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exercise-clustering: Improved the text regarding points that are adde…
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…d to the candidate set to better reflect the algorithm
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dominik-probst committed Jul 3, 2024
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Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions exercise/5-Clustering.tex
Original file line number Diff line number Diff line change
Expand Up @@ -1347,7 +1347,7 @@ \subsection*{Task 2: Application of DBSCAN}

\item \textbf{Add Points in the $\varepsilon$-Neighborhood of $(1,2)$ to the Candidate Set $N$:}

Only $(1,1)$ is an unvisited point in the $\varepsilon$-neighborhood of $(1,2)$:
Only $(1,1)$ is within the does $\varepsilon$-Neighborhood of $(1,2)$ and does not belong to a cluster yet:

\begin{alignat*}{2}
Distance_{(1,2)\leftrightarrow(1,1)} & = \sqrt{(1-1)^2+(2-1)^2} = 1 \\
Expand Down Expand Up @@ -1405,7 +1405,7 @@ \subsection*{Task 2: Application of DBSCAN}

\item \textbf{Add Points in the $\varepsilon$-Neighborhood of $(1,1)$ to the Candidate Set $N$:}

Only $(2,1)$ is an unvisited point in the $\varepsilon$-neighborhood of $(1,1)$:
Only $(2,1)$ is within the $\varepsilon$-neighborhood of $(1,1)$ and does not belong to a cluster yet:

\begin{alignat*}{2}
Distance_{(1,1)\leftrightarrow(2,1)} & = \sqrt{(1-2)^2+(1-1)^2} = 1 \\
Expand Down Expand Up @@ -1503,7 +1503,7 @@ \subsection*{Task 2: Application of DBSCAN}

\item \textbf{Select $(4,4)$ as Random Point:}

Every unvisited point can be selected as the next point to visit. In this sample solution, we decided to use $(4,4)$ as the next point:
Every unvisited point can be selected as the next point to visit. In this sample solution, we decided to use $(4,4)$ as the next point:

\begin{enumerate}
\item \textbf{Mark $(4,4)$ as Visited:}
Expand Down Expand Up @@ -1539,7 +1539,7 @@ \subsection*{Task 2: Application of DBSCAN}

\item \textbf{Add Points in the $\varepsilon$-Neighborhood of $(4,4)$ to the Candidate Set $N$:}

Both $(3,4)$ and $(4,3)$ are unvisited points in the $\varepsilon$-neighborhood of $(4,4)$:
Both $(3,4)$ and $(4,3)$ are within the $\varepsilon$-neighborhood of $(4,4)$ and do not belong to a cluster yet:

\begin{alignat*}{2}
Distance_{(4,4)\leftrightarrow(3,4)} & = \sqrt{(4-3)^2+(4-4)^2} = 1 \\
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