Longrangefractaldynamicinvisualsearchampbeyond長距離的視覺搜索和分形動力學超越課件

RalfPlag-SchützenstrasseKarlsruhe-Germanyhttp://www.fractal-dome.de/e2dg1.shtmlScale-free-->Rethinkingwhatwestudy&measurePowerlaws!BehaviorBehavior#Typicalscale=CentraltendencyNewman,M.(2005).Powerlaws,ParetodistributionsandZipf’slaws.PhysicsLetters,2.

Deterministicrules?

Simplesetofneuronalinteractionrules(e.g.,SOC,Volterra..)?

Long-rangedynamic?

Memory?Aretherecorrelationsacrosssequenceoffixations?Whatguideseye-movements

duringvisualsearch?Find:Whatdoesvisualsearchteachus?Perceptualprocesses!Efficiency&Accuracy

MechanismsAutomaticvs.VoluntaryDistributedvs.FocusedAttentionInattention,Pre-&Post-attentionEarlyvs.latevision

SearchstrategyParallel,Serial,randomor…?

Lookforthereditem++++++++++++++++++++++LLLLLLLLLLLL300400500#ofitems510150ms/itemFeaturesearchFast(300ms)Parallel(0-10ms/item)DistributedattentionEarlyvisionFeatures...FindtheodditemDiscriminateby..Color xxxxxxxSize xxxxxxxOrientation ------l- Movementxxxx-->Depthx

ConjunctionSearchFind...combinationoffeatures

2orientations(particulararrangement)Find:LamongTs

TTTLTTTTTTTTLTTTTTTTTTTTTTTTTTL300500700#ofitems5101540ms/item0ms/itemFeatureConjunctionConjunctionsearchSlowerSequentialFocusedattentionneededLatevisionThechangeinRTand/oraccuracywithsetsizeisameasureoftheefficiencyofsearch.Inhighlyefficientsearches,attentionisdeployeddirectlytothetargetlocationand,thus,thenumberofdistractorsdoesnotinfluenceRT.Ininefficientsearchthroughitemsthatcanbeidentifiedwithoutfixation,eachadditionaldistractortypicallyadds20-40mstothetimerequiredtofindapresenttargetand40-80mstothetimerequiredtodeterminethatatargetisnotpresent(Wolfe,1998).Morerecentvisualsearchtheory…Deptheffectsonvisualsearch~1989-1997shadingtexturegradientisoluminantgradientsaerialperspectiveheight-in-planeMycontributiontoourunderstandingof‘early’vision&thefeature/conjunctiondistinctionARVO‘95Whatguidessearch?EnvironmentalinformationLotsInternalcognitiveprocessAttention.MemoryNeuronalinteractions---->DeterministicProcessSelf-OrganizedCriticality(SOC)?Horowitz,T.S.&Wolfe,J.M.(1998).Visual

Searchhasnomemory.Nature,357,575-577.

Finding:Randomrepositioningofstimuli

doesnotaffectsearchRTs

Nomemory?Dowekeeptrackofwherewelook?

Istherememoryinsearch?Memoryinvisualsearch?Memoryforlocationsinsearch(Kristjansso,2000)

Identityofobjectsaccumulatesovertime(Treisman&Gelade,1980)Implicitmemory(lotsofcontexteffects)

Olivia&Wolfe,2004)RandomrepositioningofstimulidoesnotaffectsearchRTs (Horowitz&Wolfe,1998)

Inattentionalamnesiainsearch(Wolfe,1999)(Wolfe,2003;Wolfeetal.,2000,2002)describedrepeatedsearchtasksinwhichfamiliaritywithasearchdisplayproducedlittleornoimprovementinsearchefficiencyEvidencefor…Evidence

against

Weareabletokeeptrackofwherewelook!

Inhibitionofreturn

(Klein,1982)

Failuretoreplicateinhibitionofreturn

(Wolfe&Pokorny,1990)

Horowitz,T.S.&Wolfe,J.M.(1998).Visual

Searchhasnomemory.Nature,357,575-577.

