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AnalysisEditable(wiki)versionofthispage

Contents1Distributions

1.1Intervals1.2AFactors1.3Repetitions1.4Lapses

2ForgettingCurves33DCurves4Graphs

4.1ForgettingIndexvs.Priority4.2Firstinterval4.3DFactorvs.AFactor4.4FirstGradevs.AFactor4.5Gradevs.ForgettingIndex

53DGraphs6Approximations7Matrices8Use

8.1Usestatistics8.2Usecontextmenu8.3Examples

8.3.1Use:Elementcount:Topicsandtasks8.3.2Use:Newlymemorized8.3.3Use:Efficiency:Forgettingindex8.3.4Use:Priorityprotection:Items8.3.5Use:Priorityprotection:Topics

9FAQ10Furtherreading

ThetabbeddialogavailablewithTools:Statistics:Analysis(Shift+Alt+A)inSuperMemoprovidesgraphsandtablesthatillustratethecurrentstateofthelearningprocessinthecurrentlyopenedcollection.

InadditiontoAnalysis,SuperMemoprovidesmultipleotheranalyticaltools.

Distributions

IntervalsIntervalsdistributionofinterrepetitionintervalsinagivencollection.Bychangingthesettingofthecomboboxatthebottomofthedialog,youcanseeintervaldistributionsforallelementsinthecollection,foronlyitems,andforonlytopics.

AFactorsAFactorsdistributionofAFactorsinagivencollection.ThedistributionitselfisnotusedinAlgorithmSM15,andmerelyresultsfromit.NotethattopicsanditemsusedifferentAFactorcategories.ChooseItemsonlyorTopicsonlyatthebottomtoseedistributionsforitemsortopics.IfyouchooseAllelementsyouwillseealessmeaningfulconglomeratedistributionindexedbyAFactorcategorynumber.

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RepetitionsRepetitionsdistributionofthenumberofrepetitionsofitemsortopicsinagivencollectiononlymemorizedelementsareconsideredinthedistribution,i.e.thereisnozerorepetitionscategory.

LapsesLapsesdistributionofthenumberoftimesparticularitemsinthecollectionhavebeenforgottenonlymemorizedelementsareconsidered.Youshouldneverhavemorethan10%ofitemswithmorethan34lapses.Ifthisisnotthecase,youshouldreexaminethewayinwhichyouformulateitems(see20RulesofFormulatingKnowledge).Astopicsarenever"forgotten"atrepetitiontime,therearenolapseslistedinLapsesifyouselectTopicsonlyintheelementtypecombobox.

ForgettingCurves

400forgettingcurvesareindependentlyplottedinordertocomputetheRFmatrixinAlgorithmSM15.Thesecorrespondto20repetitionnumbercategoriesand20AFactorcategories.Fordatarepresentationconvenience,thecolumnsoftheRFmatrixforthefirstrepetitionareindexedbythenumberofmemorylapsesratherthanbytheAFactor.By

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choosingapropercombinationoftabsatthebottomofthegraph,youcanselectaforgettingcurveofinterest.Horizontalaxisrepresentstimeexpressedas:(1)UFactor,i.e.theratioofsubsequentinterrepetitionintervals,or(2)days(onlyforthefirstrepetition).Verticalaxisrepresentsknowledgeretentioninpercent.

Figure: Bluecircles inthepicturerepresentdatacollectedduringrepetitions.Thelargerthecircle,thegreaterthenumberofrepetitionsrecorded.The redcurvecorrespondswiththebestfitforgettingcurveobtainedbyexponentialregression.Forillstructuredmaterialtheforgettingcurveiscrooked,i.e.notexactlyexponential.Thehorizontal greenline correspondswiththerequestedforgettingindex,whilethevertical greenline showsthemomentintimeinwhichtheapproximatedforgettingcurveintersectswiththerequestedforgettingindexline.ThismomentintimedeterminesthevalueoftherelevantRFactor,andindirectly,thevalueoftheoptimuminterval.Forthefirstrepetition,RFactorcorrespondswiththefirstoptimuminterval.ThevaluesofOFactorandRFactoraredisplayedatthetopofthegraph.Theyarefollowedbythenumberofrepetitioncasesusedtoplotthegraph.Atthebeginningofthelearningprocess,thereisnorepetitionhistoryandnorepetitiondatatocomputeRFactors.Itwilltakesometimebeforeyourfirstforgettingcurvesareplotted.Forthatreason,theinitialvalueoftheRFmatrixistakenfromthemodelofalessthanaveragestudent.Themodelofaveragestudentisnotusedbecausetheconvergencefrompoorerstudentparametersupwardsisfasterthantheconvergenceintheoppositedirection.TheDeviationparameterdisplayedatthetoptellsyouhowwellthenegativelyexponentialcurvefitsthedata.Thelesserthedeviation,thebetterthefit.Thedeviationiscomputedasasquarerootoftheaverageofsquareddifferences(asusedinthemethodofleastsquares).

