--- /dev/null
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+%
+% LOADING DOCUMENT
+%
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+\documentclass[10pt]{beamer}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% LOADING PACKAGES
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage[francais]{babel}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{graphicx}
+\usepackage{booktabs}
+\usetheme{default}
+\usepackage{tikz}
+
+\colorlet{darkred}{red!80!black}
+\colorlet{darkblue}{blue!80!black}
+\colorlet{darkgreen}{green!60!black}
+
+\usetikzlibrary{calc,decorations.pathmorphing,patterns}
+\pgfdeclaredecoration{penciline}{initial}{
+ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,
+ auto corner on length=1mm,]{
+ \pgfpathcurveto%
+ {% From
+ \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}
+ {\pgfdecorationsegmentamplitude}
+ }
+ {% Control 1
+ \pgfmathrand
+ \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}
+ {\pgfqpoint{-\pgfdecorationsegmentaspect
+ \pgfdecoratedinputsegmentremainingdistance}%
+ {\pgfmathresult\pgfdecorationsegmentamplitude}
+ }
+ }
+ {%TO
+ \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}}
+ }
+ }
+ \state{final}{}
+}
+\tikzstyle{block} = [draw,rectangle,thick,minimum height=2em,minimum width=2em]
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% BEAMER OPTIONS
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+%\setbeameroption{show notes}
+\setbeamertemplate{navigation symbols}{}
+%\setbeamercovered{transparent}
+%\AtBeginSection[]{
+%\begin{frame}{Outline}
+% \tableofcontents[currentsection]
+%\end{frame}
+%}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+%
+% PRESENTATION INFORMATION
+%
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\author{B. Auder \and
+ J. Cugliari \and
+ Y. Goude \and
+ J.-M. Poggi
+}
+\title{Disaggregated Electricity Forecasting using Clustering of
+ Individual Consumers}
+\subtitle{Réunion mi parcours}
+%\logo{}
+\institute{IRSDI - RESEARCH INITIATIVE IN INDUSTRIAL DATA SCIENCE}
+\date{19 janvier 2017}
+%\subject{tito}
+
+\begin{document}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+%
+% TITLE PAGE
+%
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\frame[plain]{\maketitle}
+%\maketitle
+
+
+\section{IRSDI follow up meeting}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}{The project in a nutshell}
+\begin{block}{Context}
+\begin{itemize}
+\item
+Industrial : Electricity load forecasting \& smart grids infrastructure
+\item
+Academic : curve's shape \& nonparametric function-valued forecast
+\item
+Past work : clustering with wavelets (RC, Wer), KWF, Enercon
+\end{itemize}
+\end{block}
+
+\begin{block}{Aims}
+\begin{itemize}
+\item evaluate the upscaling capacity of the Energycon strategy
+\item adapt KWF to an exogenous variable (e.g. meteorological)
+\end{itemize}
+\end{block}
+\end{frame}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}{Clients hierarchical structure and prediction}
+
+\begin{columns}
+\column{.6\textwidth}
+\begin{figure}[!ht]\centering
+ \includegraphics[width = \textwidth]{pics/schema.png}
+\caption{Hierarchical structure of $N$ individual clients among $K$
+groups.}\label{fig:schema-hier}
+\end{figure}
+
+\column{.4\textwidth}
+\begin{tikzpicture}[decoration=penciline, decorate]
+ \node[block, decorate] at (0, 0){$Z_t$} ;
+ \node[block, decorate] at (3, 0) {$Z_{t + 1}$} ;
+
+ \node[block, decorate] at (0, -2.5) {$\begin{pmatrix}
+ Z_{t, 1} \\ Z_{t, 2} \\ \vdots \\ Z_{t, K}
+ \end{pmatrix}$ };
+
+ \node[block, decorate] at (3, -2.5) {$\begin{pmatrix}
+ Z_{t+1, 1} \\ Z_{t+1, 2} \\ \vdots \\ Z_{t+1, k}
+ \end{pmatrix} $};
+
+ \draw[decorate, darkblue, line width = 2mm, ->] (1, 0) -- (2, 0);
+ \draw[decorate, darkgreen, line width = 2mm, ->] (1, -2.5) -- (2, -2.5);
+ \draw[decorate, black, line width = 2mm, ->] (3, -1.3) -- (3, -0.4);
+ \draw[decorate, darkred, line width = 2mm, ->] (1, -1.5) -- (2, -0.75);
+ \end{tikzpicture}
+\end{columns}
+
+\begin{itemize}
+ \item $Z_t$: aggregate demand at $t$
+ \hfill $Z_{t, k}$:demand of group $k$ at moment $t$
+ \item Groups can express tariffs, geographical dispersion, client class ...
