Convolution-based linear discriminant analysis for functional data classification

Technological advances have allowed for the rise red in more reliable and less expensive sensors to collect data over time (e.g., on temperature, heartbeat, and neural activity). Consequently, mathematical methods to examine these time series data have become necessary. One topic of intensive research in time series analysis is supervised classification. For example, biomedical researchers are interested in classifying controls versus people with heart disorders based on electrocardiograms. Several works have adapted Fisher's linear discriminant analysis (LDA) to work with functional data. However, they have poor performance when a multiplicative random effect model generates the time series; they do not exploit the periodicity of the data. To solve this problem, we propose convolution based linear discriminant analysis (cLDA). Different from the standard LDA that projects the data into a lower space, cLDA obtains filters. To show the performance of cLDA, we compared it to state-of-the-art methods in simulated and 12 empirical datasets. cLDA obtained the lowest classification error rate on average. It showed the ability to classify real-world time series. (c) 2021 Elsevier Inc. All rights reserved.