Search

• Fitness landscape metrics are used to characterise key properties of the error surfaces of conceptual rainfall runoff models (CRRM) • Enabled large-scale analysis of error surfaces from 420 CRRM combinations with different structures/catchments/error metrics & data length. • Increases in the number of model parameters increases calibration difficulty, decreases calibration efficiency and reduces parameter identifiability. • Increased catchment wetness increases relative roughness of error surfaces and relative optima dispersion. • Opens door to improved CRRM design and selection of better calibration approaches through large-scale analysis of error surfaces. The ease and efficiency with which conceptual rainfall runoff (CRR) models can be calibrated, as well as issues related to the uniqueness of their parameters, has received significant attention in literature. While several studies have tried to gain a better understanding of the underlying factors affecting these issues by examining the features of model error surfaces, this has generally been done in an ad-hoc fashion using lower-dimensional representations of higher-dimensional surfaces. In this paper, it is suggested that exploratory landscape analysis (ELA) metrics can be used to quantify key features of the error surfaces of CRR models, including their roughness and flatness, as well as their degree of optima dispersion throughout the surface. This enables key error surface features of CRR models to be compared in a consistent, efficient and easily communicable fashion for models with different combinations of attributes (e.g. model structure, catchment climate conditions, error metrics, and calibration data set lengths). Results from the application of ELA metrics to the error surfaces of 420 CRR models with different combinations of the above attributes indicate that increasing model complexity results in an increase in relative error surface roughness and relative optima dispersion and that, while increasing catchment wetness increases the relative roughness of error surfaces, it also decreases optima dispersion. This suggests that for the models considered in this study, optimisation efficiency is likely to decrease with increasing model complexity and catchment wetness, while optimisation difficulty is likely to increase and parameter uniqueness likely to decrease with model complexity and catchment dryness. While implications for choice of model complexity will need further work, this study highlights the potential value of the proposed approach to understanding the calibration efficiency, difficulty and parameter uniqueness of conceptual rainfall runoff models. [ABSTRACT FROM AUTHOR]

• ELA metrics can characterize the features of the error surfaces of ANNs. • Error surfaces of simple ANNs have a more well-defined overall shape. • Error surfaces of complex ANNs are flatter with many distributed, deep local optima. • Simple ANNs can be calibrated successfully using gradient-based methods. • Hybrid approach with global and local search are useful for complex ANN calibration. Artificial Neural Network (ANN) models have been used for hydrological and water resources modelling for several decades, where their calibration ("training") has received much attention. The aim of automated calibration processes is to identify values of the model parameters that minimize an error measure between model outputs and corresponding measured values. The degree of difficulty associated with this process is a function of the nature of the relationship between changes in values of model parameters and corresponding changes in the error measure (i.e. the features of the error surface) and the automated method used to identify the combination of model parameters that minimizes the error measure (i.e. the optimization method used to find the global optimum in the error surface). While the impact of different optimization methods has been studied extensively, how the features of the error surface change for different model structures has not. In this paper, it is demonstrated that Exploratory Landscape Analysis (ELA) metrics can be used successfully to characterize the features of the error surfaces of ANN models, thereby helping to explain the reasons for an increase or decrease in calibration difficulty, and in doing so, shedding new light on findings in existing literature. Results show that the error surfaces of single-layer multi-layer perceptrons (MLPs) with fewer hidden nodes have a more well-defined overall shape and have fewer local optima, while the error surfaces of single-layer MLPs with a larger numbers of hidden nodes are flatter and have many distributed, deep local optima. Consequently, single-layer MLPs with a smaller number of hidden nodes can be calibrated successfully using gradient-based methods, such as the back-propagation algorithm, whereas single-layer MLPs with a relatively large number of hidden nodes are best calibrated using hybrid approaches that go beyond basic gradient-based methods (for example, combination of global-based evolutionary algorithms coupled with a local search). [ABSTRACT FROM AUTHOR]