+ \item Profiling vs Prediction
+ \item We follow Misiti \textit{et al}. (2010) to construct classes of customers to better predict the aggregate.
+\end{itemize}
+\end{frame}
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}{Expected result}
+
+\includegraphics[width = \textwidth]{pics/perf.pdf}
+\end{frame}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}{Energy decomposition of the DWT}
+
+%\begin{block}{ }
+\begin{itemize}
+\item Energy conservation of the signal
+%
+ \begin{equation*}\label{eq:energy}
+ \| z\|^2_H \approx \| \widetilde{z_J} \|_2^2
+ = c_{0,0}^2 + \sum_{j=0}^{J-1} \sum_{k=0}^{2^j-1} d_{j,k} ^2 =
+ c_{0,0}^2 + \sum_{j=0}^{J-1} \| \mathbf{d}_{j} \|_2^2.
+ \end{equation*}
+% \item characterization by the set of channel variances estimated at the output of the corresponding filter bank
+ \item For each $j=0,1,\ldots,J-1$, we compute the \textcolor{blue}{absolute} and
+ \textcolor{orange}{relative} contribution representations by
+%
+ \[ \underbrace{\hbox{cont}_j = ||\mathbf{d_j}||^2}_{\fbox{\textcolor{blue}{AC}}}
+ \qquad \text{and} \qquad
+ \underbrace{\hbox{rel}_j =
+ \frac{||\mathbf{d_j}||^2}
+ {\sum_j ||\mathbf{d_j}||^2 }}_{\fbox{\textcolor{orange}{RC}}} .\]
+ %\item They quantify the relative importance of the scales to the global dynamic.
+% \item Only the wavelet coefficients $\set{d_{j,k}}$ are used.
+% \item RC normalizes the energy of each signal to 1.
+\end{itemize}
+%\end{block}
+%\end{frame}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+%\begin{frame}
+% \frametitle{Schema of procedure}
+ \begin{center}
+ \includegraphics[width = 7cm, height = 2cm]{./pics/Diagramme1.png}
+ % Diagramme1.png: 751x260 pixel, 72dpi, 26.49x9.17 cm, bb=0 0 751 260
+ \end{center}
+
+ \begin{footnotesize}
+ \begin{description}
+ \item [0. Data preprocessing.] Approximate sample paths of $z_1(t),\ldots,z_n(t)$ %by the truncated wavelet series at the scale $J$ from sampled data $\mathbf{z}_1, \ldots, \mathbf{z}_n$.
+ \item [1. Feature extraction.] Compute either of the energetic components using absolute contribution (AC) or relative contribution (RC).
+ \item [2. Feature selection.] Screen irrelevant variables. \begin{tiny} [Steinley \& Brusco ('06)]\end{tiny}
+ %\item [3. Determine the number of clusters.] Detecting significant jumps %in the transformed distortion curve.
+ %\begin{tiny} [Sugar \& James ('03)]\end{tiny}
+ %\item [4. Clustering.] Obtain the $K$ clusters using PAM algorithm.
+ \end{description} \end{footnotesize}
+
+ \end{frame}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}
+ \frametitle{A function-based distance}
+
+\begin{columns}
+\column{0.6\textwidth}
+ \begin{itemize}
+ \item Distance based on wavelet-correlation between two time series
+ \item Can be used to measure relationship between two functions
+ %variables, i.e. temperature and load.
