Multi-layer Perceptrons for Functional Data Analysis: A Projection Based Approach
In this paper, we propose a new way to use Functional Multi-Layer Perceptrons (FMLP). In our previous work, we introduced a natural extension of Multi Layer Perceptrons (MLP) to functional inputs based on direct manipulation of input functions. We propose here to rely on a representation of input and weight functions thanks to projection on a truncated base. We show that the proposed model has the universal approximation property. Moreover, parameter estimation for this model is consistent. The new model is compared to the previous one on simulated data: performances are comparable but training time it greatly reduced.
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