Lecture 7(a)- On Parametric Estimation for Gaussian Data Classification

# Lecture 7(a)- On Parametric Estimation for Gaussian Data Classification

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PATTERN RECOGNITION Professor Aly A. Farag Computer Vision and Image Processing Laboratory University of Louisville URL: www.cvip.uofl.edu ; E-mail: aly.farag@louisville.edu Planned for ECE 620 and ECE 655 - Summer 2011 TA/Grader: Melih Aslan; CVIP Lab Rm 6, msaslan01@lousiville.edu Lecture 7: Parameter Estimation for Gaussian Classification Maximum-Likelihood & Bayesian Parameter Estimation • Introduction • Maximum-Likelihood Estimation • Example of a Specific Case • The Gaussian Case: unknown and • Bias • Appendix: ML Problem Statement Introduction – Data availability in a Bayesian framework • We could design an optimal classifier if we knew: – P( i ) (priors) – P(x | i ) (class-conditional densities) Unfortunately, we rarely have this complete information! – Design a classifier from a training sample • Priors estimation is usually easy to accomplish • Samples are often too small for class-conditional estimation (large dimension of feature space!) Pattern Classification, Chapter 3 2 Gaussian Case: – P(x | i ) is normal; i.e., P(x | i ) ~ N( i , i ) • Characterized by 2 parameters i , i – Estimation techniques • Maximum-Likelihood (ML) and the Bayesian estimations • Results are nearly identical, but the approaches are different Pattern Classification, Chapter 3 3 • Parameters in ML estimation – Parameters are fixed but unknown! Parameters are fixed but unknown!...
View Full Document

### Page1 / 18

Lecture 7(a)- On Parametric Estimation for Gaussian Data Classification

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online