KeyPressRTsvs.EyeMovements

Finding:Randomrepositioningofstimuli

doesnotaffectsearchRTs

Non-systematiceye-movementsEngle,1977;Ellis&Stark,1988;Scinto&Pillalamarri,1986;Krendel&Wodinsky,1960;Groner&Groner,1982Aks,D.J.ZelinskyG.&SprottJ.C.(2002).MemoryAcrossEye-Movements:1/fDynamicinVisualSearch.NonlinearDynamics,PsychologyandLifeSciences,6(1),1-15.GregoryZelinsky

SUNY-StonybrookJulienC.Sprott

UW-MadisonEye-movementstudyCollaboratorsOverviewQUESTIONS.Whatguidescomplicatedeyemovements?Randomornon-randomprocess?Istherememoryacrossfixations?Mightneuralinteractionsdrivesearch?

METHODOFTESTING.Challengingvisualsearchtask

KEYANALYSES

‘Heavy-tail’distributions?Powerlawrelation?Coloringofnoise-->Memoryacrosseye-movementsFourieranalysis

VisualSearchTaskTTTTTTTFindtheupright“T”TTTTTTTTTTTTTTTTTTTTTTTTTTTTMethod.Eachtrialcontained81Ts.400trialslasting2.5

hours.1secondcentralfixationEight20-minutesessionsseparatedby5-minuterestGenerationVdualpurkinje-image(DPI)tracker

Maptrajectoryofeyes: Duration&x,ycoordinatesforeachfixation.

----------------------------------------------------------

Differencesbetweenfixations

xn–xn+1&

yn–yn+1

Distance=

(x2+y2)1/2

Direction=Arctan(y/x).

AnalysesProbabilityDistributionsPowerspectra(FFT)

Descriptive&CorrelationalStatisticsAdditionaltests..Results24fixationspertrial(onaverage)7.6seconds(SD=6.9sec)pertrial(316ms/item).Meanfixationduration=212ms(SD=89ms)10,215fixationsacrosscompletesearchexperiment.Conventionalsearchstats…Focusingonthedynamic…What’sthecentraltendency?SeriesofFixationDifferences(yn+1-yn)Scatterplotof10,215eyefixationsfortheentirevisualsearchexperiment.

EyeFixationsDelayPlotofFixationsyn

-vs-yn+1Across8sessionsweseescaling:Fixationfrequencydecreasedfrom1888to657Fixationdurationincreasedfrom206to217ms.Changesinfixationposition…

xn–xn+1decreased

yn–yn+1increased

Notypicalscale!ScalingfromContextsensitivity--->Scale-freeprocess

Powerlaws!Rethinkingwhatwestudy&measureHeavy-taildistributionsPower-laws,Pareto&80/20lawsSmalleventsarecommon;largeonesarerare!xn

-vs-xn+1Heavy-taildistributionsSmalleventsarecommon;largeonesarerare!yn

-vs-yn+1Network--->DistributionBarabasi,A.&Bonabeau,E.(2003).Scale-FreeNetworks.ScientificAmerican,288,60-69./~networks/gallery.htmEdelman&Tononi,2000SpectralanalysisFast-FourierTransform(FFT)

Powervs.FrequencyRegressionslope=powerexponentfaf-2=1/f2BrownnoiseNoisytimeseriesWhitePinkBrownWhiteNoisePinkNoiseBrownNoise1/f0noise--flatspectrum=nocorrelationacrossdatapointsShort&Longrange=01/fnoise--shallowslope=subtlelongrangecorrelation1/f2noise--steepslope=

Predictablelong-range,‘undulating’correlationShortrange=0(successiveeventsuncorrelated)Powerlawindicates…Fractalproperties:

Scale-free(meansw/measuringresolution)Self-similar(statistically)Critical+flexible(1/f)Memory

Steepnessoftheslope(onalog-logscale)reflects..CorrelationacrossdatapointsWhite--nomemoryPink-subtle,long-rangeBrown-uncorrelatedinshortest-range+Predictablelong-rangePower

SpectraonrawfixationsPower

Spectraoffirstdifferencesacrossfixations=-.6Distanceacrosseyefixations

(x2+y2)1/2=-.47=-0.3=-1.8AdditionalfractalmeasuresAutocorrelationRelativeDispersion(SD/M)IteratedFunctionsSystems(IFS)RescaledrangeR/S(Hurstexponent)--

runningsumofdeviationsfrommean/SDevaluatepersistence&anti-persistenceIteratedFunctionSystems

--IFSTest--

(Peak&Frame,1994;

Stewart,1989).

