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-
-\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}
-
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-% TITLE PAGE
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-
-\frame[plain]{\maketitle}
-%\maketitle
-
-
-\section{IRSDI follow up meeting}
-
-%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-% FRAME:
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-
-\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:
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-
-\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:
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-
-\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}
-
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-
-%\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}
-
-%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
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-
-\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:
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-
-\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:
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-
-\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}
-
-
-%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
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-
-\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}
-
-%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
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-
-\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}
-
-
-%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
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-
-\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:
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-
-\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:
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-
-\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:
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-
-\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:
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-
-\begin{frame}
-\frametitle{Misc jc}
-
-\begin{itemize}
-\item simulated dataset : howto ?
-\item temperature
-\item Rcpp
-\end{itemize}
-
-
-
projects / epclust.git / blobdiff