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Figure:InSuperMemo16,forgettingcurvescanbenormalizedoverAFactors(AllAFs)atdifferentrepetitioncategories(AllReps)(asinthepictureabove).Asaresult,youcandisplay:

1. yourcumulativeforgettingcurve( bluedots )2. itsnegativeexponentialapproximationusedbySuperMemo( redline )3. individualdatapointsfromallforgettingcurvescollectedbySuperMemo( yellowcircles ).

Time(normalized)standsat100%formaximumUfactorforeachentryoftheRFmatrix.Decaystandsforthedecayconstantoftheforgettingcurve.Casesshowsthenumberofrepetitioncasesusedinplottingthegraph.RepetitionsstandsforthenumberofrepetitionsexecutedwhendeterminingRFactors.Deviationisasquarerootoftheaverageofsquareddifferencesbetweenthedataandtheapproximatedforgettingcurve.

3DCurves

Thesegraphsshowtheforgettingcurvesin3dimensions.Thereare20graphsavailablewithAFactortabsatthebottom.EachgraphcorrespondstoadifferentAFactor(from1.2to6.9).TheXaxisrepresentstime(asinForgettingcurves).TheYaxisrepresentsrepetitioncategory(roughlycorrespondingtotherepetitionnumber).TheverticalZaxisrepresentsretentioninpercent(i.e.howmuchisrememberedatagivenmomentintime).Forbettervisibility,youcanrotate3DforgettingcurveswithRotate,orsmooththemwithSmooth.RotateswingsthegraphonitsZaxisby90degreesclockwise(asviewedfromabove).ThismeansthatXandYaxesgetswapped.NotethatsmoothingproceedsalongtheYaxis.Thismakesitpossibletoalignincompletelyplottedforgettingcurvesfromdifferentrepetitioncategories.However,onceyouclickRotate,Yaxissmoothingwillproduceadifferentresult(e.g.afterthefirstRotate,smoothingwillreducekinksalongtherepetitioncategories).Forthebestillustrationoftheforgettingprocess,smooththegraphbeforeyourotateit.

Figure:Exemplary3DgraphofforgettingcurvesforAFactor=3.6.ThegraphhasbeensmoothedalongtheYaxis(byaveragingresultscorrespondingtodifferentrepetitioncategories),androtatedonceforbettervisibility(theslopeillustratesforgettingintimethatisroughlysimilarforvariousrepetitioncategoriesexceptthosewithhighrepetition

numberthatmayreflectscarcityofdataforlongintervals).

Graphs

ForgettingIndexvs.PriorityForgettingIndexvs.Prioritythisgraphshowsyouhowforgettingdependsonthepriorityofthelearningmaterial.Ifyoualwaysgothroughyouroutstandingmaterialintimeandifyousticktothe20rulesofknowledgeformulation,yourmeasuredforgettingindexshouldbethesameastherequestedforgettingindex.Thisgraphwillthenshowaflatstraightlinepassinghorizontallyattheleveloftheforgettingindex.However,onceyoustartoverloadingthelearningprocessandusingPostponeorMercy,yourmeasuredforgettingindexwillincrease.Ifyoualwayssortyourrepetitionsbypriority(e.g.byleavingLearn:Sorting:Autosortrepetitionschecked),youshouldstillensurethatyourmeasuredforgettingindexequalstherequestedforgettingindexforhighpriorityelements(i.e.ontheleftsideofthegraph).Yourmeasuredforgettingindexforlowprioritymaterialwillbehigher,andthegreatertheoverloadthegreaterthedifference.Ifyouchangeyourrepetitionsortingcriteriabyincreasingrandomizationofrepetitions,thisgraphwillbeflatterandthemeasuredforgettingindexforhighprioritymaterialwillbehigher.

