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.

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

2007 ◽  
Vol 4 (6) ◽  
pp. 3953-3978 ◽  
Author(s):  
M. Herbst ◽  
M. C. Casper
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Performance Measures ◽  
Model Identification ◽  
Self Organizing Map ◽  
Watershed Model ◽  
Self Organizing Maps ◽  
Statistical Measures ◽  
Self Organizing

Abstract. The reduction of information contained in model time series through the use of aggregating statistical measures is very high compared to the amount of information that one would like to draw from it for model identification and calibration purposes. Applied within a model identification context, aggregating statistical performance measures are inadequate to capture details on time series characteristics. It has been readily shown that this loss of information on the residuals 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 the model realizations among the Monte-Carlo simulations 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).

scholarly journals Mapping model behaviour using Self-Organizing Maps

2008 ◽  
Vol 5 (6) ◽  
pp. 3517-3555 ◽  
Author(s):  
M. Herbst ◽  
H. V. Gupta ◽  
M. C. Casper
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Model Performance ◽  
Model Parameters ◽  
Self Organizing Map ◽  
Watershed Model ◽  
Monte Carlo Data ◽  
Statistical Measures ◽  
Trade Offs ◽  
Self Organizing

Abstract. Hydrological model evaluation and identification essentially depends on the extraction of information from model time series and its processing. However, the type of information extracted by statistical measures has only very limited meaning because it does not relate to the hydrological context of the data. To overcome this inadequacy we exploit the diagnostic evaluation concept of Signature Indices, in which model performance is measured using theoretically relevant characteristics of system behaviour. In our study, a Self-Organizing Map (SOM) is used to process the Signatures extracted from Monte-Carlo simulations generated by a distributed conceptual watershed model. The SOM creates a hydrologically interpretable mapping of overall model behaviour, which immediately reveals deficits and trade-offs in the ability of the model to represent the different functional behaviours of the watershed. Further, it facilitates interpretation of the hydrological functions of the model parameters and provides preliminary information regarding their sensitivities. Most notably, we use this mapping to identify the set of model realizations (among the Monte-Carlo data) that most closely approximate the observed discharge time series in terms of the hydrologically relevant characteristics, and to confine the parameter space accordingly. Our results suggest that Signature Index based SOMs could potentially serve as tools for decision makers inasmuch as model realizations with specific Signature properties can be selected according to the purpose of the model application. Moreover, given that the approach helps to represent and analyze multi-dimensional distributions, it could be used to form the basis of an optimization framework that uses SOMs to characterize the model performance response surface. As such it provides a powerful and useful way to conduct model identification and model uncertainty analyses.

scholarly journals Mapping model behaviour using Self-Organizing Maps

2009 ◽  
Vol 13 (3) ◽  
pp. 395-409 ◽  
Author(s):  
M. Herbst ◽  
H. V. Gupta ◽  
M. C. Casper
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Model Performance ◽  
Model Parameters ◽  
Self Organizing Map ◽  
Watershed Model ◽  
Monte Carlo Data ◽  
Statistical Measures ◽  
Trade Offs ◽  
Self Organizing

Abstract. Hydrological model evaluation and identification essentially involves extracting and processing information from model time series. However, the type of information extracted by statistical measures has only very limited meaning because it does not relate to the hydrological context of the data. To overcome this inadequacy we exploit the diagnostic evaluation concept of Signature Indices, in which model performance is measured using theoretically relevant characteristics of system behaviour. In our study, a Self-Organizing Map (SOM) is used to process the Signatures extracted from Monte-Carlo simulations generated by the distributed conceptual watershed model NASIM. The SOM creates a hydrologically interpretable mapping of overall model behaviour, which immediately reveals deficits and trade-offs in the ability of the model to represent the different functional behaviours of the watershed. Further, it facilitates interpretation of the hydrological functions of the model parameters and provides preliminary information regarding their sensitivities. Most notably, we use this mapping to identify the set of model realizations (among the Monte-Carlo data) that most closely approximate the observed discharge time series in terms of the hydrologically relevant characteristics, and to confine the parameter space accordingly. Our results suggest that Signature Index based SOMs could potentially serve as tools for decision makers inasmuch as model realizations with specific Signature properties can be selected according to the purpose of the model application. Moreover, given that the approach helps to represent and analyze multi-dimensional distributions, it could be used to form the basis of an optimization framework that uses SOMs to characterize the model performance response surface. As such it provides a powerful and useful way to conduct model identification and model uncertainty analyses.

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.

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.

