Discriminant Analysis. Two classification problems Discrimination Cluster.

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 Element 1st

Gene Analysis

Identification of features

.23 ….

Matrix PatternRecognition

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