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Abstract:
In this paper, we consider the active learning problem in
trigonometric polynomial networks and give a necessary and
sufficient condition of sample points to provide the optimal
generalization capability. By analyzing the condition from the
functional analytic point of view, we clarify the mechanism of
achieving the optimal generalization capability. We also show that
a set of training examples satisfying the condition does not only
provide the optimal generalization but also reduces the
computational complexity and memory required for the calculation of
learning results. Finally, we give examples of sample points
satisfying the condition and show that one of the examples further
reduces the computational complexity and memory required for the
calculation.
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