\documentclass[10pt]{beamer}
\usetheme{metropolis}
\usepackage{appendixnumberbeamer}
\usepackage{booktabs} % You should use \toprule, \midrule, and \bottomrule in tables
\usepackage{tabularx} % Helps with scaling the table to content
\usepackage{natbib}
\usepackage{algorithm} % `algorithm` environment
\usepackage{algorithmic} % pseudocode
\usepackage{pgfplots} % Because figures with DIKZ & pgfplots are superior
\usepackage{tikz}
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% Figures & graphics
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\usetikzlibrary{calc}
\usetikzlibrary{positioning}
\usetikzlibrary{shapes.geometric}
\usepgfplotslibrary{colorbrewer}
\usepgfplotslibrary{external}
\usepgfplotslibrary{fillbetween}
\usepgfplotslibrary{groupplots}
\usepgfplotslibrary{dateplot}
\pgfplotsset{compat=1.14}
\usepackage{caption} % In presentation we should keep the caption little smaller
\captionsetup[figure]{font=scriptsize}
\usepackage{comment} % Just to show you the possible colors (see below)
\newcommand{\themename}{\textbf{\textsc{metropolis}}\xspace}
\newcommand{\rom}[1]
{\MakeUppercase{\romannumeral #1}}
\newcommand{\shapelet} {s} % one shapelet
\newcommand{\shapelets} {\mathcal{S}} % set of shapelets
\newcommand{\oneseries} {T} % one time series
\newcommand{\allseries} {\mathcal{T}} % set of time series
\newcommand{\featurevector}{\phi} % feature vector
\newcommand{\landau}[1] {\mathcal{O}\left(#1\right)} % complexity symbol
\renewcommand{\natural}{\mathds{N}} % natural numbers
\newcommand{\longmethod}{Wasserstein Time Series Kernel}
\DeclareMathOperator{\kernel} {k} % generic kernel
\DeclareMathOperator{\basekernel} {\kernel_{\text{base}}} % base kernel
\DeclareMathOperator{\dist} {dist} % distance function
\DeclareMathOperator{\metric} {\dist} % synonym for `\dist`
\DeclareMathOperator{\wasserstein}{W\!} % Wasserstein distance
\DeclareMathOperator{\Method} {WTK} % use this as an operator and make it
\title{A Wasserstein Subsequence Kernel for Time Series}
\subtitle{}
\date{\today}
\author{\textbf{Christian Bock, Matteo Togninalli}, Elisabetta Ghisu, Thomas Gumbsch, \\ Bastian Rieck, Karsten Borgwardt}
\institute{Department of Biosystems Science and Engineering \\ Machine Learning and Computational Biology Group}
\titlegraphic{
\hfill
\includegraphics[width=1.4cm]{eth_logo_kurz_pos.pdf}
}
% An example to change citation style in presentation
% \setcitestyle{numbers}
% \setcitestyle{authoryear}
\begin{document}
\maketitle
\begin{frame}{ETH Colors}
\begin{tikzpicture}
\footnotesize
\fill[ETHa] (0,0) rectangle (0.5,0.5);
\node at (0,-0.2) {ETHa};
\fill[ETHb] (1,0) rectangle (1.5,0.5);
\node at (1,-0.2) {ETHb};
\fill[ETHc] (2,0) rectangle (2.5,0.5);
\node at (2,-0.2) {ETHc};
\fill[ETHd] (3,0) rectangle (3.5,0.5);
\node at (3,-0.2) {ETHd};
\fill[ETHe] (4,0) rectangle (4.5,0.5);
\node at (4,-0.2) {ETHe};
\fill[ETHf] (5,0) rectangle (5.5,0.5);
\node at (5,-0.2) {ETHf};
\fill[ETHg] (6,0) rectangle (6.5,0.5);
\node at (6,-0.2) {ETHg};
\fill[ETHh] (7,0) rectangle (7.5,0.5);
\node at (7,-0.2) {ETHh};
\fill[ETHi] (8,0) rectangle (8.5,0.5);
\node at (8,-0.2) {ETHi};
\end{tikzpicture}
\end{frame}
\begin{frame}{Table of contents (internal)}
\setbeamertemplate{section in toc}[sections numbered]
\tableofcontents[hideallsubsections]
\end{frame}
\section{Motivation}
\begin{frame}{Time Series Classification in a Nutshell}
