diff --git a/Readme.md b/Readme.md
index 0abac8c..b0202ef 100644
--- a/Readme.md
+++ b/Readme.md
@@ -21,8 +21,8 @@ Dieses Repo beinhaltet die $\LaTeX$ Informationen für die Zusammenfassung im Fa
- [x] Äquivalenztabelle aus Übung 6 (Prädikatenlogik)
- [x] Skolemisierungsverfahren hinzufügen
- [ ] Unifikationsverfahren hinzufügen
-- [ ] Kosinusähnlichkeit hinzufügen (Übung 8)
-- [ ] Mahalanobis Abstand hinzufügen (Übung 8)
+- [x] Kosinusähnlichkeit hinzufügen (Übung 8)
+- [x] Mahalanobis Abstand hinzufügen (Übung 8)
## Hinweise
Requires you to enable [--shell escape](https://tex.stackexchange.com/questions/516604/how-to-enable-shell-escape-or-write18-visual-studio-code-latex-workshop)
diff --git a/chapters/Maschinelles Lernen/Ähnlichkeitsbasiertes Lernen.tex b/chapters/Maschinelles Lernen/Ähnlichkeitsbasiertes Lernen.tex
index ff8c880..ab3a8ef 100644
--- a/chapters/Maschinelles Lernen/Ähnlichkeitsbasiertes Lernen.tex
+++ b/chapters/Maschinelles Lernen/Ähnlichkeitsbasiertes Lernen.tex
@@ -5,6 +5,13 @@
\section{Ähnlichkeitsmaß}
\label{aehnlichkeitsmass}
+ \begin{wrapfigure}{h}{.4\textwidth}
+ \vspace{-30mm}
+ \includegraphics[width = .4\textwidth]{manhattan_euclidean_1.pdf}\\
+ \includegraphics[width = .4\textwidth]{cosine1.pdf}
+ \vspace{-20mm}
+ \end{wrapfigure}
+
\paragraph{Euklidischer Abstand}
\large
$$dist_e(a,b))\sqrt{\sum^n_{i=1}\left(a[i]-b[i]\right)^2}$$
@@ -15,6 +22,23 @@
$$dist_m(a,b)=\sum^n_{i=1}|a[i]-b[i]|$$
\normalsize
+ \paragraph{Kosinus-Ähnlichkeit}
+ \large
+ $$dist_c(a,b)=\cos(\theta)$$
+ $$=\frac{a\cdot b}{||a||\cdot||b||} = \frac{\sum^n_{i=1}a_i\cdot b_i}{\sqrt{\sum^n_{i=1}a_i^2}\cdot\sqrt{\sum^n_{i=1}b_i^2}}$$
+ \normalsize
+
+ \paragraph{Mahalanobis-Abstand}
+ berücksichtigt die Richtung, in die die Daten verteilt sind.\\
+ ($\sum^{-1}$ ist die inverse der Kovarianzmatrix)
+ \large
+ $$dist_{\text{Mahalanobis}}(a,b) = \sqrt{[a_1-b_1,\dots,a_n-b_n]\sum^{-1}\begin{bmatrix}
+ a_1-b_1\\
+ \vdots\\
+ a_n-b_n
+ \end{bmatrix}}$$
+ \normalsize
+
\section{K-Nächste-Nachbarn}
\label{k-nearest-neighbour}
Beim \say{K-Nächste-Nachbarn}-Verfahren wird dem System eine Reihe von gelabelten Trainingsdaten übergeben.
diff --git a/images/cosine1.pdf b/images/cosine1.pdf
new file mode 100644
index 0000000..c0e6508
--- /dev/null
+++ b/images/cosine1.pdf
@@ -0,0 +1,471 @@
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