Added classification chapter
This commit is contained in:
Clemens Dautermann
parent
f20007b599
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f18b99c981
11 changed files with 1552 additions and 203 deletions
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@ -48,6 +48,17 @@ Die wohl bekannteste und am häufigsten zitierte Definiton des maschinellen Lern
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Beim maschinellen lernen werden Computer also nicht mit einem bestimmten Algorythmus programmiert um eine Aufgabe zu lösen, sondern lernen eigenständig diese Aufgabe zu bewältigen. Dies geschieht zumeist, indem das Programm aus einer großen, bereits \glqq gelabelten'', Datenmenge mit Hilfe bestimmter Methoden, die im Folgenden weiter erläutert werden sollen, lernt, gewisse Muster abzuleiten um eine ähnliche Datenmenge selber \glqq labeln'' zu können. Als Label bezeichent man in diesem Fall die gewünschte Ausgabe des Programmes. Dies kann beispielsweise eine Klassifikation sein. Soll das Programm etwa handgeschriebene Ziffern erkennen können, so bezeichnet man das (bearbeitete) Bild der Ziffer als \glqq Input Verctor'' und die Information welche Ziffer der Copmputer hätte erkennen sollen, als \glqq Label ''. Soll jedoch maschinell erlernt werden, ein simuliertes Auto zu fahren, so bestünde der Input Vector aus Sensorinformationen und das Label würde aussagen, in welche Richtung das Lenkrad hätte gedreht werden sollen, wie viel Gas das Programm hätte geben sollen oder andere Steuerungsinformationen. Der Input Vector ist also immer die Eingabe, die der Computer erhält um daraus zu lernen und das Label ist die richtige Antwort, die vom Programm erwartet wurde. Für maschinelles Lernen wird also vor allem eins benötigt: Ein enormer Datensatz, der bereits gelabelt wurde, damit das Programm daraus lernen kann.\newline
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||||
Natürlich werden für maschinelles Lernen trotzdem Algorythmen benötigt. Diese Algorythmen sind jedoch keine problemspezifischen Algorythmen, sondern Algorythmen für maschinelles Lernen. Eine der populärsten Methoden des maschinellen Lernens ist das sogenannte \glqq Neuronale Netz''.
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||||
\subsection{Klassifizierungsprobleme}
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||||
Als Klassifizierfung bezeichnet man das Finden einer Funktion, die eine Menge von Eingabevariablen zu einer diskreten Menge von Ausgabevariablen, die auch als Klassen oder Labels bezeichnet werden, zuordnet. Dies kann beispielsweise das Erkennen von Mail Spam sein. Die Eingabevariablen sind die E-Mails und sie sollen den zwei Klassen \glqq Spam'' und \glqq nicht Spam'' zugeortnet werden.\\
|
||||
Das in Dieser Arbeit gegebene Beispiel ist auch ein Klassifizierungsproblem. Die gegebenen Bilder von Ziffern sollen den zehn Klassen \glqq 0 bis 9'' zugeordnet werden. Die Bilder sind hier die Eingabevariablen und die Klassen null bis neun beschreibt die endliche Menge diskreter Labels.\\
|
||||
Das Erste Beispiel würde man als \glqq Binärklassifizierung'' bezeichnen, da zwei Klassen unterschieden werden. Letzteres wird als \glqq Multiklassenklassifizierung'' bezeichnet, da mehr als zwei Klassen unterschieden werden. Die Binärklassifizierung ist in Abbildung \ref{Classification} verbildlicht.
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.4\linewidth]{../graphics/Classification.png}
|
||||
\caption{Binärklassifizierung}
|
||||
\label{Classification}
|
||||
\end{figure}
|
||||
\\
|
||||
Die zwei Klassen wären hier \glqq grün'' und \glqq blau''. Die Linie stellt die Klassengrenze dar, die die zwei Klassen unterscheidet. Es sind außerdem einige Ausreißer in den Daten vorhanden.
