Ch4-Pattern_Classification-OLD

# Ch4-Pattern_Classification-OLD - Speech Recognition Pattern...

This preview shows pages 1–11. Sign up to view the full content.

Speech Recognition Pattern Classification

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

View Full Document
2/13/12 Veton Këpuska 2 Pattern Classification  u Introduction  u Parametric classifiers  u Semi-parametric classifiers  u Dimensionality reduction  u Significance testing
2/13/12 Veton Këpuska 3 Pattern Classification u Goal:  To classify objects (or patterns) into categories (or  classes)  u Types of Problems:  1. Supervised Classes are known beforehand, and data samples of  each class are available  2. Unsupervised Classes (and/or number of classes) are not known  beforehand, and must be inferred from data  Feature Extraction Classifier Class i Feature Vectors x Observation s

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

View Full Document
2/13/12 Veton Këpuska 4 Probability Basics  u Discrete probability mass function (PMF):  P ( i ω ) u Continuous probability density function (PDF):  p(x) u Expected value:  E(x)   = i i P 1 ) ( ϖ = 1 ) ( dx x p = dx x xp x E ) ( ) (
2/13/12 Veton Këpuska 5 Kullback-Liebler Distance  u Can be used to compute a distance between two probability  mass distributions,  P ( zi ), and  Q ( zi) u Makes use of inequality log  ≤  - 1  u Known as relative entropy in information theory u The divergence of  P ( zi ) and  Q ( zi)  is the symmetric sum ( 29 ( 29 ( 29 ( 29 0 log || = i i i i z Q z P z P Q P D ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 = - = - i i i i i i i i i i i z P z Q z Q z P z P z Q z P z P 0 1 log ( 29 ( 29 P Q D Q P D || || +

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

View Full Document
2/13/12 Veton Këpuska 6 Bayes Theorem u Define: {w i} a set of M mutually exclusive classes P(w i) a priori  probability for class w i p( x |w i) PDF for feature vector  x  in class w i P(w i| x ) A posteriori probability of w i given  x
2/13/12 Veton Këpuska 7 Bayes Theorem Bayes Rule: From Bayes Rule: Where:   ) ( ) ( ) | ( ) | ( x p P x p x P i i i ϖ = = = M i i i P x p x p 1 ) ( ) | ( ) ( ) ( ) | ( ) ( ) | ( i i i P x p x p x P =

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

View Full Document
2/13/12 Veton Këpuska 8 Bayes Decision Theory  u The probability of making an error given  is:   P(error| x )=1-P( w i| x ) if decide class w i u To minimize  P ( error | x ) (and  P ( error )):   Choose w i if  P(w i| x )>P(w j| x )   j ≠i
2/13/12 Veton Këpuska 9 Bayes Decision Theory u For a two class problem this decision rule means:  Choose w 1  if else  w 2  u This rule can be expressed as a likelihood ratio:  ) ( ) ( ) | ( ) ( ) ( ) | ( 2 2 1 1 x p P x p x p P x p ϖ ) ( ) ( ) | ( ) | ( 1 2 2 1 P P x p x p

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

View Full Document
2/13/12 Veton Këpuska 10 Bayes Risk  u Define cost function  ij  λ and conditional risk  R ( i ω | x ):  n ij  λ is cost of classifying  as  ω when it is really  ω n R ( i ω | x ) is the risk for classifying  as class  i ω u Bayes risk  is the minimum risk which can be achieved:
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 43

Ch4-Pattern_Classification-OLD - Speech Recognition Pattern...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online