+ \item The strength of the relation is hierarchically decomposed across
+ scales without losing of time location
+ \end{itemize}
+
+ Drawback: needs more computation time and storage (complex values)
+\column{0.4\textwidth}
+ \includegraphics[width = \textwidth]{pics/conso-week.png}
+
+ \includegraphics[width = .96\textwidth]{pics/wsp-week.png}
+
+\end{columns}
+ \end{frame}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}{A 2-stages strategy (Energycon)}
+
+\includegraphics[width = \textwidth]{pics/2-stage_strategy.png}
+
+\footnotetext[1]{
+ J. Cugliari, Y. Goude and J. M. Poggi, "Disaggregated electricity forecasting using wavelet-based clustering of individual consumers," 2016 IEEE International Energy Conference (ENERGYCON), Leuven, 2016, pp. 1-6.
+ }
+
+\end{frame}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}{Data description}
+
+\begin{columns}
+\column{0.45\textwidth}
+\begin{block}{Available}
+\begin{itemize}
+\item
+EDF : 25K professional clients, sampled @ 30min, 5 semesters
+\item
+external open data
+\end{itemize}
+\end{block}
+
+\begin{block}{Accesible}
+ \begin{itemize}
+ \item simulated (very large) data
+ \end{itemize}
+\end{block}
+\column{0.55\textwidth}
+\includegraphics[width = \columnwidth]{pics/indiv.jpg}
+%\textcolor{red}{A picture here?}
+\end{columns}
+
+\end{frame}
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}{Computing resources}
+\begin{block}{2 academic testing architectures}
+\begin{itemize}
+\item Orsay's cluster (500Gb RAM, 80 cores)
+\item \texttt{pulpito} : Lyon 2's box with 2 quadricores (HT x 2), 72Gb RAM
+\end{itemize}
+\end{block}
+
+\begin{block}{1 industrial real-scale architecture}
+\begin{itemize}
+\item mini cluster @ EDF labs
+\end{itemize}
+\end{block}
+
+\end{frame}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}{Strategies for upscaling}
+
+\begin{itemize}
+\item From 25K to 25M: in 1000 chunks of 25K
+\item Reference values:
+\begin{itemize}
+\item $K'=200$ super consumers (SC)
+\item $K\ast=15$ final clusters
+\end{itemize}
+\end{itemize}
+
+
+
+\begin{block}{1st strategy}
+\begin{itemize}
+\item Do 1000 times ONLY Energycon's 1st-step strategy on 25K clients
+
+\item With the $1000 \times K'$ SC perform a 2-step run
+ leading to $K^\ast$ clusters
+\end{itemize}
+\end{block}
+
+\begin{block}{2nd strategy}
+\begin{itemize}
+\item Do 1000 times Energycon's 2-step strategy on 25K clients
+ leading to $1000\times K^\ast$ intermediate clusters
+\item Treat the intermediate clusters as individual curves and perform
+ a single 2-step run to get $K^\ast$ final clusters
+\end{itemize}
+\end{block}
+
+\end{frame}
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}
+\frametitle{Course + Workshop}
+
+\begin{block}{1-day IRSDI-ECAS Course}
+\begin{itemize}
+\item
+GAM : from classical to distributed environments
+\item
+October 19, 2017 @ EDF Labs, Paris-Saclay, France
+\item
+Simon Wood \& Matteo Fasiolo (University Walk, Bristol, UK)
+\end{itemize}
+\end{block}
+
+
+\begin{block}{1-day Worshop}
+\begin{itemize}
+\item
+Individual Electricity Consumers, Data, Packages and Methods
+\item
+October 20, 2017 @ EDF Labs, Paris-Saclay, France
+\item
+5 keynote speakers
+\begin{itemize}
+\item
+Souhaib Ben Taieb, Monash University, Melbourne, Australia
+\item
+Ram Rajagopal, Stanford Univ., USA
+\item
+Gavin Shaddick, University of Bath, UK
