discriminant analysis. two classification problems discrimination cluster
TRANSCRIPT
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