Ended presentation

Author: lamferzon

Presentation/Images/steel_plates_1.jpg

@@ -10,9 +10,17 @@
 \usepackage{fancyvrb}
 \usepackage{pdfpages}
 \usepackage{siunitx}
+\usepackage{multirow}
 \usepackage{adjustbox}
 \justifying 
 
+\setbeamercolor{block title}{fg=black, bg=green!50!black}
+\setbeamercolor{block body}{fg=green!50!black, bg=green!50!black!30!white}
+\setbeamercolor{block title alerted}{fg=black, bg=orange!50!white}
+\setbeamercolor{block body alerted}{fg=orange, bg=orange!30!white}
+\setbeamercolor{block title example}{fg=black, bg=blue!50!white}
+\setbeamercolor{block body example}{fg=blue, bg=blue!30!white}
+
 \title[Implementation of the PLS algorithm]{Implementation in MATLAB of the Partial Least Squares algorithm for classification}
 \subtitle{Case study: fault detection and diagnosis on steel plates}
 \author[L. Ferrari, L. Leoni]{Lorenzo Ferrari \and Lorenzo Leoni}

Presentation/Images/steel_plates_2.jpg

@@ -2,14 +2,27 @@ \section{Fault detection and isolation on steel plates}
 
 \begin{frame}
 	\frametitle{Dataset description}
-	The steel plates faults dataset comes from research by Semeion, Research Center of Sciences of Communication. The aim of the research was to correctly classify the type of surface defects in stainless steel plates. Below is some information about the dataset:
-	\begin{itemize}
-		\item number of fault classes: $6 + 1$ (no faults);
-		\item number of attributes: $27$;
-		\item number of instances: $1941$;
-		\item absence of missing values.
-	\end{itemize}
-	Unfortunately, no further details on the covariates are available.
+	\begin{columns}
+		\begin{column}{0.50\textwidth}
+			\justifying
+			The steel plates faults dataset comes from research by Semeion, Research Center of Sciences of Communication. The aim of the research was to correctly classify the type of surface defects in stainless steel plates. Some information about the dataset:
+			\begin{itemize}
+				\item number of fault classes: $6 + 1$ (no faults);
+				\item number of attributes: $27$;
+				\item number of instances: $1941$;
+				\item absence of missing values.
+			\end{itemize}
+			Unfortunately, no further details on the covariates are available.
+		\end{column}
+		\begin{column}{0.50\textwidth}
+			\begin{figure}
+				\centering
+				\includegraphics[width=0.75\textwidth]{Images/steel_plates_1.jpg}\\
+				\vspace{0.5cm}
+			    \includegraphics[width=0.75\textwidth]{Images/steel_plates_2.jpg}
+			\end{figure}
+		\end{column}
+	\end{columns}
 \end{frame}
 
 \begin{frame}
@@ -58,7 +71,7 @@ \section{Fault detection and isolation on steel plates}
 \end{frame}
 
 \begin{frame}
-	\frametitle{Validation $70-30$ of the PLS2 model with $\alpha = 13$}
+	\frametitle{Validation $70/30$ of the PLS2 model with $\alpha = 13$}
 	\begin{figure}
 		\begin{subfigure}[b]{0.49\textwidth}
 			\includegraphics[width=\textwidth]{Images/confusion_all_5_PLS2.pdf}
@@ -74,22 +87,29 @@ \section{Fault detection and isolation on steel plates}
 \begin{frame}
 	\frametitle{Score matrix $T$ with $\alpha = 1$, $2$ and $3$}
 	\begin{figure}
-		\begin{subfigure}[b]{0.49\textwidth}
+		\begin{subfigure}[b]{0.70\textwidth}
 			\includegraphics[width=\textwidth]{Images/scatter_T_a1_p5.pdf}
 		\end{subfigure}
-		\hfill
-		\begin{subfigure}[b]{0.49\textwidth}
+	\end{figure}
+\end{frame}
+
+\begin{frame}
+	\begin{figure}
+		\begin{subfigure}[b]{0.70\textwidth}
 			\includegraphics[width=\textwidth]{Images/scatter_T_a2_p5.pdf}
 		\end{subfigure}
 	\end{figure}
 \end{frame}
 
