Optimal online time-series segmentation

When time series are processed, the difficulty increases with the size of the series. This fact is aggravated when time series are processed online, since their size increases indefinitely. Therefore, reducing their number of points, without significant loss of information, is an important field of research. This article proposes an optimal online segmentation method, called OSFS-OnL, which guarantees that the number of segments is minimal, that a preset error limit is not exceeded using the L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L \infty $$\end{document}-norm, and that for that number of segments the value of the error corresponding to the L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document}-norm is minimized. This new proposal has been compared with the optimal OSFS offline segmentation method and has shown better computational performance, regardless of its flexibility to apply it to online or offline segmentation.