\relax \ifx\hyper@anchor\@undefined \global \let \oldcontentsline\contentsline \gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} \global \let \oldnewlabel\newlabel \gdef \newlabel#1#2{\newlabelxx{#1}#2} \gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} \AtEndDocument{\let \contentsline\oldcontentsline \let \newlabel\oldnewlabel} \else \global \let \hyper@last\relax \fi \bibstyle{amsrn} \citation{Papa:Duda:00} \citation{Papa:Falcao:04} \select@language{english} \@writefile{toc}{\select@language{english}} \@writefile{lof}{\select@language{english}} \@writefile{lot}{\select@language{english}} \@writefile{toc}{\contentsline {chapter}{\numberline {1}Design of robust pattern classifiers based on optimum-path forests}{337}{chapter.1}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{337}{section.1.1}} \newlabel{xxx:sec:intro}{{1}{337}{Introduction\relax }{section.1.1}{}} \citation{Papa:Duda:00} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces (a)~Complete weighted graph for a simple training set. (b)~Resulting optimum-path forest from (a) for $f_{max}$ and two given prototypes (circled nodes). The entries $(x,y)$ over the nodes are, respectively, cost and label of the samples. (c)~Test sample (gray square) and its connections (dashed lines) with the training nodes. (d)~The optimum path from the most strongly connected prototype, its label $2$, and classification cost $0.4$ are assigned to the test sample.}}{338}{figure.1.1}} \newlabel{xxx:fig:example}{{1}{338}{Introduction\relax }{figure.1.1}{}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {}}}{338}{figure.1.1}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {}}}{338}{figure.1.1}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(c)}{\ignorespaces {}}}{338}{figure.1.1}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(d)}{\ignorespaces {}}}{338}{figure.1.1}} \citation{Papa:Vapnik:92} \citation{Papa:Zahn:71} \citation{Papa:Hubert:74} \citation{Papa:Malik:00} \citation{Papa:Blum:01} \citation{Papa:Kuncheva:04} \citation{Papa:Vapnik:92} \citation{Papa:Kuncheva:04} \citation{Papa:Reyzin:06} \citation{Papa:Tang:06} \citation{Papa:Panda:06} \citation{Papa:Collobert:04} \@writefile{toc}{\contentsline {section}{\numberline {2}Related works}{339}{section.1.2}} \newlabel{xxx:sec:relatedworks}{{2}{339}{Related works\relax }{section.1.2}{}} \citation{Papa:site-libsvm} \citation{Papa:Arica:BAS:03} \@writefile{toc}{\contentsline {section}{\numberline {3}Optimum path classifier}{340}{section.1.3}} \newlabel{xxx:sec:classifier}{{3}{340}{Optimum path classifier\relax }{section.1.3}{}} \citation{Papa:Falcao:04} \citation{Papa:Falcao:04} \newlabel{xxx:alg:opf}{{1}{341}{Optimum path classifier\relax }{algorithm.1}{}} \citation{Papa:LotufoMM:00} \citation{Papa:Cormen:90} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Training}{342}{subsection.1.3.1}} \newlabel{xxx:ssec:training}{{3.1}{342}{Training\relax }{subsection.1.3.1}{}} \citation{Papa:Cousty:07} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces (a) MST of the graph shown in Figure~\ref {xxx:fig:example}a where the optimum prototypes share the arc of weight $0.6$. (b) The classification of the test sample (gray square) $t$ as in Figure~\ref {xxx:fig:example}c assigns the optimum path $P^\ast (t)$ from $R(t)\in S^\ast $ to $t$ passing through $s^\ast $.}}{343}{figure.1.2}} \newlabel{xxx:fig:mst-classification}{{2}{343}{Training\relax }{figure.1.2}{}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {}}}{343}{figure.1.2}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {}}}{343}{figure.1.2}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Classification}{343}{subsection.1.3.2}} \newlabel{xxx:eq:classification}{{2}{343}{Classification\relax }{equation.2}{}} \@writefile{toc}{\contentsline {section}{\numberline {4}Learning Algorithm}{344}{section.1.4}} \newlabel{xxx:sec:learning}{{4}{344}{Learning Algorithm\relax }{section.1.4}{}} \newlabel{xxx:alg:learning}{{2}{344}{Learning Algorithm\relax }{algorithm.2}{}} \newlabel{xxx:eq:lr}{{5}{345}{Learning Algorithm\relax }{equation.5}{}} \citation{Papa:Vapnik:92} \citation{Papa:Kuncheva:04} \citation{Papa:MPEG-7:02} \citation{Papa:Collins:1998} \citation{Papa:Collins:1998} \@writefile{toc}{\contentsline {section}{\numberline {5}Results}{346}{section.1.5}} \newlabel{xxx:sec:results}{{5}{346}{Results\relax }{section.1.5}{}} \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces (a) Painted database with outliers. (b) OPF learning curve on $Z_2$.}}{346}{figure.1.3}} \newlabel{xxx:fig:painted}{{3}{346}{Results\relax }{figure.1.3}{}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {}}}{346}{figure.1.3}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {}}}{346}{figure.1.3}} \bibcite{Papa:Arica:BAS:03}{{1}{}} \@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Mean and standard deviation of the accuracies for each database.}}{347}{table.1.1}} \newlabel{xxx:tab:Stats}{{1}{347}{Results\relax }{table.1.1}{}} \@writefile{toc}{\contentsline {section}{\numberline {6}Conclusions and future work}{347}{section.1.6}} \newlabel{xxx:sec:conclusion}{{6}{347}{Conclusions and future work\relax }{section.1.6}{}} \bibcite{Papa:Blum:01}{{2}{}} \bibcite{Papa:Vapnik:92}{{3}{}} \bibcite{Papa:site-libsvm}{{4}{}} \bibcite{Papa:Collins:1998}{{5}{}} \bibcite{Papa:Collobert:04}{{6}{}} \bibcite{Papa:Cormen:90}{{7}{}} \bibcite{Papa:Cousty:07}{{8}{}} \bibcite{Papa:Duda:00}{{9}{}} \bibcite{Papa:Falcao:04}{{10}{}} \bibcite{Papa:Hubert:74}{{11}{}} \bibcite{Papa:Kuncheva:04}{{12}{}} \bibcite{Papa:LotufoMM:00}{{13}{}} \bibcite{Papa:MPEG-7:02}{{14}{}} \bibcite{Papa:Panda:06}{{15}{}} \bibcite{Papa:Reyzin:06}{{16}{}} \bibcite{Papa:Malik:00}{{17}{}} \bibcite{Papa:Tang:06}{{18}{}} \bibcite{Papa:Zahn:71}{{19}{}} \newlabel{[bibenv:1]}{13.21579pt}