FixationSeriesStartPinkNoiseBrownNoiseWhiteNoise1/f

1/f

1/f

Brown(ish)noiseClusteringalongdiagonalsrevealsshort-term,highlycorrelatedconsecutivedatapointsRawFixationsFixationdifferences

Pink(ish)noiseTriangularmicrostructureassociatedw/long-term,looselycorrelatedconsecutivedatapointsClusteringindicatescorrelatedfixations.Directionoffixationsshow

anti-correlatedmovementsaindicatedbyabsenceofmaindiagonals.IFSTest:FixationdirectionIFStestsyieldspatternsconsistentw/FFTresultsSummaryofresults:Sequenceof…Absoluteeyepositions-->1/fbrownnoise

Short-termmemory.

Differences-across-fixations--> 1/fpinknoiseLonger-termmemory.

Long-rangefractals?Interactiondominantdynamics

SOC(phasetransition&criticalphenomena)

Bak,P

VanOrden,G,Holden,J&Turvey,M.(2003).Self-organizationofcognitiveperformance.JournalofExperimentalPsychology:General,132(3),331-350.

Thornton,T.&Gilden,D.L.(inpress).Provenanceofcorrelationsinpsychologicaldata.PsychonomicBulletin&Review.

Lattka-VolterraShortrangeARMA

Wagenmakers,E.,Farrel,S.&Ratcliff,R.(2005).Humancognition&apileofsand.Adiscussiononserialcorrelation&self-organizedcriticality.JournalofExperimentalPsychology:General,134(1),108-116.ModifiedrandomwalksPercolation(forest-fire)models(Bigcontroversy!!)Sourceof1/fdynamic?Moresourcesof1/fnoise..SeeNewman,M.(2005).Powerlaws,ParetodistributionsandZipf’slaws.PhysicsLetters,2.

CombiningexponentialsInversesofquantitlesYuleprocessHighlyoptimizedtolerancemodelsCoherentnoisemechanismRandommultiplicativemechanismFragmentationModelHebb,1969;Rummelhardt&McClelland,1985~Grossberg,19xx;

Neuronalinteractions--->

implicitguidanceCaneyemovementsbedescribedbyasimplesetofneuronalinteractionrules(e.g.,SOC)toproduce1/fbehavior?

IncreasingNeuralActivation--->

04SOCNetwork

(AdaptedfromBak,Tang,&Wiesenfeld,1987)04SOCNetwork

(AdaptedfromBak,Tang,&Wiesenfeld,1987)

IncreasingNeuralActivation--->

Stimulate1neuron

Z(x,y)=initiallystimulatedsite

Asindividualneuronsareactivatedbeyondathreshold(of3),activity(4)isdispersedtosurroundingcells.Thresholdrule:ForZ(x,y)>Zcr=3

Activityintheoriginalsiteisdepletedtozero.

Z(x,y)->Z(x,y)-4Surroundingactivityincreasesby1Z(x,y)->Z(x,y)+104NeuralSOC…NeuralSOCw/eyemovementstrailsEyemovementsarepulledtothesite(s)ofgreatestactivationComplex&effectivesearch

ForZ(x,y)>ZcrZ(x,y)->Z(x,y)-4Z(x+

1,y)->Z(x+

1,y)+1Z(x,y+

1)->Z(x,y+

1)+1SimplesetofSOCrules..

{…canproduce:RESULTS

Rawfixations-->(1/f2brownnoise)Fixationdifferences-->(1/fpinknoise)

MODEL?.

Self-organizedcriticality(SOC;Bak,Tang,&Wiesenfeld,1987)vs.Lattka-Volterra,ARMAetc

Mainzer,K.(1997).Thinkingincomplexity:Thecomplexdynamicsofmatter,mind&mankind.Berlin:Springer.Pg.128Palmer,S.(1999).VisionScience:Photonstophenomenology.Boston:MIT.FEFIPSLPNSCRASCONCLUSIONSLong-rangedynamicacrosseye-movements!

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