|
||||
\subsection{Regressionsprobleme}
|
||||
\subsection{Gefahren von maschinellem Lernen}
|
||||
\subsubsection{Eignung der Datensätze}
|
||||
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@ -3,7 +3,7 @@
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\defcounter {refsection}{0}\relax
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\contentsline {section}{\numberline {1}Was ist maschinelles Lernen?}{3}{section.1}%
|
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {1.1}Klassifizierungsprobleme}{4}{subsection.1.1}%
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\contentsline {subsection}{\numberline {1.1}Klassifizierungsprobleme}{3}{subsection.1.1}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {1.2}Regressionsprobleme}{4}{subsection.1.2}%
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\defcounter {refsection}{0}\relax
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@ -25,19 +25,19 @@
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|||
\defcounter {refsection}{0}\relax
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||||
\contentsline {section}{\numberline {3}Neuronale Netze}{4}{section.3}%
|
||||
\defcounter {refsection}{0}\relax
|
||||
\contentsline {subsection}{\numberline {3.1}Maschinelles Lernen und menschliches Lernen}{4}{subsection.3.1}%
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\contentsline {subsection}{\numberline {3.1}Maschinelles Lernen und menschliches Lernen}{5}{subsection.3.1}%
|
||||
\defcounter {refsection}{0}\relax
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||||
\contentsline {subsection}{\numberline {3.2}Der Aufbau eines neuronalen Netzes}{5}{subsection.3.2}%
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\contentsline {subsection}{\numberline {3.2}Der Aufbau eines neuronalen Netzes}{6}{subsection.3.2}%
|
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\defcounter {refsection}{0}\relax
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||||
\contentsline {subsection}{\numberline {3.3}Berechnung des Ausgabevektors}{6}{subsection.3.3}%
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\contentsline {subsection}{\numberline {3.3}Berechnung des Ausgabevektors}{7}{subsection.3.3}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {3.4}Der Lernprozess}{8}{subsection.3.4}%
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\contentsline {subsection}{\numberline {3.4}Der Lernprozess}{9}{subsection.3.4}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {3.5}Fehlerfunktionen}{9}{subsection.3.5}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsubsection}{\numberline {3.5.1}MSE -- Durchschnittlicher quadratischer Fehler}{9}{subsubsection.3.5.1}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsubsection}{\numberline {3.5.2}MAE -- Durchschnitztlicher absoluter Fehler}{9}{subsubsection.3.5.2}%
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\contentsline {subsubsection}{\numberline {3.5.2}MAE -- Durchschnitztlicher absoluter Fehler}{10}{subsubsection.3.5.2}%
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\defcounter {refsection}{0}\relax
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||||
\contentsline {subsubsection}{\numberline {3.5.3}Kreuzentropiefehler}{10}{subsubsection.3.5.3}%
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\defcounter {refsection}{0}\relax
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||||
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@ -45,38 +45,38 @@
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\defcounter {refsection}{0}\relax
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\contentsline {subsubsection}{\numberline {3.6.1}Lernrate}{12}{subsubsection.3.6.1}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {3.7}Verschiedene Layerarten}{13}{subsection.3.7}%
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\contentsline {subsection}{\numberline {3.7}Verschiedene Layerarten}{12}{subsection.3.7}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsubsection}{\numberline {3.7.1}Convolutional Layers}{13}{subsubsection.3.7.1}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsubsection}{\numberline {3.7.2}Pooling Layers}{15}{subsubsection.3.7.2}%
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\contentsline {subsubsection}{\numberline {3.7.2}Pooling Layers}{16}{subsubsection.3.7.2}%
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\defcounter {refsection}{0}\relax
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\contentsline {section}{\numberline {4}PyTorch}{18}{section.4}%
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\contentsline {section}{\numberline {4}PyTorch}{19}{section.4}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {4.1}Datenvorbereitung}{18}{subsection.4.1}%
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\contentsline {subsection}{\numberline {4.1}Datenvorbereitung}{19}{subsection.4.1}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {4.2}Definieren des Netzes}{18}{subsection.4.2}%
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\contentsline {subsection}{\numberline {4.2}Definieren des Netzes}{19}{subsection.4.2}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {4.3}Trainieren des Netzes}{18}{subsection.4.3}%
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\contentsline {subsection}{\numberline {4.3}Trainieren des Netzes}{19}{subsection.4.3}%
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\defcounter {refsection}{0}\relax
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\contentsline {section}{\numberline {5}Fallbeispiel I:\newline Ein Klassifizierungsnetzwerk f\IeC {\"u}r handgeschriebene Ziffern}{18}{section.5}%
|
||||
\contentsline {section}{\numberline {5}Fallbeispiel I:\newline Ein Klassifizierungsnetzwerk f\IeC {\"u}r handgeschriebene Ziffern}{19}{section.5}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {5.1}Aufgabe}{18}{subsection.5.1}%
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\contentsline {subsection}{\numberline {5.1}Aufgabe}{19}{subsection.5.1}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {5.2}Der MNIST Datensatz}{18}{subsection.5.2}%
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\contentsline {subsection}{\numberline {5.2}Der MNIST Datensatz}{19}{subsection.5.2}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {5.3}Fragmentbasierte Erkennung}{18}{subsection.5.3}%
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\contentsline {subsection}{\numberline {5.3}Fragmentbasierte Erkennung}{19}{subsection.5.3}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {5.4}Ergebnis}{18}{subsection.5.4}%
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\contentsline {subsection}{\numberline {5.4}Ergebnis}{19}{subsection.5.4}%
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\defcounter {refsection}{0}\relax
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\contentsline {section}{\numberline {6}Fallbeispiel II:\newline Eine selbsttrainierende KI f\IeC {\"u}r Tic-Tac-Toe}{18}{section.6}%
|
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\contentsline {section}{\numberline {6}Fallbeispiel II:\newline Eine selbsttrainierende KI f\IeC {\"u}r Tic-Tac-Toe}{19}{section.6}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {6.1}Das Prinzip}{18}{subsection.6.1}%
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\contentsline {subsection}{\numberline {6.1}Das Prinzip}{19}{subsection.6.1}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {6.2}Chance-Tree Optimierung}{18}{subsection.6.2}%
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\contentsline {subsection}{\numberline {6.2}Chance-Tree Optimierung}{19}{subsection.6.2}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {6.3}L\IeC {\"o}sung mittels eines neuronalen Netzes}{18}{subsection.6.3}%
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\contentsline {subsection}{\numberline {6.3}L\IeC {\"o}sung mittels eines neuronalen Netzes}{19}{subsection.6.3}%
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\defcounter {refsection}{0}\relax
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\contentsline {subsection}{\numberline {6.4}Vergleich}{18}{subsection.6.4}%
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\contentsline {subsection}{\numberline {6.4}Vergleich}{19}{subsection.6.4}%
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\defcounter {refsection}{0}\relax
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\contentsline {section}{\numberline {7}Schlusswort}{18}{section.7}%
|
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\contentsline {section}{\numberline {7}Schlusswort}{19}{section.7}%
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