2.2.3.3 Approaches used for simulations

 For simulations presented in this thesis, the winner is always the expert with the

best performance (i.e., lowest criterion value), but the gate and the way the experts are

adapted and monitored vary. Most of the algorithms in the gated competitive experts

framework require repeated training of the non-linear experts through the whole data set.

In this thesis, we try to develop an online segmentation method, with only one run

through the data. Therefore the training is done in an online fashion, at the same time as

the segmentation, and the output of the system is chosen to be only the output of the

winner at that particular time step (2.10).

 output(n) = output ,,,,,.. ,,, (n) (2.10)

 This would ensure that the experts actually track the regimes, and are updated as

more information comes. We can assume that if some process parameters exhibit a slow

change (like the lung compliance), this approach will adapt the experts so that they still

recognize each type of breath. Following are the approaches chosen for the simulations,

the first is supervised, and the other ones are unsupervised.

* Approach I: For every type of expert, first a sequential change point detection is
 performed, where the experts are trained on a sample data set of the regime they are
 supposed to explain, and then by processing all the data through the experts, the
 criterion is monitored, and a winner is chosen at every time step without adapting
 the experts. Since the data we consider is not even piecewise stationary (there are
 changes in any regime from one segment to the other), this approach is not
 expected to perform well.

* Approach II: The simplest gate model is the identical to the hard competition (2.10)
 and will be the first tested in the simulations. In this approach the experts are
 trained before the segmentation, as in approach I, but at every time step the winner
 is updated.
 g (n)=
 (2.10)
 g p(n) = 0 for ta winner(n)