Abstract
In this paper a new Back-Propagation (BP) algorithm cost function is appropriately studied for the modeling of air pollution time series. The underlying idea is that of modifying the error definition in order to improve the capabilities of this kind of models to forecast episodes of poor air quality. The proposed error definition can be regarded as a generalization of the traditional squared error cost function thanks to the presence of a parameter α which allows to obtain the ordinary BP as a special case when α = 1. A criterion for choosing this parameter is stated based on setting a-priori a maximum level of allowable false alarms. The goodness of the proposed approach is assessed by means of case studies both on synthetic and measured air quality data.
Similar content being viewed by others
References
G. Finzi and G. Nunnari, “Air Quality Forecast and Alarm Systems, Chapter 16A,” in Air Quality Modelling—Theories, Methodologies, Computational Techniques and Available Databases and Software, vol. 2-Advanced Topics, P. Zannetti (Ed.), The EnviroComp Institute and Air & Wast Management Association, 2005, pp. 397–452.
J. K. Agganwal, Multisensor Fusion for Computer Vision, Springer, Berlin, Germany, 1993.
J. L. Crowley and Y. Z. Demazeau, “Principles and Technique for Sensor Data Fusion,” Signal Process., vol. 32, no. 1, 1993, pp. 5–27.
M. A. Abidi and R. C. Gonzalez (Eds.), Data fusion in robotics and machine intelligence, Academic, San Diego, 1992.
H. Li, B. S. Manjunath, and S. K. Mitra, “Multisensor Image Fusion Using the Wavelet Transform,” Graph. Models and Image Process., vol. 57, no. 3, 1995, pp. 235–245.
L. A. Klein, Sensor and Data Fusion Concepts and Applications, SPIE Opt. Engineering, Tutorial Texts, vol. 14, 1993.
G. Nunnari, A. Nucifora, and C. Randieri, “The Application of Neural Techniques to the Modelling of Time_series of Atmospheric Pollution Data,” Ecol. Model., vol. 111, 1998, pp. 187–205.
M. W. Gardner and S. R. Dorling, “Artificial Neural Networks (the Multilayer Perceptron), a Review of Applications in the Atmospheric Sciences,” Atmos. Environ., vol. 33, 1999, pp. 709–719.
J. Kukkonen, L. Partanen, A. Karppinen, J. Ruuskanen, H. Junninen, M. Kolehmainen, H. Niska, S. Dorling, T. Chatterton, R. Foxall, and G. Cawley, “Extensive Evaluation of Neural Network Models for the Prediction of NO2 and PM10 Concentration, Compared with Deterministic Modelling System and Measurements in Central Helsinki,” Atmos. Environ., vol. 37, 2003, pp. 4539–4550.
A. B. Chelani, R. C. V. Chalapati, K. M. Phadke, and M. Z. Hasan, “Prediction of Sulphure Dioxide Concentration Using Artificial Neural Network,” Environ. Model. Softw., vol. 17, 2002, pp. 161–168.
U. Schlink, S. Dorling, E. Pelikan, G. Nunnari, G. Cawley, H. Junninen, A. Greig, R. Foxall, K. Eben, T. Chatterton, J. Vondrácek, M. Richter, M. Dostal, L. Bertucco, M. Kolehmainen, and M. Doyle, “A Rigorous Inter-comparison of Ground-Level Ozone Predictions,” Atmos. Environ., vol. 37, 2003, pp. 3237–3253.
S. R. Dorling, R. J. Foxall, P. D. Mandic, and G. C. Cawley, “Maximum Likelihood Cost Functions for Neural Networks Models of Air Quality Data,” Atmos. Environ., vol. 37, 2003, pp. 3435–3443.
R. Battiti, “First and Second Order Methods for Learning: Between Steepest Descent and Newton’s Method,” Neural Comput., vol. 4, no. 2, 1992, pp. 141–166.
F. D. Foresee and M. T. Hagan, Gauss-Newton Approximation to Bayesian Regularization, Proceedings of the 1997 International Joint Conference on Neural Networks, 1997, pp. 1930–1935.
M. T. Hagan and M. Menhaj, “Training Feedforward Networks with the Marquardt Algorithm,” IEEE Trans. Neural Netw., vol. 5, no. 6, 1994, pp. 989–993.
D. J. C. MacKay, “Bayesian Interpolation,” Neural Comput., vol. 4, no. 3, 1992, pp. 415–447.
D. E. Rumelhart, G. E. Hinton, and L. McLelland, Parallel Distributed Processing Exploration in the Microstructure of Cognition, vol. 1, MIT, Cambridge, 1986, pp. 45–76.
R. M. Van Aalst and F. A. A. M. De Leeuw, National Ozone Forecasting System and International Data Exchange in Northwest Europe, European Topic Centre on Air Quality, 1997.
K. De Jong, An Analysis of the Behaviour of a Class of Genetic Adaptive Systems. PhD thesis, University of Michigan, 1975.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nunnari, G., CannavÓ, F. A New Cost Function for Air Quality Modeling. J VLSI Sign Process Syst Sign Im 49, 281–290 (2007). https://doi.org/10.1007/s11265-007-0077-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11265-007-0077-2