[DMDB] Fix error, add short remark on projections

semester4/dmdb/parts/06_vector-search/00_intro-trees-clustering.tex

@@ -8,7 +8,7 @@ We have at least four metrics for the quality of results:
     \item \bi{Cosine Distance} $D_C$: defined as $1 - S_C$, values range from $0$ to $2$ and the closer to $0$, the better (lower = better)
     \item \bi{Euclidian distance}: The norm of the vector between the two vectors. Values are from $0$ to $\8$, the lower the better.
 \end{itemize}
-$S_C(A, B) = \frac{A \cdot B}{||A|| \cdot ||B||}$, a
+$S_C(A, B) = \frac{A \cdot B}{||A|| \cdot ||B||}$
 
 
 \subsection{Trees/Clustering}

semester4/dmdb/parts/06_vector-search/02_hash-index.tex

@@ -1,6 +1,6 @@
 \subsection{Hash Index}
 To measure the quality of \acrshort{ann} in comparison to \acrshort{knn}, we use $\texttt{recall@k} = |\texttt{ANN\_result} \cap \texttt{KNN\_result}| \div k$.
-This however is not always a good metric, as two vastly different results, one objectively worse can score equally well.
+This however is not always a good metric, as for two vastly different results, the objectively worse one can score equally well.
 
 Alternative methods mentioned are \texttt{RDE@k} and \texttt{TDK@k}, but not elaborated any further.
 

semester4/dmdb/parts/08_quick-overview/03_qp.tex

@@ -24,6 +24,7 @@ Given $B$ frames of memory and $N$ records, we have (typically I/Os in pages to
 
 
 \subsubsection{Projection}
+Remember that we need the sort-based and bash-based approach to eliminate duplicates.
 \begin{itemize}
     \item \bi{Partitioning}: $\texttt{Cost}_\texttt{part}(R) = \texttt{cnt}(R) + \texttt{cnt}(R')$ with
           $\texttt{cnt}(R') = \texttt{cnt}(R) Q$, with $Q$ the fraction of selected attributes divided by total attributes