Discriminant Analysis. Two classification problems Discrimination Cluster.

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Transcripción de la presentación:

Discriminant Analysis

Two classification problems Discrimination Cluster

The discrimination problem Given two populations with known distributions, classify a new element in one of the two populations

Examples Classify: Bones as human or not Consumer as reliable or not (credit scoring) A patient as ill or healthy An art work as made by author A or B. Automatic classification (letters, coins, bills,...)

Basic Data Data Matrix Element n1th Group A Group B Element n2th Element 1st

Gene Analysis

Identification of features.23 …. Matrix Pattern Recognition Classify as known or unknown

Classification problems A 4 ? 100 euros? 1000 dracmas?

Model formulation

Costs

Particular case: Normal Populations Classify P2

Understanding the rule

Posterior probabilities

Interpretation Classify A Classify B A B

Fisher A B Clasificar en población B Clasificar en A

Enfoque de Fisher

Varios grupos

ejemplo

Discriminación cuadrática

Clasificación logística

Problemas del modelo lineal No hay garantía de que las probabilidades estén entre cero y uno, pueden tomar valores negativos o mayores que uno. Es heterocedástico. Si estimamos el modelo lineal con variable de clasificación –1 +1 se obtiene la función lineal discriminante.

Otros enfoques: Redes neuronales Métodos no paramétricos Máquinas de vector soporte

redes neuronales Aproximar la función mediante

Máquinas de vector soporte