Chapter 14 . Time-Series Prediction of Chlorophyll a in Lakes
287
2. Consideration of a time lag between inputs and outputs improved performance
on mesotrophic, temperate lakes, but reduced performance on warmer eutrophic
lakes. This may be due to fundamental differences in the algal community
structures between these classes of lakes.
3. Higher numbers of hidden nodes in combination with low error of stopped
training caused a clear increase in model variance indicative of overfitting.
4. Aggregation of replicated model predictions by averaging (bagging) reduced
high variance caused by overfitting. Thus bagging can be recommended to
modellers as a technique for reducing the dependence of ANN model
performance on tuning stopping error, hidden node number, weight decay
parameters etc.
5. Non-linearity provided by ANN hidden layer neurons brought a consistent
prediction advantage in the Myponga Reservoir and Lake Burrninjuck models.
These databases are therefore good candidates for future work using rule
discovery techniques by means of evolutionary computation.
Acknowledgements
We are very grateful to Michio Kumagai, Lake Biwa Research Institute, Japan,
Myriam Bormans, CSIRO Land and Water, Australia, Noriko Takamura, National
Institute for Environmental Studies, Japan, Mike Burch, Australian Water Quality
Centre, Australia, and Bomchul Kim, Kangwon National University, South Korea,
for making invaluable lake data available for the present study.
References
Abu-Mostafa YS (1989) The Vapnik-Chervonenkis dimension: information versus
complexity in leaming. Neural Computation 1 :312-317
Baxt W G, White H (1995) Bootstrapping Confidence Intervals for Clinical Input Variable
Effects in a Network Trained to Identify the Presence of Acute Myocardial Infarction.
Neural Computation 7:624-638
Breiman L (1996) Bagging predictors. Machine Leaming 26(2):123-140
Cheng B, Titterington DM (1994) Neural networks: a review from a statistical perspective.
Statistical Science 9:2-54
Efron B, Tibshirani R (1993) An introduction to the bootstrap. Chapman and Hall, New
York
Ferguson AJD (1997) The role of modelling in the control of toxic blue-green algae.
Hydrobiologia 349: 1-4
Finnoff W, Hergert F, Zimmermann HG (1993) Improving model selection by
nonconvergent methods. Neural Networks 6:771-783
French M, Recknagel F (1994) Modelling algal blooms in freshwaters using artificial neural
networks. In: Zannetti (Ed) Computer Techniques in Environmental Studies V, Vol. II:
Environmental Systems. Computer Mechanics Publications, Southhampton, Boston
287
2. Consideration of a time lag between inputs and outputs improved performance
on mesotrophic, temperate lakes, but reduced performance on warmer eutrophic
lakes. This may be due to fundamental differences in the algal community
structures between these classes of lakes.
3. Higher numbers of hidden nodes in combination with low error of stopped
training caused a clear increase in model variance indicative of overfitting.
4. Aggregation of replicated model predictions by averaging (bagging) reduced
high variance caused by overfitting. Thus bagging can be recommended to
modellers as a technique for reducing the dependence of ANN model
performance on tuning stopping error, hidden node number, weight decay
parameters etc.
5. Non-linearity provided by ANN hidden layer neurons brought a consistent
prediction advantage in the Myponga Reservoir and Lake Burrninjuck models.
These databases are therefore good candidates for future work using rule
discovery techniques by means of evolutionary computation.
Acknowledgements
We are very grateful to Michio Kumagai, Lake Biwa Research Institute, Japan,
Myriam Bormans, CSIRO Land and Water, Australia, Noriko Takamura, National
Institute for Environmental Studies, Japan, Mike Burch, Australian Water Quality
Centre, Australia, and Bomchul Kim, Kangwon National University, South Korea,
for making invaluable lake data available for the present study.
References
Abu-Mostafa YS (1989) The Vapnik-Chervonenkis dimension: information versus
complexity in leaming. Neural Computation 1 :312-317
Baxt W G, White H (1995) Bootstrapping Confidence Intervals for Clinical Input Variable
Effects in a Network Trained to Identify the Presence of Acute Myocardial Infarction.
Neural Computation 7:624-638
Breiman L (1996) Bagging predictors. Machine Leaming 26(2):123-140
Cheng B, Titterington DM (1994) Neural networks: a review from a statistical perspective.
Statistical Science 9:2-54
Efron B, Tibshirani R (1993) An introduction to the bootstrap. Chapman and Hall, New
York
Ferguson AJD (1997) The role of modelling in the control of toxic blue-green algae.
Hydrobiologia 349: 1-4
Finnoff W, Hergert F, Zimmermann HG (1993) Improving model selection by
nonconvergent methods. Neural Networks 6:771-783
French M, Recknagel F (1994) Modelling algal blooms in freshwaters using artificial neural
networks. In: Zannetti (Ed) Computer Techniques in Environmental Studies V, Vol. II:
Environmental Systems. Computer Mechanics Publications, Southhampton, Boston