Chapter 16
Multivariate Time Series Prediction of Marine
Zooplankton by Artificial Neural Networks
C.H. Reick· A. Grünewald . B. Page
16.1
Introduction
Most applications of Neural Networks are based On their high adaptivity to almost
any set of given input-output relations ("patterns"). An example is pattern
recognition: here, a usually complex input, e.g. a picture of a number, has to be
mapped on a much simpler output, e.g. the binary representation of that number.
Networks trained to reproduce such input-output relations can be used to identify
a complex input from the much simpler output.
In applications to time series prediction these input-output relations relate past
to future data. But here the task is not to reproduce a previously known inputoutput relation. Instead one wants the Neural Network to produce correctly from
known past data presently unknown future data. Here another feature of Neural
Networks comes into play, namely their ability to generalize. Neural Networks
cannot only be trained to learn particular input-output relations. During training
they also seem to develop a more general representation of these relations. On the
basis of these relations predictions can be performed. The nature of this more
general representation is not very clear and may depend on the chosen network
structure, but one can understand it as a kind of inter- or extrapolation of the
trained input-output relations. Operationally the ability of a Neural Network to
generalize is usually defined as its ability to produce correct outputs - Le.
predictions in the present context - for inputs that have not been used during
training (see e.g. Hertz et al. (1991». It is clear that an appropriate generalization
may fail, but there are striking examples where this generalization works
extremely weil, e.g. for the prediction of the (secondary) protein structure from its
sequence of amino acids (Rost and Sander 1993) or the prediction of chaotic
dynamics (Wan 1994).
Multivariate Time Series Prediction of Marine
Zooplankton by Artificial Neural Networks
C.H. Reick· A. Grünewald . B. Page
16.1
Introduction
Most applications of Neural Networks are based On their high adaptivity to almost
any set of given input-output relations ("patterns"). An example is pattern
recognition: here, a usually complex input, e.g. a picture of a number, has to be
mapped on a much simpler output, e.g. the binary representation of that number.
Networks trained to reproduce such input-output relations can be used to identify
a complex input from the much simpler output.
In applications to time series prediction these input-output relations relate past
to future data. But here the task is not to reproduce a previously known inputoutput relation. Instead one wants the Neural Network to produce correctly from
known past data presently unknown future data. Here another feature of Neural
Networks comes into play, namely their ability to generalize. Neural Networks
cannot only be trained to learn particular input-output relations. During training
they also seem to develop a more general representation of these relations. On the
basis of these relations predictions can be performed. The nature of this more
general representation is not very clear and may depend on the chosen network
structure, but one can understand it as a kind of inter- or extrapolation of the
trained input-output relations. Operationally the ability of a Neural Network to
generalize is usually defined as its ability to produce correct outputs - Le.
predictions in the present context - for inputs that have not been used during
training (see e.g. Hertz et al. (1991». It is clear that an appropriate generalization
may fail, but there are striking examples where this generalization works
extremely weil, e.g. for the prediction of the (secondary) protein structure from its
sequence of amino acids (Rost and Sander 1993) or the prediction of chaotic
dynamics (Wan 1994).