Review of the self-organizing map (SOM) approach in water resources: Analysis, modelling and application

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Abstract

The use of artificial neural networks (ANNs) in problems related to water resources has received steadily increasing interest over the last decade or so. The related method of the self-organizing map (SOM) is an unsupervised learning method to analyze, cluster, and model various types of large databases. There is, however, still a notable lack of comprehensive literature review for SOM along with training and data handling procedures, and potential applicability. Consequently, the present paper aims firstly to explain the algorithm and secondly, to review published applications with main emphasis on water resources problems in order to assess how well SOM can be used to solve a particular problem. It is concluded that SOM is a promising technique suitable to investigate, model, and control many types of water resources processes and systems. Unsupervised learning methods have not yet been tested fully in a comprehensive way within, for example water resources engineering. However, over the years, SOM has displayed a steady increase in the number of applications in water resources due to the robustness of the method.

Introduction

Modelling of hydrological processes that are embedded with high complexity, dynamism, and non-linearity in both spatial and temporal scales is of prime importance for hydrologists and water resources engineers. In many cases, however, the lack of physical understanding of the complex processes involved creates problems to find efficient models. Over the last decades artificial neural networks (ANNs) have been subject to an increasing interest in water resources problems. This has led to a tremendous surge in research activities (ASCE, 2000b, Maier and Dandy, 2000, Dawson and Wilby, 2001, Alp and Cigizoglu, 2007, Darsono and Labadie, 2007, Iliadis and Maris, 2007, Raduly et al., 2007). The increasing number of applications of ANNs in modelling of hydrological processes is related to their ability to relate input and output variables in complex systems without any requirement of a detailed understanding of the physics of the process involved (Dawson and Wilby, 2001). According to ASCE, 2000a, ASCE, 2000b, an ANN is a massively parallel-distributed information processing system resembling biological neural networks of the human brain and capable of solving large-scale complex problems such as pattern recognition, non-linear modelling, classification, and control. The feed-forward multi-layer perceptron (MLP) is the most widely used ANN for prediction and forecasting of water resources variables (Maier and Dandy, 2000). Detailed reviews of ANNs along with assessments of their application in water resources and hydrology can be found in Maier and Dandy, 2000, ASCE, 2000a, ASCE, 2000b, and Dawson and Wilby (2001). The self-organizing map (SOM; also called Kohonen map or topology preserving feature map) is a kind of ANN method which is capable of clustering, classification, estimation, prediction, and data mining (Alhoniemi et al., 1999, Vesanto and Alhoniemi, 2000, Kohonen, 2001) in a wide-spread range of disciplines regarding signal recognition, organization of large collections of data, process monitoring and analysis, and modelling as well as water resources problems. Typical for an SOM is that the desired solutions or targets are not given and the network intelligently learns to cluster the data by recognizing different patterns.

Despite the rather broad existing literature about ANN methods, in particular feed-forward MLPs (i.e., Maier and Dandy, 2000, ASCE, 2000a, ASCE, 2000b, Dawson and Wilby, 2001), there is a notable lack of comprehensive literature review on the efficiency of unsupervised learning techniques. Consequently, the main objective of this paper is to explain the SOM algorithm and to review the successes or failures of published applications with main emphasis on water resources and related disciplines. The paper is organized into two main parts. In the first part, the feed-forward MLP and SOM methods are explained along with a presentation of their structural differences. In the second part, published applications of the SOM method in water resources problems and related disciplines are reviewed and evaluated. We close the paper by giving some future avenues for the application of SOMs in water resources.

Section snippets

Feed-forward multi-layer perceptron (MLP)

As stated above, the most commonly used ANN in water resources and hydrology is the feed-forward MLP as shown in Fig. 1. In this figure, each neuron is represented by a circle and each connection weight by a line, and the structure of an individual neuron is shown. Each individual neuron computes an output, based on the weighted sum of all its inputs, according to a non-linear function called the activation function such as the hyperbolic tangent(see Fig. 1 and Eq. (1)):f(x)=21+2(x)1or the

Applications in water resources and hydrology

In the former section, we briefly discussed the SOM structure, and its basic concepts along with procedures required to apply the SOM algorithm to a data set. In this section, we review some successful SOM applications with emphasis on innovative and creative solutions for analysis, estimation and prediction of various hydrological processes such as precipitation, river flow, rainfall–runoff, surface water quality, and other related disciplines such as climate and environment.

Conclusion and discussion

Over the last decades, SOMs have increasingly been used for analysis, estimation and prediction of various hydrological processes such as river flow, rainfall–runoff, precipitation, surface water quality, and related issues such as climate and environment. These studies indicate that in many cases, SOM can outperform other methods to solve various problems in water resources and hydrology. However, like feed-forward MLP applications, SOM applications are generally dependent on ad-hoc approaches

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