+\item
+Bei Chen, IBM Research, Ireland
+\item
+Jack Kelly, University of London, Imperial College of Science, UK
+\end{itemize}
+\end{itemize}
+\end{block}
+\end{frame}
+
+
+\section{Point sur les codes}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}{Résumé point sur le code (BA, JC @ Lyon déc 2016)}
+
+Nous avons réussi à
+\begin{itemize}
+\item
+faire une fresh installation du code de BA sur une nouvelle machine
+(problèmes divers liés à la compilation, configuration, libraries exotiques)
+\item
+conduire des expériences sur les données pour mesurer le temps de calcul (le code est blazing fast: 30sec pour obtenir 500 groupes sur 4 procs)
+\item
+identifier de problèmes : manque un installateur et une interface de pretraitement indépendant du calcul
+\end{itemize}
+
+A faire:
+\begin{itemize}
+\item
+finir les experiences (sur nb de classes, nb de curves / chunk, nb de procs) et sur d'autres architectures
+\item
+interface matrice -> binaire
+\item
+obtenir les courbes synchrones
+\end{itemize}
+
+Piste à explorer pour les comparaisons: \texttt{h2o}
+\end{frame}
+
+\section{Expériences numériques}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}
+\frametitle{Code C/MPI}
+
+\begin{enumerate}
+\item [0]] Sérialisation des données : on écrit d'abord la longueur de la série puis les puissances sont codées sur 3 octets, permettant une excellente compression et une lecture facile (accès en O(1) à n'importe quelle série)
+
+\item [1]] Algorithme PAM appliqué en parallèle via la librairie MPI.
+
+\item [2]] Agrégation des médoïdes obtenus, (re-)sérialisation, puis on ré-applique l'algorithme PAM.
+
+\end{enumerate}
+
+\begin{itemize}
+\item
+ %Plusieurs astuces : sérialisation des données, calcul en parallèle
+\item
+ Très rapide : environ 5 minutes from raw to 1st stage clustering
+ \item
+ Divergences par rapport à Energycon (moyennes au lieu d'aggrégation)
+ \end{itemize}
+
+ %\begin{verbatim}
+ %> time ./ppam.exe serialize 2009.csv 2009.bin 1 0
+ %real 7m34.182s
+ %\end{verbatim}
+\end{frame}
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}
+\frametitle{R Code}
+
+\begin{itemize}
+\item Enercon's code update
+\item \texttt{data.table} is used for readings and writtings \footnote{\texttt{tidyverse} toolbox is much slower}
+\item Disk spaces of the plain text associated object
+\item Timmings on \texttt{pulpito} (16 cores, 64Gb RAM, SSD)
+\end{itemize}
+\begin{center}
+\begin{tabular}{lccc}\toprule
+Task & Time & Memory & Disk \\ \midrule
+Raw (15Gb) to matrix & 7 min &
+ 30 Gb\footnote{\texttt{ff} is a promising alternative if needed} &
+ 2.7 Gb \\
+Compute contributions & 7 min & <1Gb & 7 Mb \\
+1st stage clustering & 3 min & <1Gb & -- \\
+Aggregation & 1 min & 6Gb & 30 Mb \\
+Wer distance matrix & 40 min & 64Gb\footnote{Embarransgly parallel but still too slow} & 150 Kb \\
+Forecasts & 10 min & <1Gb & --\\
+\bottomrule
+\end{tabular}
+\end{center}
+\end{frame}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}
+\frametitle{Why wer distance is so slow ?}
+
+
+\begin{block}{2nd step strategy (Enercon way)}
+% We proceed as follows:
+ \begin{itemize}
+ \item Transform data $z_1(t), \ldots, z_n(t)$ using the CWT and Morlet wavelet to obtain $n$ matrices of size $J\times N$.
+ \item Compute the wer-based dissimilarity matrix
+ \item Obtain the PAM-based clustering.
