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).