FirstintervalFirstintervalthelengthofthefirstintervalafterthefirstrepetitiondependsonthenumberoftimesagivenitemhasbeenforgotten.Notethatthefirstrepetitionheremeansthefirstrepetitionafterforgetting,notthefirstrepetitionever.Inotherwords,atwicerepeateditemwillhavetherepetitionnumberequaltooneafterithasbeenforgottentherepetitionnumberwillnotequalthree.Thefirstintervalgraphshowsexponentialregressioncurvethatapproximatesthelengthofthefirstintervalfordifferentnumbersofmemorylapses(includingthezerolapsescategorythatcorrespondswithnewlymemorizeditems).Inthegraphbelow,bluecirclescorrespondtodatacollectedinthelearningprocess(thegreaterthecircle,themorerepetitionshavebeenrecorded).

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Figure:Inthegraphabove,whichincludesdatafromover130,000repetitions,newlymemorizeditemsareoptimallyrepeatedaftersevendays.However,itemsthathavebeenforgotten10times(whichisrareinSuperMemo)willrequireanintervaloftwodays.(Duetologarithmicscaling,thesizeofthecircleisnotlinearlyproportionaltothedatasample

thenumberofrepetitioncasesforlapses=0isbyfarlargerthanforlapses=10,ascanbeseeninDistributions:Lapses.)

DFactorvs.AFactorDFactorvs.AFactorDFAFgraphshowsdecayconstantsofthepowerapproximationofRFactorsalongcolumnsoftheRFmatrix.YouneedtounderstandSuperMemoAlgorithmtounderstandthisgraph.ThehorizontalaxisrepresentsAFactor,whiletheverticalaxisrepresentsDFactor(i.e.DecayFactor).DFactorisadecayconstantofthepowerapproximationofcurvesthatcanbeinspectedintheApproximationstaboftheAnalysisdialogbox.

FirstGradevs.AFactorFirstGradevs.AFactorGAFgraphcorrelatesthefirstgradeobtainedbyanitemwiththeultimateestimationofitsAFactorvalue.Ateachrepetition,thecurrentelement'soldAFactorestimationisremovedfromthegraphandthenewestimationisadded.ThisgraphisusedbySuperMemoAlgorithmtoquicklyestimatethefirstvalueofAFactoratthemomentwhenallweknowaboutanelementisthefirstgradeithasscoredinitsfirstrepetition.

Gradevs.ForgettingIndexGradevs.ForgettingIndexFIGgraphcorrelatestheexpectedforgettingindexwiththegradescoredatrepetitions.YouneedtounderstandSuperMemoAlgorithmtounderstandthisgraph.Youcanimaginethattheforgettingcurvegraphmightusetheaveragegradeinsteadoftheretentiononitsverticalaxis.Ifyoucorrelatedthisgradewiththeforgettingindex,youwouldarriveattheFIGgraph.Thisgraphisusedtocomputeanestimatedforgettingindexthatisinturnusedtonormalizegrades(fordelayedoradvancedrepetitions)andestimatethenewvalueofitem'sAFactor.Thegradeiscomputedusingtheformula:Grade=Exp(A*FI+B),whereAandBareparametersofanexponentialregressionrunoverrawdatacollectedduringrepetitions.

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3DGraphs

3DgraphsthatvisuallyrepresentRF,OF,andCasesmatrices(see:Matricesbelow)

Approximations

20powerapproximationcurvesthatshowthedeclineofRFactorsalongcolumnsoftheRFmatrix.YouneedtounderstandSuperMemoAlgorithmtounderstandthesegraphs.ForeachAFactor,withincreasingvaluesoftherepetitionnumber,thevalueofRFactordecreases(atleasttheoreticallyitshoulddecrease).PowerregressionisusedtoillustratethedegreeofthisdeclinethatisbestreflectedbythedecayconstantcalledhereDFactor.BychoosingtheAFactortabatthebottomofthegraph,youcanviewacorrespondingRFactorapproximationcurve.Thehorizontalaxisrepresentstherepetitionnumbercategory,whiletheverticalaxisrepresentsRFactor.ThevalueofDFactorisshownatthetopofthegraph.ThebluepolylineshowsRFactorsasderivedfromrepetitiondata.TheredcurveshowsthefixedpointpowerapproximationofRFactor.ThegreencurveshowsthefixedpointpowerapproximationofRFactorderivedfromtheOFmatrixthisisequivalenttosubstitutingtheDFactorobtainedbyfixedpointpowerapproximationofRFactorsfortheDFactorobtainedfromDFAFlinearregression.Afixedpointapproachisusedforbothapproximationssincefortherepetitionnumberequaltotwo,RFactorequalsAFactor.

Matrices

YouneedtounderstandSuperMemoAlgorithmtounderstandthesetables.