As the derivative of the sigmoid activation function approaches zero, the back propagation algorithm involves flat spots on the error surface of multilayer perceptron (MLP) neural networks, which means the hidden neurons of MLP were saturated. Flat spots can slow down the gradient search and hamper convergence. In this paper, we propose a grading technique to gradually level off the potential flat spots to a sloping surface in a look-ahead mode; and thereby progressively renew the saturated hidden neurons. We introduce a criterion to measure the saturation level of MLP, and then we modify the error function by using a proposed piecewise error function that switches between two cases, regarding the level of MLP saturation. These two cases include the standard error function, when MLP is not saturated, and the modified error function, when MLP is saturated. We recorded considerable improvements, especially in convergence rate and generalization, on the tested benchmark problems. [ABSTRACT FROM AUTHOR]

Vertical accuracy of the processed Shuttle Radar Topographic Mission (SRTM) digital elevation model (DEM) was evaluated using spot height as well as reference DEM. Terrain dependency of error was also explored in relation to elevation, slope and aspect of the terrain. The positive mean error (6.77 ± 1.79 m) indicated that the SRTM DEM was slightly underestimating the elevation and this pattern gradually increases towards higher elevation. The observed root mean square error (RMSE) (27.58 ± 4.22 m) for the region do not fulfill the 16 m RMSE specification of the SRTM mission. High magnitude errors are typical to steep slope (due to overestimation) and in stream valley (due to underestimation). The magnitude of residuals for NW, W and SW facing slope was smaller as compared to their complementary angle. Results also indicated a S and NE components in SRTM DEM because of underestimation and overestimation of elevation, respectively. [ABSTRACT FROM AUTHOR]

This paper gives a detailed analysis of the error surfaces of certain recurrent networks and explains some difficulties encountered in training recurrent networks. We show that these error surfaces contain many spurious valleys, and we analyze the mechanisms that cause the valleys to appear. We demonstrate that the principle mechanism can be understood through the analysis of the roots of random polynomials. This paper also provides suggestions for improvements in batch training procedures that can help avoid the difficulties caused by spurious valleys, thereby improving training speed and reliability. [ABSTRACT FROM AUTHOR]

Abstract: Previous papers have noted the difficulty in obtaining neural models which are stable under simulation when trained using prediction-error-based methods. Here the differences between series–parallel and parallel identification structures for training neural models are investigated. The effect of the error surface shape on training convergence and simulation performance is analysed using a standard algorithm operating in both training modes. A combined series–parallel/parallel training scheme is proposed, aiming to provide a more effective means of obtaining accurate neural simulation models. Simulation examples show the combined scheme is advantageous in circumstances where the solution space is known or suspected to be complex. [Copyright &y& Elsevier]

The limitation of processing power, battery life and memory capacity of portable terminals requires reducing encoding complexity in mobile communications. Motion estimation (ME) is the most computationally intensive module in a typical video codec, which determines not only the encoder’s performance but also the reconstructed video quality. In this paper, a fast ME algorithm for H.264/AVC baseline profile coding is proposed based on the analysis of motion vector field and error surface, and the statistical distributions of different type macroblocks (MBs). Simulation results showed that: in comparison with MVFAST, the proposed algorithm can decrease the computational load over 7.2% with no requirement of expanding memory capacity while maintaining the same video quality as MVFAST. Furthermore, its simplicity makes it easy to be implemented on hardware. [ABSTRACT FROM AUTHOR]

Perceptrons are typically trained to minimize mean square error (MSE). In computer-aided diagnosis (CAD), model performance is usually evaluated according to other more clinically relevant measures. The purpose of this study was to investigate the relationship between MSE and the area (Az) under the receiver operating characteristic (ROC) curve and the high-sensitivity partial ROC area (0.90Az′). A perceptron was used to predict lesion malignancy based on two mammographic findings and patient age. For each performance measure, the error surface in weight space was visualized. Comparison of the surfaces indicated that minimizing MSE tended to maximize Az, but not 0.90Az′. [Copyright &y& Elsevier]