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Discriminant Analysis

Explore the discrimination problem of classifying new elements in populations with known distributions, such as bones as human or not, or patients as ill or healthy. Understand model formulation and interpretation using Fisher's approach for various groups. Learn about discriminant analysis, cluster discrimination, and classification problems. Discover the identification of features through gene analysis and pattern recognition.

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Discriminant Analysis

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  1. Discriminant Analysis

  2. Two classification problems • Discrimination • Cluster

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

  4. 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, ...)

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

  6. Gene Analysis

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

  8. Classification problems A ? 4 100 euros? 1000 dracmas?

  9. Model formulation

  10. Costs

  11. Particular case: Normal Populations Classify P2

  12. Understanding the rule

  13. Posterior probabilities

  14. Interpretation Classify B B Classify A A

  15. Fisher Clasificar en población B Clasificar en A B A

  16. Enfoque de Fisher

  17. Varios grupos

  18. ejemplo

  19. Discriminación cuadrática

  20. Clasificación logística

  21. 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.

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