考虑到这种情况则可以有两个或两个以上的breakevenpoint.ppt

InformationRetrievalModels上次课回顾本次课大纲VectorSpaceModelIntuitionCosinesimilarity#1.COSSimilarity#2.EvaluationLatentSemanticModelVectorSpaceModel:ProsProblemswithLexicalSemanticsIssuesintheVSMSingularValueDecompositionSingularValuesLow-rankApproximationLatentSemanticIndexing(LSI)WhatitisLSITermmatrixTDocumentmatrixDRetrievalwithLSIImprovedRetrievalwithLSIExampleLatentSemanticAnalysisEmpiricalevidenceLSIhasmanyotherapplicationsLanguageModelsIRbasedonLanguageModel(LM)FormalLanguage(Model)StochasticLanguageModelsStochasticLanguageModelsStochasticLanguageModelsUnigramandhigher-ordermodelsThefundamentalproblemofLMsUsingLanguageModelsinIRLanguageModelsforIRRetrievalbasedonprobabilisticLMQuerygenerationprobability(1)InsufficientdataInsufficientdataMixturemodelBasicmixturemodelsummaryExampleAlternativeModelsofTextGenerationRetrievalUsingLanguageModelsQueryLikelihoodDocumentLikelihoodModelComparisonLanguagemodels:pro&conComparisonWithVectorSpace本次课小结ResourcesThankYou!阅读材料#2EvaluationMatrixLow-rankApproximationforLSIEigenvalues&EigenvectorsMatrix-vectormultiplicationMatrixvectormultiplicationEigenvalues&EigenvectorsExampleLetbeasquarematrixwithmlinearlyindependenteigenvectors
Theorem:Existsaneigendecomposition

ColumnsofUareeigenvectorsofS
Diagonalelementsofareeigenvaluesof
Diagonaldecomposition:why/howDiagonaldecomposition-exampleExamplecontinuedIfisasymmetricmatrix:
Theorem:Existsa(unique)eigendecomposition
whereQisorthogonal:
Q-1=QT
ColumnsofQarenormalizedeigenvectors
Columnsareorthogonal.
(everythingisreal)
Timeout!SingularValueDecompositionSingularValueDecompositionSVDexampleSVDcanbeusedtocomputeoptimallow-rankapproximations.
Approximationproblem:FindAkofrankksuchthat

AkandXarebothmnmatrices.
Typically,wantk<<r.

SolutionviaSVDApproximationerrorSVDLow-rankapproximationPerformingthemaps