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(pdftex.def) Requested size: 172.5pt x 129.37639pt. <../graphics/mnist_5/conv_only/mnist_5_upper_edges.png, id=336, 462.528pt x 346 .896pt> @@ -1501,7 +1499,7 @@ File: ../graphics/mnist_5/conv_only/mnist_5_upper_edges.png Graphic file (type png) Package pdftex.def Info: ../graphics/mnist_5/conv_only/mnist_5_upper_edges.png - used on input line 372. + used on input line 373. (pdftex.def) Requested size: 68.99895pt x 51.7463pt. <../graphics/mnist_5/conv_only/mnist_5_left_edges.png, id=337, 462.528pt x 346. 896pt> @@ -1509,7 +1507,7 @@ File: ../graphics/mnist_5/conv_only/mnist_5_left_edges.png Graphic file (type p ng) Package pdftex.def Info: ../graphics/mnist_5/conv_only/mnist_5_left_edges.png -used on input line 377. +used on input line 378. 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(pdftex.def) Requested size: 68.99895pt x 51.7463pt. <../graphics/features.png, id=342, 833.1125pt x 388.45125pt> File: ../graphics/features.png Graphic file (type png) -Package pdftex.def Info: ../graphics/features.png used on input line 398. +Package pdftex.def Info: ../graphics/features.png used on input line 399. (pdftex.def) Requested size: 345.0pt x 160.86047pt. -Underfull \hbox (badness 10000) in paragraph at lines 309--405 +Underfull \hbox (badness 10000) in paragraph at lines 310--406 [] @@ -1544,38 +1542,38 @@ ly/mnist_5_right_edges.png>] [16 <../graphics/features.png>] <../graphics/MaxpoolSample2.png, id=363, 164.25pt x 68.547pt> File: ../graphics/MaxpoolSample2.png Graphic file (type png) -Package pdftex.def Info: ../graphics/MaxpoolSample2.png used on input line 416 +Package pdftex.def Info: ../graphics/MaxpoolSample2.png used on input line 417 . 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File: ../graphics/mnist_5/conv_only/mnist_5_lower_edges.png Graphic file (type png) Package pdftex.def Info: ../graphics/mnist_5/conv_only/mnist_5_lower_edges.png - used on input line 444. + used on input line 445. (pdftex.def) Requested size: 68.99895pt x 51.7463pt. File: ../graphics/mnist_5/conv_only/mnist_5_right_edges.png Graphic file (type png) Package pdftex.def Info: ../graphics/mnist_5/conv_only/mnist_5_right_edges.png - used on input line 449. + used on input line 450. (pdftex.def) Requested size: 68.99895pt x 51.7463pt. <../graphics/mnist_5/conv_pool/upper_horiz_pooled.png, id=366, 462.528pt x 346. 896pt> @@ -1583,7 +1581,7 @@ File: ../graphics/mnist_5/conv_pool/upper_horiz_pooled.png Graphic file (type p ng) Package pdftex.def Info: ../graphics/mnist_5/conv_pool/upper_horiz_pooled.png -used on input line 454. +used on input line 455. (pdftex.def) Requested size: 68.99895pt x 51.7463pt. <../graphics/mnist_5/conv_pool/left_vert_pooled.png, id=367, 462.528pt x 346.89 6pt> @@ -1591,7 +1589,7 @@ File: ../graphics/mnist_5/conv_pool/left_vert_pooled.png Graphic file (type png ) Package pdftex.def Info: ../graphics/mnist_5/conv_pool/left_vert_pooled.png us -ed on input line 459. +ed on input line 460. (pdftex.def) Requested size: 68.99895pt x 51.7463pt. <../graphics/mnist_5/conv_pool/lower_horiz_pooled.png, id=368, 462.528pt x 346. 896pt> @@ -1599,7 +1597,7 @@ File: ../graphics/mnist_5/conv_pool/lower_horiz_pooled.png Graphic file (type p ng) Package pdftex.def Info: ../graphics/mnist_5/conv_pool/lower_horiz_pooled.png -used on input line 464. +used on input line 465. 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(pdftex.def) Requested size: 68.99895pt x 51.7463pt. <../graphics/mnist_5/conv_pool/left_vert_avgpooled.png, id=371, 462.528pt x 346 .896pt> @@ -1623,7 +1621,7 @@ File: ../graphics/mnist_5/conv_pool/left_vert_avgpooled.png Graphic file (type png) Package pdftex.def Info: ../graphics/mnist_5/conv_pool/left_vert_avgpooled.png - used on input line 479. + used on input line 480. (pdftex.def) Requested size: 68.99895pt x 51.7463pt. <../graphics/mnist_5/conv_pool/lower_horiz_avgpooled.png, id=372, 462.528pt x 3 46.896pt> @@ -1631,7 +1629,7 @@ File: ../graphics/mnist_5/conv_pool/lower_horiz_avgpooled.png Graphic file (typ e png) Package pdftex.def Info: ../graphics/mnist_5/conv_pool/lower_horiz_avgpooled.pn -g used on input line 484. +g used on input line 485. 