\input{nutshell.tex}
\end{frame}
\section{Feature Space: Subsequences and Optimal Transport}
\begin{frame}{Subsequence Extraction}
\input{subsequence_extraction.tex}
\end{frame}
\begin{frame}{Subsequence Distance Matrix}
\input{subsequences_distance.tex}
\end{frame}
\section{Optimal Transport and the Wasserstein Distance}
\begin{frame}{Optimal Transport}
\input{OT_history.tex}
\end{frame}
\begin{frame}{The Swiss Kantorovich Problem}
\input{kantorovich_0.tex}
\end{frame}
\begin{frame}{The Swiss Kantorovich Problem}
\input{kantorovich_1.tex}
\end{frame}
% \begin{frame}{Wasserstein Distance on Time Series}
% \centering
% \begin{columns}
% \begin{column}{columnwidth=0.33\linewidth}
% \subcaptionbox{Subsequence distance matrix\label{sfig:Subsequence distance matrix}}{
% \includegraphics[height=3.0cm, width=3.5cm]{figures/subsequence_distances.pdf}
% }
% \end{column}
% \subcaptionbox{Optimal transport plan\label{sfig:Optimal transport plan}}{%
% \includegraphics[height=3.0cm, width=3.5cm]{figures/optimal_transport.pdf}
% }
% \subcaptionbox{Transport plan visualisation\label{sfig:Intuition transport plan}}
% {%
% \begin{tikzpicture}
% \begin{axis}[%
% axis lines = none,
% height = 4.5cm,
% width = 7.0cm,
% ]
% \addplot[Set1-A, thick, no marks] table[x=x, y=a, col sep=comma] {./data/overview_TS_uneq_length_1.csv};
% \addplot[
% Set1-B, thick, no marks,
% y filter/.expression = {
% y - 10
% },
% ] table[x=x, y=a, col sep=comma] {./data/overview_TS_2.csv};
% \draw[draw opacity=0.8, line width=0.6pt] (0.00,0.05) -- (20.00,-10.03);
% \draw[draw opacity=0.8, line width=0.6pt] (5.00,0.08) -- (25.00,-9.75);
% \draw[draw opacity=0.8, line width=0.6pt] (10.00,1.38) -- (30.00,-7.66);
% \draw[draw opacity=0.8, line width=0.6pt] (15.00,3.95) -- (35.00,-6.24);
% \draw[draw opacity=0.8, line width=0.6pt] (20.00,1.87) -- (60.00,-9.92);
% \draw[draw opacity=0.8, line width=0.6pt] (25.00,0.15) -- (0.00,-9.98);
% \draw[draw opacity=0.8, line width=0.15882352941176556pt] (30.00,-0.04) -- (70.00,-10.03);
% \draw[draw opacity=0.8, line width=0.6pt] (35.00,0.01) -- (90.00,-10.01);
% \draw[draw opacity=0.8, line width=0.15882352941176434pt] (40.00,-0.01) -- (65.00,-9.98);
% \draw[draw opacity=0.8, line width=0.6pt] (45.00,-0.00) -- (10.00,-10.01);
% \draw[draw opacity=0.8, line width=0.30588235294117666pt] (50.00,-0.01) -- (75.00,-9.98);
% \draw[draw opacity=0.8, line width=0.45294117647058646pt] (55.00,0.00) -- (85.00,-10.01);
% \draw[draw opacity=0.8, line width=0.6pt] (60.00,-0.00) -- (105.00,-9.99);
% \draw[draw opacity=0.8, line width=0.6pt] (65.00,-0.01) -- (5.00,-10.03);
% \draw[draw opacity=0.8, line width=0.4529411764705877pt] (70.00,0.01) -- (80.00,-9.96);
% \draw[draw opacity=0.8, line width=0.15882352941176434pt] (75.00,0.02) -- (15.00,-9.99);
% \draw[draw opacity=0.8, line width=0.30588235294117666pt] (80.00,0.38) -- (50.00,-9.60);
% \draw[draw opacity=0.8, line width=0.30588235294117666pt] (85.00,1.56) -- (55.00,-8.53);
% \end{axis}
% \end{tikzpicture}
% }
% \end{figure}
% \end{columns}
% \end{frame}
\section{A Wasserstein Kernel for Time Series}
\input{wtk.tex}
\section{Results}
\input{results.tex}
\section{Take aways}
\begin{frame}[standout]
Questions?
\end{frame}
\begin{frame}[allowframebreaks]{References}
\bibliography{ref}
\bibliographystyle{abbrvnat}
\end{frame}
\appendix
\end{document}

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