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SPR_LectureHandouts_Chapter_04_Part1_ParzenWindows

# SPR_LectureHandouts_Chapter_04_Part1_ParzenWindows -...

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1 Electrical and Computer Engineering Department Saurabh Prasad Pattern Recognition Chapter 4 Pattern Recognition ECE 8443 Chapter 4 Nonparametric Classification Techniques Electrical and Computer Engineering Department, Mississippi State University.

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2 Electrical and Computer Engineering Department Saurabh Prasad Pattern Recognition Chapter 4 Introduction Density Estimation Parzen Windows Outline
3 Electrical and Computer Engineering Department Saurabh Prasad Pattern Recognition Chapter 4 Introduction All Parametric densities are unimodal (have a single local maximum), whereas many practical problems involve multi modal densities Exception: GMMs Nonparametric procedures can be used with arbitrary distributions and without the assumption that the forms of the underlying densities are known There are two types of nonparametric methods: Estimating P (x | ω j ) Bypass probability and go directly to a posteriori probability estimation

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4 Electrical and Computer Engineering Department Saurabh Prasad Pattern Recognition Chapter 4 4 Density Estimation Basic idea: Probability that a vector x will fall in region R is: P is a smoothed (or averaged) version of the density function p( x ). If we have a sample of size n, the probability that k points fall in R is then: and the expected value for k is: E(k) = nP (3) = (1) ' dx ) ' x ( p P (2) ) P 1 ( P k n P k n k k =