the same time. As a result, data rates of 10-20 MHz are achievable, independently on the number of neurons in the map. The proposed SOM dissipates the power in-between 100 mW and 1 W, depending on the number of neurons in the map. For the comparison, the same network realized on PC achieves in simulations data rates in-between 10 Hz and 1 kHz. Data rate is in this case linearly dependend on the number of neurons.

Self-Organizing Maps with Asymmetric Neighborhood Function

2007 ◽  
Vol 19 (9) ◽  
pp. 2515-2535 ◽  
Author(s):  
Takaaki Aoki ◽  
Toshio Aoyagi
Keyword(s):  
Principal Component ◽  
Two Dimensions ◽  
Data Sets ◽  
Self Organizing Map ◽  
Self Organizing Maps ◽  
Neighborhood Function ◽  
Som Algorithm ◽  
The One ◽  
Low Dimensional ◽  
Self Organizing

The self-organizing map (SOM) is an unsupervised learning method as well as a type of nonlinear principal component analysis that forms a topologically ordered mapping from the high-dimensional data space to a low-dimensional representation space. It has recently found wide applications in such areas as visualization, classification, and mining of various data. However, when the data sets to be processed are very large, a copious amount of time is often required to train the map, which seems to restrict the range of putative applications. One of the major culprits for this slow ordering time is that a kind of topological defect (e.g., a kink in one dimension or a twist in two dimensions) gets created in the map during training. Once such a defect appears in the map during training, the ordered map cannot be obtained until the defect is eliminated, for which the number of iterations required is typically several times larger than in the absence of the defect. In order to overcome this weakness, we propose that an asymmetric neighborhood function be used for the SOM algorithm. Compared with the commonly used symmetric neighborhood function, we found that an asymmetric neighborhood function accelerates the ordering process of the SOM algorithm, though this asymmetry tends to distort the generated ordered map. We demonstrate that the distortion of the map can be suppressed by improving the asymmetric neighborhood function SOM algorithm. The number of learning steps required for perfect ordering in the case of the one-dimensional SOM is numerically shown to be reduced from O(N3) to O(N2) with an asymmetric neighborhood function, even when the improved algorithm is used to get the final map without distortion.

Sign in / Sign up

Export Citation Format

Share Document