Constrained Gaussian Mixture Model Framework for Automatic ...
Mixture model
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![Page 1: Mixture model](https://reader030.fdocuments.net/reader030/viewer/2022032505/55c5a335bb61eb43468b4833/html5/thumbnails/1.jpg)
Mixture Model
Hong Chulju
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Index•Gaussian Distribution
• Multivariate Gaussian Distribution
• Latent Variable Model
• Mixture Model
• EM Algorithm
• Gaussian Mixture Model Example
• Gaussian Mixture Model vs k-Means Clustering
• Mel Frequency Cepstrum Coefficient
• Speaker identification
• Speaker diarization
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Review : Gaussian Distributiona.k.a. Normal Distribution
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Gaussian Distribution Likelihood
N(165, 5)
N(165, 10)
N(165, 15)
Which one is the fittest?
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Gaussian Distribution Likelihood
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Multivariate Gaussian Distribution
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Latent Variable Model a.k.a. Hidden Variable Model
관찰되지 않고 숨겨져 있는 변수
관찰된 변수로부터 추정
Latent Variable
Latent Variable Model
숨겨진 변수로부터 관찰된 변수가 도출되었다고 가정
관찰된 변수 + 숨겨진 변수를 이용하여 모델링
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Latent Variable Model a.k.a. Hidden Variable Model
Observable: Height
Hidden: Gender
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Mixture Model전체 모집단에 있는 여러 개의 부분 모집단을 표현하기 위한 확률 모델
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Mixture Model Example
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Gaussian Mixture Model
Guassian distribution pdf
Mixture Model Revisited
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Gaussian Mixture Model
How to solve it?
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Expectation-Maximization Algorithm
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EM Algorithm : GMM example
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EM Algorithm : GMM example
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EM Algorithm : GMM example
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GMM vs k-Means Clustering
GMM
k-Means Clustering
Latent Variable based clustering
Observable Variable based clustering
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More
Generalization of Mixture Model
(http://en.wikipedia.org/wiki/Hidden_Markov_model)
Hidden Markov Model
Algorithm for decoding HMM
(http://en.wikipedia.org/wiki/Viterbi_algorithm)
Viterbi Algorithm
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MFCCsMel Frequency Cepstrum Coefficients
1. Mel Frequency?
2. Cepstrum?
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CepstrumSpectrum > cepStrum
http://www.speech.cs.cmu.edu/15-492/slides/03_mfcc.pdf
1. Spectrum?
2. Why Cepstral analysis?
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Mel FrequencyMel-Frequency analysis of speech is based on human perception experiments
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MFCCs revisitedMel Frequency Cepstrum Coefficients
1. 주어진 신호(time-amplitude)를 푸리에 변환한다.
2. 푸리에 변환된 신호(frequency-amplitude)를 Mel-Scale로 변환한다.
3. Mel-Scale로 변환된 신호에 log를 취한다.
4. 여기에 이산 코사인 변환을 취한다.
구하는 방법
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Speaker Diarization
Features (Observable): MFCCs 12+a elements, etc
Latent Variable : Speaker
#Components : # Speakers
http://cslu.ohsu.edu/~bedricks/courses/cs655/hw/hw4/hw4.html
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Practice 1: GMM
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Practice 2: Speaker Diarization
Hmm
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Questions?