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Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): -(hyperref) removing `\newline' on input line 504. +(hyperref) removing `\newline' on input line 505. [18 <../graphics/mnist_5/conv_pool/upper_horiz_pooled.png> <../graphics/mnist_5 /conv_pool/left_vert_pooled.png> <../graphics/mnist_5/conv_pool/lower_horiz_poo @@ -1661,7 +1659,7 @@ led.png> <../graphics/mnist_5/conv_pool/right_vert_pooled.png> <../graphics/mni st_5/conv_pool/upper_horiz_avgpooled.png> <../graphics/mnist_5/conv_pool/left_v ert_avgpooled.png> <../graphics/mnist_5/conv_pool/lower_horiz_avgpooled.png> <. ./graphics/mnist_5/conv_pool/right_vert_avgpooled.png>] [19] -Underfull \hbox (badness 10000) in paragraph at lines 521--525 +Underfull \hbox (badness 10000) in paragraph at lines 522--526 \T1/LinuxBiolinumT-TLF/m/n/10 Quelle: https://towardsdatascience.com/common-los s-functions-in-machine- [] @@ -1689,11 +1687,11 @@ p/Max-pooling_/_Pooling \openout7 = `Grundlagen_des_maschinellen_lernens.lof'. [21] -Package atveryend Info: Empty hook `BeforeClearDocument' on input line 528. -Package atveryend Info: Empty hook `AfterLastShipout' on input line 528. +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 529. +Package atveryend Info: Empty hook `AfterLastShipout' on input line 529. (./Grundlagen_des_maschinellen_lernens.aux) -Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 528. -Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 528. +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 529. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 529. Package rerunfilecheck Info: File `Grundlagen_des_maschinellen_lernens.out' has not changed. (rerunfilecheck) Checksum: B310243FE389BD4A3D39E25B868838EA;2989. @@ -1714,7 +1712,7 @@ un.xml'. 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zXaD$p|DP^DU;q2lzvuf;&c9##=hyA`_y2!g{{G(omw)SP{(Ze1U;pFV*Tc*A|M_}& z`u;yZ-cEmSSNH$rVSf7)_J2M+{H&h&!2kZgU$=MLpP2pS-Tt~?pH6SL|975WeqZJH s_x68(y%fKDMS1P5_SG-%@2mO#^Y{GvpI?vX-}@{7pxt59p&8r^01p}5=>Px# diff --git a/doc/Grundlagen_des_maschinellen_lernens.tex b/doc/Grundlagen_des_maschinellen_lernens.tex index 89235e7..fc8c4c5 100644 --- a/doc/Grundlagen_des_maschinellen_lernens.tex +++ b/doc/Grundlagen_des_maschinellen_lernens.tex @@ -46,7 +46,7 @@ Die wohl bekannteste und am häufigsten zitierte Definiton des maschinellen Lern \end{flushright} \end{quote} 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 -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''. +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''. Dies wird für die zwei Hauptproblemklassen, die man unterscheidet, verwendet. Klassifizierungs und Regressionsprobleme. \subsection{Klassifizierungsprobleme} 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.\\ @@ -60,6 +60,7 @@ Das Erste Beispiel würde man als \glqq Binärklassifizierung'' bezeichnen, da z \\ 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} +Als Regressionsproblem hingegen bezeichnet man das Finden einer Funktion, die eine Menge von Eingabevariablen einer Stetigen Menge von Ausgabevariablen zuordnet. Wenn beispielsweise ein Bild eines Menschen gegeben ist, könnte ein Regressionsproblem sein, seine Höhe oder sein Gewicht zu bestimmen. \subsection{Gefahren von maschinellem Lernen} \subsubsection{Eignung der Datensätze} \subsubsection{Overfitting} diff --git