?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=How+to+Solve+Classification+and+Regression+Problems+on+High-Dimensional+Data+with+a+Supervised+Extension+of+Slow+Feature+Analysis&rft.creator=Escalante-B.%2C+Alberto-N.&rft.creator=Wiskott%2C+Prof.+Dr.+Laurenz&rft.subject=Machine+Learning&rft.subject=Machine+Vision&rft.subject=Neural+Nets&rft.description=Supervised+learning+from+high-dimensional+data%2C+e.g.%2C+multimedia+data%2C+is+a+challenging+task.+We+propose+an+extension+of+slow+feature+analysis+(SFA)+for+supervised+dimensionality+reduction+called+graph-based+SFA+(GSFA).+The+algorithm+extracts+a+label-predictive+low-dimensional+set+of+features+that+can+be+post-processed+by+typical+supervised+algorithms+to+generate+the+%EF%AC%81nal+label+or+class+estimation.+GSFA+is+trained+with+a+so-called+training+graph%2C+in+which+the+vertices+are+the+samples+and+the+edges+represent+similarities+of+the+corresponding+labels.+A+new+weighted+SFA+optimization+problem+is+introduced%2C+generalizing+the+notion+of+slowness+from+sequences+of+samples+to+such+training+graphs.+We+show+that+GSFA+computes+an+optimal+solution+to+this+problem+in+the+considered+function+space%2C+and+propose+several+types+of+training+graphs.+For+classi%EF%AC%81cation%2C+the+most+straightforward+graph+yields+features+equivalent+to+those+of+(nonlinear)+Fisher+discriminant+analysis.+Emphasis+is+on+regression%2C+where+four+different+graphs+were+evaluated+experimentally+with+a+subproblem+of+face+detection+on+photographs.+The+method+proposed+is+promising+particularly+when+linear+models+are+insufficient%2C+as+well+as+when+feature+selection+is+difficult.&rft.date=2013-02&rft.type=Preprint&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.identifier=http%3A%2F%2Fcogprints.org%2F8966%2F1%2FEscalanteWiskott-Cogprints-2013.pdf&rft.identifier=++Escalante-B.%2C+Alberto-N.+and+Wiskott%2C+Prof.+Dr.+Laurenz++(2013)+How+to+Solve+Classification+and+Regression+Problems+on+High-Dimensional+Data+with+a+Supervised+Extension+of+Slow+Feature+Analysis.++%5BPreprint%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F8966%2F