Functional data learning using convolutional neural networks
Jose Galarza Tamer Oraby
In this paper, we show how convolutional neural networks (CNN) can be used in
regression and classification learning problems of noisy and non-noisy
functional data. The main idea is to transform the functional data into a 28 by
28 image. We use a specific but typical architecture of a convolutional neural
network to perform all the regression exercises of parameter estimation and
functional form classification. First, we use some functional case studies of
functional data with and without random noise to showcase the strength of the
new method. In particular, we use it to estimate exponential growth and decay
rates, the bandwidths of sine and cosine functions, and the magnitudes and
widths of curve peaks. We also use it to classify the monotonicity and
curvatures of functional data, algebraic versus exponential growth, and the
number of peaks of functional data. Second, we apply the same convolutional
neural networks to Lyapunov exponent estimation in noisy and non-noisy chaotic
data, in estimating rates of disease transmission from epidemic curves, and in
detecting the similarity of drug dissolution profiles. Finally, we apply the
method to real-life data to detect Parkinson's disease patients in a
classification problem. The method, although simple, shows high accuracy and is
promising for future use in engineering and medical applications.