Exploring the multiscale changeability of precipitation using the entropy concept and self-organizing maps

2019 ◽  
Vol 11 (3) ◽  
pp. 655-676
Author(s):  
Kiyoumars Roushangar ◽  
Farhad Alizadeh ◽  
Jan Adamowski ◽  
Seyed Mehdi Saghebian
Keyword(s):  
Time Series ◽  
Annual Precipitation ◽  
Optimum Number ◽  
Self Organizing Map ◽  
Self Organizing Maps ◽  
Time Frequency ◽  
Modes Of Variability ◽  
Rain Gauges ◽  
Spatio Temporal ◽  
Self Organizing

Abstract This study utilized a spatio-temporal framework to assess the dispersion and uncertainty of precipitation in Iran. Thirty-one rain gauges with data from 1960 to 2010 were selected in order to apply the entropy concept and study spatio-temporal variability of precipitation. The variability of monthly, seasonal and annual precipitation series was studied using the marginal disorder index (MDI). To investigate the intra-annual and decadal distribution of monthly and annual precipitation values, the apportionment disorder index (ADI) and decadal ADI (DADI) were applied to the time series. The continuous wavelet transform was used to decompose the ADI time series into time-frequency domains. The decomposition of the ADI series into different zones helped to identify the dominant modes of variability and the variation of those modes over time. The results revealed the high disorderliness in the amount of precipitation for different temporal scales based on disorder indices. Based on the DI outcome for all rain gauges, a self-organizing map (SOM) was trained to find the optimum number of clusters (seven) of rain gauges. It was observed from the clustering that there was hydrologic similarity in the clusters apart from the geographic neighborhood.

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.

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.

scholarly journals The Spread of the COVID-19 Outbreak in Brazil: An Overview by Kohonen Self-Organizing Map Networks

Medicina ◽  
2021 ◽  
Vol 57 (3) ◽  
pp. 235
Author(s):  
Diego Galvan ◽  
Luciane Effting ◽  
Hágata Cremasco ◽  
Carlos Adam Conte-Junior
Keyword(s):  
The Self ◽  
Self Organizing Map ◽  
Virus Spread ◽  
Self Organizing Maps ◽  
The North ◽  
Som Clustering ◽  
Unsupervised Neural Networks ◽  
Mining Tools ◽  
Temporal Spread ◽  
Self Organizing

Background and objective: In the current pandemic scenario, data mining tools are fundamental to evaluate the measures adopted to contain the spread of COVID-19. In this study, unsupervised neural networks of the Self-Organizing Maps (SOM) type were used to assess the spatial and temporal spread of COVID-19 in Brazil, according to the number of cases and deaths in regions, states, and cities. Materials and methods: The SOM applied in this context does not evaluate which measures applied have helped contain the spread of the disease, but these datasets represent the repercussions of the country’s measures, which were implemented to contain the virus’ spread. Results: This approach demonstrated that the spread of the disease in Brazil does not have a standard behavior, changing according to the region, state, or city. The analyses showed that cities and states in the north and northeast regions of the country were the most affected by the disease, with the highest number of cases and deaths registered per 100,000 inhabitants. Conclusions: The SOM clustering was able to spatially group cities, states, and regions according to their coronavirus cases, with similar behavior. Thus, it is possible to benefit from the use of similar strategies to deal with the virus’ spread in these cities, states, and regions.

scholarly journals Geospatial Analysis of Extreme Weather Events in Nigeria (1985–2015) Using Self-Organizing Maps

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Adeoluwa Akande ◽  
Ana Cristina Costa ◽  
Jorge Mateu ◽  
Roberto Henriques
Keyword(s):  
Extreme Precipitation ◽  
Large Scale ◽  
Northern Region ◽  
Extreme Weather Events ◽  
Self Organizing Map ◽  
Spatial And Temporal Patterns ◽  
Self Organizing Maps ◽  
The North ◽  
Precipitation Regimes ◽  
Self Organizing

The explosion of data in the information age has provided an opportunity to explore the possibility of characterizing the climate patterns using data mining techniques. Nigeria has a unique tropical climate with two precipitation regimes: low precipitation in the north leading to aridity and desertification and high precipitation in parts of the southwest and southeast leading to large scale flooding. In this research, four indices have been used to characterize the intensity, frequency, and amount of rainfall over Nigeria. A type of Artificial Neural Network called the self-organizing map has been used to reduce the multiplicity of dimensions and produce four unique zones characterizing extreme precipitation conditions in Nigeria. This approach allowed for the assessment of spatial and temporal patterns in extreme precipitation in the last three decades. Precipitation properties in each cluster are discussed. The cluster closest to the Atlantic has high values of precipitation intensity, frequency, and duration, whereas the cluster closest to the Sahara Desert has low values. A significant increasing trend has been observed in the frequency of rainy days at the center of the northern region of Nigeria.

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