OFmatrixmatrixofoptimalfactorsindexedbytherepetitionnumberandAFactor(exceptforthefirstrepetition,AFactorisreplacedwithmemorylapses)RFmatrixmatrixofretentionfactorsCasesmatrixofrepetitioncasesusedtocomputethecorrespondingentriesoftheRFmatrix(doubleclickanentrytoviewtherelevantforgettingcurve).Thismatrixcanbeeditedmanually(e.g.ifyouwanttochangetheweightofsomemeasurementsduringrepetitions)IntervalsmatrixofoptimumintervalsderivedfromtheOFmatrixDFactorsvectorofDFactorvaluesfordifferentAFactorvalues(alsorepetitioncasesusedincomputingparticularDFactors)

Use

Graphsofchangesinthestatisticsofthelearningprocessovertime.Thesegraphsrecorddailychangestostatisticssuchasthenumberofmemorizeditems,measuredforgettingindexorthenumberofoutstandingitemsforagivenday.Thefirstnonzerovalueofthedayisrecorded.Ifthatvalueincreasesafterwards,thatincreaseisignored(exceptafewcasessuchasthestatisticofnewlymemorizeditems,etc.).Ifyouhaveabreakinlearning,thelastrecordednonzerovaluewillpropagatethroughtheperiodinwhichyoudidnotuseSuperMemo(exceptafewcasessuchasthestatisticsofrepetitionsmade,etc.).

Tozoominonaportionofthegraph(asinpicturesbelow),sweeptheportionsofthegraphsthataretoberemovedwiththemouse,i.e.pointatthedayoffocus,movethemouseleftandreleasethemousebutton.Thiscutsawaypartofthegraphinthedirectionthatthemousewasmoved.YoucanalsouseCtrl+LeftandCtrl+Rightbuttonstozoomin(seebelow)

UsestatisticsHerearethestatisticsrecordeddailybySuperMemoanddisplayedontheUsetab:

1.Workdone

Usetimeyourdailytotaltimeinwhichyouactivelyusedagivencollection(asrecordedinTools:SleepChart)RecalltimeyourdailytotaltimewhichyouspentontryingtorecallanswerstoquestionsRepetitionsyourdailyrecordednumberofitemandtopicreviewsItemrepetitionsyourdailyrecordofitemrepetitionsReviewsyourdailyrecordoftopicreviews

2. OutstandingnumberofoutstandingelementsscheduledforagivendayOutstandingnumberofalloutstandingelementsscheduledforagivendayOutstandingitemsnumberofoutstandingitemsscheduledforagivenday

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Outstandingtopicsnumberofoutstandingtopicsscheduledforagivenday3. Burden

BurdencurrentBurdenparameterrecord.Burdenestimatesthenumberofelementsscheduledforrepetitiondailyontheassumptionofnodelaysinthelearningprocess.Burdenisthesumofintervalreciprocals.Burden=Itemburden+TopicburdenItemburdencurrentBurdenforitemsTopicburdencurrentBurdenfortopics

4. Elementcount

Elementstotalnumberofelementsinthecollectionasrecordedonagivenday(i.e.topics+items+tasks)ItemsnumberofitemsinthecollectionasrecordedonagivendayTopicsandtasksnumberoftopicsandtasksinthecollectionasrecordedonagivenday(seeanexemplarygraphbelow)Tasklist(nameofthecurrentlyselectedtasklist)numberoftasksonthecurrentlyusedtasklist(itsnameisdisplayedinparenthesis).UsetheTasklistcomboboxintheToolstoolbartochangethecurrentlyselectedtasklist.

5.Memorized

Memorizednumberofelementstakingpartinthelearningprocess(i.e.notdismissedandnotpending)MemorizeditemsnumberofitemstakingpartinthelearningprocessMemorizedtopicsnumberoftopicstakingpartinthelearningprocess

6. Newlymemorized

Newlymemorizednewelementsmemorizedonagivenday(seeanexemplarygraphbelow)NewitemsnewitemsmemorizedonagivendayNewtopicsnewtopicsmemorizedonagivenday

7. Efficiency

ForgettingindexmeasuredforgettingindexRetentionretentionasmeasuredoneachdayTopicloadproportionoftopicsscheduledforreviewonagivendayamongallelementsscheduled.Topicload=Outstandingtopics/Outstandingelements.Topicloadisexpressedinpercentforanygivenday.Topicloadshouldnotbeconfusedwithproportionoftopicsinsortingcriteria.Proportionoftopicsisdeterminedindependentofthetopicloadifpossible(e.g.forzerotopicload,youcannotachieveproportiongreaterthanzero,etc.).Ifyoudonotuseautosorting,topicloadtellsyouwhatproportionofyourrepetitionsismadeoftopics.

