Ch3-Pattern_Classification2-a

Ch3-Pattern_Classification2-a - Speech Recognition Pattern...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Speech Recognition Pattern Classification 2
Background image of page 1

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

View Full DocumentRight Arrow Icon
May 13, 2009 Veton Këpuska 2 Pattern Classification  Introduction  Parametric classifiers  Semi-parametric classifiers  Dimensionality reduction  Significance testing 
Background image of page 2
May 13, 2009 Veton Këpuska 3 Semi-Parametric Classifiers Mixture densities ML parameter estimation Mixture implementations Expectation maximization (EM)
Background image of page 3

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

View Full DocumentRight Arrow Icon
May 13, 2009 Veton Këpuska 4 Mixture Densities PDF is composed of a mixture of m components densities  { ϖ 1 ,…, ϖ 2 }: Component PDF parameters and mixture weights P( ϖ j ) are  typically unknown, making parameter estimation a form of  unsupervised learning . Gaussian mixtures assume Normal components: = = m j j j P p p 1 ) ( ) | ( ) ( ϖ x x ) , ( ~ ) | ( k k k N p Σ μ x
Background image of page 4
May 13, 2009 Veton Këpuska 5 Gaussian Mixture Example: One  Dimension p(x)=0.6p 1 (x)+0.4p 2 (x) p1(x)~N(- σ , σ 2 )                 p 2 (x) ~N(1.5 σ , σ 2 )
Background image of page 5

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

View Full DocumentRight Arrow Icon
May 13, 2009 Veton Këpuska 6 Gaussian Example First 9 MFCC’s from [s]: Gaussian PDF
Background image of page 6
May 13, 2009 Veton Këpuska 7 Independent Mixtures [s]: 2 Gaussian Mixture Components/Dimension
Background image of page 7

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

View Full DocumentRight Arrow Icon
May 13, 2009 Veton Këpuska 8 Mixture Components [s]: 2 Gaussian Mixture Components/Dimension
Background image of page 8
May 13, 2009 Veton Këpuska 9 ML Parameter Estimation: 1D Gaussian Mixture Means   ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ∑ ∑ = = = - - = = = = = = = = - = - = = = = = = n i i k n i i i k k i k i k k i n i k i k k i i k k k k i k k i x k k k k i n i k k i k i n i i k k k n i m j j j i n i i k x P x x P x P x p P x p x p x x p P L x p x e x p P x p x p x p L P x p x p L k k i 1 1 1 2 2 2 1 1 1 1 1 | | | | since 0 | log | 2 1 | | 1 log log | log log log 2 2 ϖ μ σ π
Background image of page 9

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

View Full DocumentRight Arrow Icon
May 13, 2009 Veton Këpuska 10 Gaussian Mixtures: ML Parameter  Estimation The maximum likelihood solutions are of the form:
Background image of page 10
May 13, 2009 Veton Këpuska 11 Gaussian Mixtures: ML Parameter  Estimation The ML solutions are typically solved iteratively: Select a set of initial estimates for  P ( ϖ k ) µ k Σ k Use a set of  samples to re-estimate the mixture  parameters until some kind of convergence is  found Clustering procedures are often used to provide  the initial parameter estimates Similar to  K -means clustering procedure ˆ ˆ ˆ
Background image of page 11

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

View Full DocumentRight Arrow Icon
May 13, 2009 Veton Këpuska 12 Example: 4 Samples, 2 Densities 1. Data: X = { x 1 ,x 2 ,x 3 ,x 4 } = {2 , 1 , -1 , -2} 2. Init: p(x| ϖ 1 )~N(1,1), p(x| ϖ 2 )~N(-1,1), P( ϖ i )=0.5 3. Estimate: 1.
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/11/2012 for the course ECE 5526 taught by Professor Staff during the Summer '09 term at FIT.

Page1 / 38

Ch3-Pattern_Classification2-a - Speech Recognition Pattern...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online