+\end{itemize}
+
+\begin{block}{Current choices on the computation}
+\begin{itemize}
+\item From (\texttt{Rwave} \& \texttt{sowas}) to \texttt{biwavelt}
+\item About 1 sec to compute \texttt{werd(x, y)} with current
+ filtering ($J \sim 52$ with 13 octaves, 4 voices )
+\item Need to compute $n (n - 1) / 2$ pairwise distances
+ (20K, 130K, 500K entries for $n = 200, 500, 1000$)
+\item Need an efficient \texttt{werd} function (maybe in
+ RcppParallel ?)
+\end{itemize}
+
+\end{block}
+
+
+\end{block}
+
+\end{frame}
+
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}{CWT}
+
+\begin{block}{Continuous WT}
+Starting with a mother wavelet $\psi$ consider $\psi_{a, \tau} = a^{-1/2} \psi\left(\frac{t-\tau}{a}\right)$.
+
+The CWT of a function $z\in L^2 (\mathbb{R})$ is,
+$$ W_z(a, \tau) = \int_{-\infty}^{\infty} z(t) \psi_{a, \tau}^* (t) dt$$
+
+As for Fourier transform, a spectral approach is possible.
+
+
+\begin{eqnarray*}
+S_z(a, \tau) &=& |W_z(a, \tau)|^2 \qquad\qquad \hbox{wavelet spectrum} \\
+\mathcal{W}_{z, x}(a, \tau) &=& W_z(a, \tau)W_x^*(a, \tau) \qquad \hbox{cross-wavelet transform}
+\end{eqnarray*}
+
+%$$ S_z(a, \tau) = |W_z(a, \tau)|^2 \qquad \hbox{wavelet spectrum}$$
+
+%$$ \mathcal{W}_{z, x}(a, \tau) = W_z(a, \tau)W_x(a, \tau)^* \qquad \hbox{cross-wavelet transform}$$
+\end{block}
+
+\end{frame}
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}{Wavelet coherence}
+\begin{block}{ }
+\begin{equation*} \label{coherence}
+R_{z,x}^2(a,\tau) = \frac{ |\tilde{\mathcal{W}}_{x,y}(a, \tau)|^2 }{|\tilde{\mathcal{W}}_{x,x}(a, \tau)| |\tilde{\mathcal{W}}_{y,y}(a, \tau) | },
+\end{equation*}
+
+Based on the extended $R^2$ coefficient, we can construct an coefficient of determination between two wavelet spectrums
+
+\begin{equation*}\label{eq:wer}
+ WER_{z, x}^2 = \frac{
+ \int_0^\infty \left( \int_{-\infty}^\infty |\tilde{\mathcal{W}}_{z, x}(a, \tau)| d\tau \right)^2 da} { \int_0^\infty \left( \int_{-\infty}^\infty |\tilde{\mathcal{W}}_{z, z}(a, \tau)| d\tau \int_{-\infty}^\infty |\tilde{\mathcal{W}}_{x, x}(a, \tau)| d\tau\right) da}.
+ \end{equation*}
+
+And obtain a dissimilarity based on it
+
+\begin{equation*}\label{eq:dist-wer}
+ d(z, x) = \sqrt{ JN(1 - \widehat{WER}_{z, x}^2)}
+\end{equation*}
+\end{block}
+\end{frame}
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+%\begin{frame} \frametitle{Wavelet coherence}
+%\begin{block}{ }
+% We proceed as follows:
+% \begin{itemize}
+% \item Transform data $z_1(t), \ldots, z_n(t)$ using the CWT and Morlet wavelet to obtain $n$ matrices of size $J\times N$.
+% \item Compute a dissimilarity matrix with the coherency based dissimilarity.
+% \item Using PAM obtain clusters $k=8$ clusters.
+% \end{itemize}
+%
+% Rand Index (AC, WER) = 0.26
+%
+%\end{block}
+%
+%\end{frame}
+
+
+\end{document}
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FRAME:
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\begin{frame}
+\frametitle{Misc jc}
+
+\begin{itemize}
+\item simulated dataset : howto ?
+\item temperature
+\item Rcpp
+\end{itemize}
+
+
+
projects / epclust.git / commitdiff