8. Overloadthenumberofexecutedrepetitionsdividedbythenumberofoutstandingrepetitions(i.e.thepercentoftheactuallyexecutedrepetitions)ElementsthepercentofalloutstandingrepetitionsexecutedItemsthepercentofoutstandingitemrepetitionsexecutedTopicsthepercentofoutstandingtopicreviewsdone

9. Priorityprotectionyourprocessingcapacityforhighprioritymaterialonagivenday.IfyourgraphoscillatesaroundPriorityof3%,youwillknowthatonlytop3%ofyourlearningmaterialisguaranteedatimelyrepetition.Youcanincreasethatnumberbydoingmorework,reducinginflowofnewmaterial,deprioritizinglessimportantelements,orreducingtherandomizationdegreefortheoutstandingqueuesortingcriteria.ReadaboutthisimportantparameterinPrioritizationRulebookinthepriorityqueuearticle

Itemsthehighestpriorityitem(withthelowest%)thatwasmissedinrepetitions.(Theactual%intheoutstandingqueuecanbemuchhigher(becauseyoumostlyreviewhighpriorities))Topicsthehighestprioritytopic(withthelowest%)thatwasmissedinrepetitions.(seeanexemplarygraphbelow)

UsecontextmenuNext(Ctrl+Tab)switchtothenextmajorUsestatistictabPrevious(Shift+Ctrl+Tab)switchbacktothepreviousmajorUsestatistictabFirst(Home)switchtothefirstmajorUsestatistictab(WorkdoneinSuperMemo15)

Cutoffleft(Ctrl+Rightarrow)cutofftheleftpartofthegraphtozoominontherestofitCutoffright(Ctrl+Leftarrow)cutofftherightpartofthegraphtozoominontherestofitCutofftop(Ctrl+Downarrow)cutoffthetoppartofthegraphtozoominontherestofitClose(Esc)closetheAnalysiswindow

Examples

Use:Elementcount:Topicsandtasks

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Figure:Exemplarygraphshowingthetotalnumberoftopicsstoredinthecollection.Thedatadisplayedatthebottomdependsonthepositionofthemouse.Inthisexample,itindicatesthatonMar6,2009,therewere251,228topicsintheincrementalreadingprocess.

Use:Newlymemorized

Figure:Exemplarygraphshowingthenumberofelementsmemorizedonindividualdays.Bysweepingawaytheleftandrightpartofthegraph,itispossibletozoominonasmallsectionofthelearningprocess.TheperiodshownonthegraphspansfromJul1,2008toMar19,2009.

Use:Efficiency:Forgettingindex

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Figure:Exemplarygraphenablingamoremeaningfulanalysisoftheforgettingindex.ChangestoforgettingindexinAnalysisusethedailymeasuredforgettingindex(previously:lessinformativecumulativemeasuredforgettingindexvaluewastakenfortheentireperiodsincethelastuseofTools:Statistics:Resetparameters:Forgettingindex

record).Notethatthepriorityqueuemaydistorttheactualretentioninyourcollectionasmeasuredvaluesareprimarilytakenfromtopprioritymaterial.Thusmeasuredforgettingindexshouldbeunderstoodas"forgettingindexmeasuredatrepetitions",notas"overallmeasuredforgettingindex".

Use:Priorityprotection:Items

Figure:Exemplarygraphshowingthehighestpriorityitem(withthelowestpriority%)thatwasmissedinrepetitionsonagivenday.Inthepicture,youcanseetheincreaseintheitempriorityprotectionfrom0.5%to11%withinamonth.Thisispossiblebyfocusingonhonestprioritization,doinglotsofrepetitions,avoidingmassupprioritizations,etc.

Use:Priorityprotection:Topics

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Figure:Exemplarygraphshowingthehighestprioritytopic(withthelowestpriority%)thatwasmissedinrepetitions.Thedatadisplayedatthebottomdependsonthepositionofthemouse.Inthisexample,itindicatesthatonJun26,2013,theworstmissamongsttopicswasatopicwithPriorityequalto7.613%ofthequeueofthemostimportanttopicsto

review.

FAQ

IworrymygraphslookweirdandIdosomethingwrong

Furtherreading

FAQ:MemoryandlearningSuperMemoTheorySuperMemoAlgorithm

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