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@@ -317,8 +317,8 @@ LDA and it improves recognition performances with respect to PCA and LDA.
 In this section we will perform PCA-LDA recognition with NN classification.
 
 Varying the values of M_pca and M_lda we obtain the average recognition accuracies 
-reported in figure \ref{ldapca_acc}. Peak accuracy of 94.7% can be observed for M_pca=115, M_lda=41;
-howeverer accuracies above 92% can be observed for M_pca values between 90 and 130 and 
+reported in figure \ref{ldapca_acc}. Peak accuracy of 93% can be observed for M_pca=115, M_lda=41;
+howeverer accuracies above 90% can be observed for M_pca values between 90 and 130 and 
 M_lda values between 30 and 50.
 
 Recognition accuracy is significantly higher than PCA, and the run time is roughly the same,
@@ -332,6 +332,53 @@ vaying between 0.11s(low M_pca) and 0.19s(high M_pca).
 \end{center}
 \end{figure}
 
+DD RANK OF SCATTER MATRICES
+
+Testing with M_lda=50 and M_pca=115 gives 92.9% accuracy. The results of such test can be
+observed in the confusion matrix shown in figure \ref{ldapca_cm}.
+
+\begin{figure}
+\begin{center}
+\includegraphics[width=20em]{fig/cmldapca.pdf}
+\caption{PCA-LDA NN Recognition Confusion Matrix Mlda=50, Mpca=115}
+\label{ldapca_cm}
+\end{center}
+\end{figure}
+
+Two recognition examples are reported below: success(figure \ref{succ_ldapca}), failure(figure \ref{fail_ldapca})
+
+\begin{figure}
+\begin{center}
+\includegraphics[width=7em]{fig/ldapcaf2.pdf}
+\includegraphics[width=7em]{fig/ldapcaf1.pdf}
+\label{fail_ldapca}
+\caption{Failure case for PCA-LDA. Test face left. NN right}
+\end{center}
+\end{figure}
+
+\begin{figure}
+\begin{center}
+\includegraphics[width=7em]{fig/ldapcas1.pdf}
+\includegraphics[width=7em]{fig/ldapcas2.pdf}
+\label{succ_ldapca}
+\caption{Success case for PCA-LDA. Test face left. NN right}
+\end{center}
+\end{figure}
+
+The PCA-LDA method allows to obtain a much higher recognition accuracy compared to PCA.
+The achieved separation between classes and reduction between inner class-distance 
+that makes such results possible can be observed in figure \ref{subspaces}, in which 
+the 3 features of the subspaces obtained are graphed.
+
+\begin{figure}
+\begin{center}
+\includegraphics[width=12em]{fig/SubspaceQ1.pdf}
+\includegraphics[width=12em]{fig/SubspaceQL1.pdf}
+\label{subspaces}
+\caption{Generated Subspaces (3 features). PCA on the left. PCA-LDA on the right}
+\end{center}
+\end{figure}
+
 # Question 3, LDA Ensemble for Face Recognition, PCA-LDA Ensemble 
 
 # References