Wavelet-based Functional Data Analysis for Classication and Change Point Detection

Abstract

Data collection and analysis, performed close to the source and transferred to other devices for different analysis, are the major paradigms of the Internet of Things (IoT). Usually, the raw data comes in the form of a time-series sequence that can be considered as functions, and as such can be examined by the functional analysis apparatus. Among others, the two major tasks in data analysis are (1) categorical signal classification and (2) change detection in signal statistical parameters. Here, we study both problems: featureless signal classification using discriminative interpolation regularized with the ℓ1 norm is performed using Classification by Discriminative Interpolation with Sparsity (CDIS), and the non-parametric density– difference estimation within a wavelet expansion framework for change detection is suggested using Wavelet–based Least Squares Density–Difference (WLSDD). Finally, we propose a novel method for estimating the density–difference between two distributions, called Regularized Wavelet–based Density–Difference (RWDD).