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C.H. Reick . A. Grünewald . B. Page
if for DElAY trammg cycles the validation error improves less than TOL.
Accordingly, as intended, a too long training is prevented, if no significant
improvement can be expected.
It is clear that the choice of the three parameters DElAY, MAXCYC and TOL is
decisive for a proper work of our early stopping algorithm. Therefore one has to
perform some extra training runs to identify viable values for them. They should
be chosen such that the training is stopped either because a "global" minimum is
detected, or because the network improvement gets insignificant but not because
MAXCYC is reached ? this parameter should guarantee only an "emergency stop".
16.4
Case Study: Zooplankton Prediction
In this section we apply crossvalidation and early stopping to an environmental
data set from Greve (1988). The data document the zooplankton development
from 1975 to 1994 at a position close to Helgoland island in the German North
Sea. Every second or third workday the plankton was fished with a net of mesh
size 150 J.!m. Simultaneously several other measurements were made: temperature,
salinity etc. and in particular the water flow through the net. Each plankton
organism from the catch was then visually inspected under a microscope,
identified and counted. By the known water flow the number of individuals could
then be converted into the density of organisms (individuals per cubic meter),
called abundance in the following. The result is a large data set with the
abundances of 45 groups of zooplankton organisms ("taxa") at more than 3200
points of time. In addition we have data for two phytoplankton groups (diatoms
and flagellates) from separate catches at the same position (measured as carbon
mass per cubic meter) and data for seven physical parameters (water temperature,
salinity, phosphate concentration, etc.). Unfortunately the catches were taken
irregularly (all two or three days). To apply time series prediction methods one
has to make the data equidistant. To this end we averaged all data of
approximately one week (actually we averaged over 365.25/52=7.01923 days to
account for intercalary days) so that the final data set has 52 data points for each
of the twenty years.
The main problem with these data is that they are taken from a single point in a
floating environment. Therefore the plankton organisms from two successive
catches may not belong to the same population so that even on the level of
populations there may be no deterministic relationship between two data points.
Moreover it is known that plankton often comes in patches so that also the
representativity of these random sampie plankton measurements is questionable.
And indeed, our extensive prediction studies of this data set indicate that short
time predictions of the abundance are not possible. Nevertheless, if one restriets
oneself to the prediction of only the order of magnitude of the abundances, a
C.H. Reick . A. Grünewald . B. Page
if for DElAY trammg cycles the validation error improves less than TOL.
Accordingly, as intended, a too long training is prevented, if no significant
improvement can be expected.
It is clear that the choice of the three parameters DElAY, MAXCYC and TOL is
decisive for a proper work of our early stopping algorithm. Therefore one has to
perform some extra training runs to identify viable values for them. They should
be chosen such that the training is stopped either because a "global" minimum is
detected, or because the network improvement gets insignificant but not because
MAXCYC is reached ? this parameter should guarantee only an "emergency stop".
16.4
Case Study: Zooplankton Prediction
In this section we apply crossvalidation and early stopping to an environmental
data set from Greve (1988). The data document the zooplankton development
from 1975 to 1994 at a position close to Helgoland island in the German North
Sea. Every second or third workday the plankton was fished with a net of mesh
size 150 J.!m. Simultaneously several other measurements were made: temperature,
salinity etc. and in particular the water flow through the net. Each plankton
organism from the catch was then visually inspected under a microscope,
identified and counted. By the known water flow the number of individuals could
then be converted into the density of organisms (individuals per cubic meter),
called abundance in the following. The result is a large data set with the
abundances of 45 groups of zooplankton organisms ("taxa") at more than 3200
points of time. In addition we have data for two phytoplankton groups (diatoms
and flagellates) from separate catches at the same position (measured as carbon
mass per cubic meter) and data for seven physical parameters (water temperature,
salinity, phosphate concentration, etc.). Unfortunately the catches were taken
irregularly (all two or three days). To apply time series prediction methods one
has to make the data equidistant. To this end we averaged all data of
approximately one week (actually we averaged over 365.25/52=7.01923 days to
account for intercalary days) so that the final data set has 52 data points for each
of the twenty years.
The main problem with these data is that they are taken from a single point in a
floating environment. Therefore the plankton organisms from two successive
catches may not belong to the same population so that even on the level of
populations there may be no deterministic relationship between two data points.
Moreover it is known that plankton often comes in patches so that also the
representativity of these random sampie plankton measurements is questionable.
And indeed, our extensive prediction studies of this data set indicate that short
time predictions of the abundance are not possible. Nevertheless, if one restriets
oneself to the prediction of only the order of magnitude of the abundances, a