?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Understanding+Slow+Feature+Analysis%3A+A+Mathematical+Framework&rft.creator=Sprekeler%2C+Henning&rft.creator=Wiskott%2C+Dr.++Laurenz&rft.subject=Computational+Neuroscience&rft.subject=Machine+Learning&rft.description=Slow+feature+analysis+is+an+algorithm+for+unsupervised+learning+of+invariant+representations+from+data+with+temporal+correlations.+Here%2C+we+present+a+mathematical+analysis+of+slow+feature+analysis+for+the+case+where+the+input-output+functions+are+not+restricted+in+complexity.+We+show+that+the+optimal+functions+obey+a+partial+differential+eigenvalue+problem+of+a+type+that+is+common+in+theoretical+physics.+This+analogy+allows+the+transfer+of+mathematical+techniques+and+intuitions+from+physics+to+concrete+applications+of+slow+feature+analysis%2C+thereby+providing+the+means+for+analytical+predictions+and+a+better+understanding+of+simulation+results.+We+put+particular+emphasis+on+the+situation+where+the+input+data+are+generated+from+a+set+of+statistically+independent+sources.%0D%0AThe+dependence+of+the+optimal+functions+on+the+sources+is+calculated+analytically+for+the+cases+where+the+sources+have+Gaussian+or+uniform+distribution.&rft.date=2008-08-19&rft.type=Preprint&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.identifier=http%3A%2F%2Fcogprints.org%2F6223%2F2%2FSprekelerWiskott08.pdf&rft.identifier=++Sprekeler%2C+Henning+and+Wiskott%2C+Dr.+Laurenz++(2008)+Understanding+Slow+Feature+Analysis%3A+A+Mathematical+Framework.++%5BPreprint%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F6223%2F