a/doc/Grundlagen_des_maschinellen_lernens.toc b/doc/Grundlagen_des_maschinellen_lernens.toc index 14b49c3..b629cfe 100644 --- a/doc/Grundlagen_des_maschinellen_lernens.toc +++ b/doc/Grundlagen_des_maschinellen_lernens.toc @@ -7,47 +7,47 @@ \defcounter {refsection}{0}\relax \contentsline {subsection}{\numberline {1.2}Regressionsprobleme}{4}{subsection.1.2}% \defcounter {refsection}{0}\relax -\contentsline {subsection}{\numberline {1.3}Gefahren von maschinellem Lernen}{4}{subsection.1.3}% +\contentsline {subsection}{\numberline {1.3}Gefahren von maschinellem Lernen}{5}{subsection.1.3}% \defcounter {refsection}{0}\relax -\contentsline {subsubsection}{\numberline {1.3.1}Eignung der Datens\IeC {\"a}tze}{4}{subsubsection.1.3.1}% +\contentsline {subsubsection}{\numberline {1.3.1}Eignung der Datens\IeC {\"a}tze}{5}{subsubsection.1.3.1}% \defcounter {refsection}{0}\relax -\contentsline {subsubsection}{\numberline {1.3.2}Overfitting}{4}{subsubsection.1.3.2}% +\contentsline {subsubsection}{\numberline {1.3.2}Overfitting}{5}{subsubsection.1.3.2}% \defcounter {refsection}{0}\relax -\contentsline {subsubsection}{\numberline {1.3.3}Unbewusste Manipulation der Daten}{4}{subsubsection.1.3.3}% +\contentsline {subsubsection}{\numberline {1.3.3}Unbewusste Manipulation der Daten}{5}{subsubsection.1.3.3}% \defcounter {refsection}{0}\relax -\contentsline {section}{\numberline {2}Verschiedene Techniken maschinellen lernens}{4}{section.2}% +\contentsline {section}{\numberline {2}Verschiedene Techniken maschinellen lernens}{5}{section.2}% \defcounter {refsection}{0}\relax -\contentsline {subsection}{\numberline {2.1}\IeC {\"U}berwachtes Lernen}{4}{subsection.2.1}% +\contentsline {subsection}{\numberline {2.1}\IeC {\"U}berwachtes 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{subsection}{\numberline {3.3}Berechnung des Ausgabevektors}{7}{subsection.3.3}% +\contentsline {subsection}{\numberline {3.3}Berechnung des Ausgabevektors}{6}{subsection.3.3}% \defcounter {refsection}{0}\relax \contentsline {subsection}{\numberline {3.4}Der Lernprozess}{9}{subsection.3.4}% \defcounter {refsection}{0}\relax -\contentsline {subsection}{\numberline {3.5}Fehlerfunktionen}{9}{subsection.3.5}% +\contentsline {subsection}{\numberline {3.5}Fehlerfunktionen}{10}{subsection.3.5}% \defcounter {refsection}{0}\relax -\contentsline {subsubsection}{\numberline {3.5.1}MSE -- Durchschnittlicher quadratischer Fehler}{9}{subsubsection.3.5.1}% +\contentsline {subsubsection}{\numberline {3.5.1}MSE -- Durchschnittlicher quadratischer Fehler}{10}{subsubsection.3.5.1}% \defcounter {refsection}{0}\relax \contentsline {subsubsection}{\numberline {3.5.2}MAE -- Durchschnitztlicher absoluter Fehler}{10}{subsubsection.3.5.2}% \defcounter {refsection}{0}\relax -\contentsline {subsubsection}{\numberline {3.5.3}Kreuzentropiefehler}{10}{subsubsection.3.5.3}% +\contentsline {subsubsection}{\numberline {3.5.3}Kreuzentropiefehler}{11}{subsubsection.3.5.3}% \defcounter {refsection}{0}\relax -\contentsline {subsection}{\numberline {3.6}Gradientenverfahren und Backpropagation}{11}{subsection.3.6}% +\contentsline {subsection}{\numberline {3.6}Gradientenverfahren und Backpropagation}{12}{subsection.3.6}% \defcounter {refsection}{0}\relax -\contentsline {subsubsection}{\numberline {3.6.1}Lernrate}{12}{subsubsection.3.6.1}% +\contentsline {subsubsection}{\numberline {3.6.1}Lernrate}{13}{subsubsection.3.6.1}% \defcounter {refsection}{0}\relax -\contentsline {subsection}{\numberline {3.7}Verschiedene Layerarten}{12}{subsection.3.7}% +\contentsline {subsection}{\numberline {3.7}Verschiedene Layerarten}{14}{subsection.3.7}% \defcounter {refsection}{0}\relax -\contentsline {subsubsection}{\numberline {3.7.1}Convolutional Layers}{13}{subsubsection.3.7.1}% +\contentsline 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