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DSD/first_formalization_presentation/presentation_formalization.tex

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+\documentclass[aspectratio=169,10pt]{beamer}
+\usetheme[progressbar=head,numbering=fraction,sectionpage=none]{metropolis}
+
+\usepackage{graphicx}
+\usepackage{ulem}
+\usepackage{xcolor}
+\usepackage[scale=2]{ccicons}
+\usepackage{pgfplots}
+\usepackage{booktabs}
+\usepgfplotslibrary{dateplot}
+\usepackage{hyperref}
+\usepackage{multirow}
+\usepackage{array}
+\usepackage{xspace}
+
+\title{Device State Detector (DSD): Formalization}
+\subtitle{Trust me I've read a book.}
+\date{}
+\author{Arthur Grisel-Davy}
+\institute{University of Waterloo, Canada}
+
+
+\begin{document}
+
+\maketitle
+
+\begin{frame}{Context}
+\begin{center}
+\textit{For any power trace $t$ captured on from a machine $M$, detect the state $C_i$ of the machine for every sample $t[n]$.}\\
+\vspace{1cm}
+\textit{Assign a class $C_i$, to every sample of a power trace $t[n]$ from a machine $M$ corresponding to a state of the machine, from a set of pre-established states.}
+\end{center}
+\vfill
+$\Longrightarrow$ Supervised, multi-class, mono-label, classification problem.
+\end{frame}
+
+\begin{frame}{Definitions}
+\begin{itemize}
+\item $t$: a power trace of fixed sampling rate and length $N$. $t[n] \forall n\in[1,N]$ are the samples value of $t$.
+\item $p_i$: The proto examples of the states. Power traces corresponding to the $P$ states to detect. Each proto is of length $N_i$, not necessarily equals.
+\end{itemize}
+\end{frame}
+
+\begin{frame}{Normalized distance}
+\begin{align}\label{eq:distance_original}
+    &nd: a\times b \in T^2 \rightarrow \mathbb{R} \nonumber\\
+    &nd(a,b) = \dfrac{Eucd(a,b)}{N_b}
+\end{align}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Center}
+\begin{itemize}
+\item Place sample at center of window.
+\item Compute normalized distances to each proto.
+\item Assign to closest proto.
+\end{itemize}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor}
+\includegraphics[width=\textwidth]{images/detection_real___empty_1NNcenter.pdf}
+\end{frame}
+
+\begin{frame}{Performance metric}
+\begin{itemize}
+    \item Accuracy: $Acc = \dfrac{1}{N}\sum_{n\in N}1_{(l[n] = true[n])}$
+    \item State occurrence: Count state occurrence independently of correct position or size.
+\end{itemize}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Dynamic position}
+\begin{figure}
+\centering
+\includegraphics[width=0.9\textwidth]{images/presentation_Page 1_presentation.pdf}
+\end{figure}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Dynamic position}
+\includegraphics[width=\textwidth]{images/detection_real___empty_1NNmin.pdf}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Dynamic position}
+\includegraphics[width=\textwidth]{images/detection_real_asus_1_1NNmin.png}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Dynamic position}
+\includegraphics[width=\textwidth]{images/detection_real_DELL-1_1NNmin.png}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Dynamic Distance}
+\begin{align}\label{eq:distance_original}
+    &dynd: t[n]\times p_i \in (t, protos)\nonumber\\
+    &dynd(a,b) = \min_{k\in [n-N_i,n+N_i])}(nd(t[n-k:n-k+N_i],p_i))
+\end{align}
+\end{frame}
+
+\begin{frame}{Limitations of the method}
+\begin{itemize}
+    \item Significant miss-classification between close classes.
+    \item Impossibility to detect outlier/out-of-scope patterns.
+    \item Rely too much on protos \textit{tiling} assumption.
+\end{itemize}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Shrinkage}
+\includegraphics[width=\textwidth]{images/NN_schematic_presentation_DSD_Page 1.pdf}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Shrinkage}
+\includegraphics[width=\textwidth]{images/NN_schematic_presentation_DSD_Page 2.pdf}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Shrinkage}
+\includegraphics[width=\textwidth]{images/NN_schematic_presentation_DSD_Page 3.pdf}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Shrinkage}
+\includegraphics[width=\textwidth]{images/NN_schematic_presentation_DSD_Page 4.pdf}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Shrinkage}
+\includegraphics[width=\textwidth]{images/NN_schematic_presentation_DSD_Page 5.pdf}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Shrinkage}
+\includegraphics[width=\textwidth]{images/NN_schematic_presentation_DSD_Page 6.pdf}
+\end{frame}
+
+\begin{frame}{Variable Length Normalized Distance}
+\begin{align}\label{eq:distance_original}
+    &vlnd: t[n]\times p_i \in (t, protos)\nonumber\\
+    &vlnd(a,b) = \min_{k\in [n-N_i,n+N_i])}(nd(t[n-k:n-k+N_i],p_i))
+\end{align}
+\end{frame}
+
+\begin{frame}{Checkpoint}
+Three distance measures:
+\begin{itemize}
+\item Normalized Distance, to compare distances to protos: 
+\begin{equation}nd(a,b) = \dfrac{Eucd(a,b)}{N_b}\end{equation}
+\item Dynamic Distance, to compare sample arc to protos: \begin{equation}dynd(a,b) = \min_{k\in [n-N_i,n+N_i])}(nd(t[n-k:n-k+N_i],p_i))\end{equation}
+\item Variable Length Normalized Distance, to get protos inter-distances: \begin{equation}vlnd(a,b) = \min_{k\in [n-N_i,n+N_i])}(nd(t[n-k:n-k+N_i],p_i))\end{equation}
+\end{itemize}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Shrinkage}
+\includegraphics[width=\textwidth]{images/NN_schematic_presentation_DSD_Page 7.pdf}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Shrinkage}
+\includegraphics[width=\textwidth]{images/NN_schematic_presentation_DSD_Page 8.pdf}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Shrinkage $\alpha=1$}
+\includegraphics[width=\textwidth]{images/detection_real___empty_1_1NNmin}
+\end{frame}
+\begin{frame}{1-Nearest Neighbor - Shrinkage $\alpha=0.75$}
+\includegraphics[width=\textwidth]{images/detection_real___empty_0.75_1NNmin}
+\end{frame}
+\begin{frame}{1-Nearest Neighbor - Shrinkage $\alpha=0.5$}
+\includegraphics[width=\textwidth]{images/detection_real___empty_0.5_1NNmin}
+\end{frame}
+
+\begin{frame}{1-Nearest Neighbor - Shrinkage $\alpha=2$}
+\includegraphics[width=\textwidth]{images/detection_real_DELL-1_2_1NNmin.png}
+\end{frame}
+\begin{frame}{1-Nearest Neighbor - Shrinkage $\alpha=1$}
+\includegraphics[width=\textwidth]{images/detection_real_DELL-1_1_1NNmin.png}
+\end{frame}
+
+\begin{frame}{Conclusion}
+    \begin{itemize}
+        \item DSD is an implementation of 1-NN with custom distances and shrinkage.
+        \item Can easily be adapted to multiple protos per class.
+        \item Data requirements and constraints minimal.
+        \item Detects $P+1$ classes.
+        \item One hyperparameter $\alpha$ to controle miss/un -classification tradeoff.
+    \end{itemize}
+\end{frame}
+
+\begin{frame}{Future Work}
+\begin{itemize}
+    \item Capture and label more data.
+    \item Evaluate possibility of uneven shrinkage.
+    \item Detect attacks, publish paper, save the world, accept Nobel prize.
+\end{itemize}
+    
+\end{frame}
+
+\end{document}