 \begin{frame}
 	\begin{figure}
-		\begin{subfigure}[b]{0.60\textwidth}
+		\begin{subfigure}[b]{0.80\textwidth}
 			\includegraphics[width=\textwidth]{Images/scatter_T_a3_p5.pdf}
 		\end{subfigure}
 	\end{figure}
+\end{frame}
+
+\begin{frame}
 	\begin{table}
 		\centering
 		\renewcommand\arraystretch{1.3}
@@ -103,4 +123,5 @@ \section{Fault detection and isolation on steel plates}
 			\hline
 		\end{tabular}
 	\end{table}
+	As the order reduction $\alpha$ increases, the number of fault classes that are confused with the remaining ones decreases. In particular, we can note that the error rate related to the fault class Stains decreases substantially in the passage from $\alpha = 1$ to $\alpha = 2$; indeed, from $\mathbb{R}^2$ its subspace predominates over the subspaces of the other classes. Instead, the Dirtiness class continues to be hidden from the others for any order reduction. 
 \end{frame}

Presentation/Presentation.pdf

@@ -1,5 +1,49 @@
 \section{Conclusion}
 
 \begin{frame}
-	TO DO
+	\frametitle{Comparison between PLS and PCA}
+	\begin{table}
+		\centering
+		\renewcommand\arraystretch{1.3}
+		\begin{tabular}{c|c|c}
+			\hline
+			& \textbf{PLS} & \textbf{PCA} \\
+			\hline
+			\textit{Type of technique} & Supervised & Unsupervised \\
+			\multirow{2}{3cm}{\centering \textit{Goal}} & \multirow{2}{3cm}{\centering Regression and classification} & \multirow{2}{3cm}{\centering Feature reduction for clustering}\\
+			& & \\
+			\multirow{2}{3cm}{\centering \textit{Aim of the maximization}} & \multirow{2}{3cm}{\centering Covariance between $X$ and $Y$} & \multirow{2}{3cm}{\centering Variance of $X$}\\ 
+			& & \\
+			\multirow{2}{3cm}{\centering \textit{Eigenvectors orthogonality}} & \multirow{2}{3cm}{\centering Not} & \multirow{2}{3cm}{\centering Yes}\\ 
+			& & \\
+			\multirow{2}{3cm}{\centering \textit{Type of decomposition}} & \multirow{2}{3cm}{\centering NIPALS (iterative approach)} & \multirow{2}{3cm}{\centering SVD}\\ 
+			& & \\
+			\hline
+		\end{tabular}
+	\end{table}
+\end{frame}
+
+\begin{frame}
+	\begin{figure}
+		\centering
+		\begin{subfigure}[b]{0.60\textwidth}
+			\includegraphics[width=\textwidth]{Images/PLS_vs_PCA.pdf}
+		\end{subfigure}
+	\end{figure}
+	For the central orders PCA is slightly more accurate than PLS in the reconstruction of the matrix $X$ starting from the reduced domain. For the extreme orders, instead, the two techniques are similar.
+\end{frame}
+
+\begin{frame}
+	\frametitle{Bibliography}
+	\begin{block}{Book}
+		\textbf{Fault Detection and Diagnosis in Industrial Systems}\\
+		L. H. Chiang, E. L. Russel and R. D. Braatz
+	\end{block}
+		\begin{alertblock}{Dataset}
+		\textbf{Faulty Steel Plates}\\
+		\small{\url{https://www.kaggle.com/datasets/uciml/faulty-steel-plates}}
+	\end{alertblock}
+	\begin{exampleblock}{Repository GitHub}
+		\small{\url{https://github.com/LorenzoF6/PLS_Algorithm_Implementation.git}}
+	\end{exampleblock}
 \end{frame}