Functional data learning using convolutional neural networks

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.