Part 6 HMM in Practice

1
Part 6 HMM in Practice

• CSE717, SPRING 2008
• CUBS, Univ at Buffalo

2
Practical Problems in the HMM

• Computation with Probabilities
• Configuration of HMM
• Robust Parameter Estimation (Feature
  Optimization, Tying)
• Efficient Model Evaluation (Beam Search, Pruning)

3
Dimension Reduction

• Curse of Dimensionality
• Principal Component Analysis (PCA)
• Linear Discriminative Analysis (LDA)

4
Tying

• Model Tying
• State Tying
• Mixture Tying

d o g
b a g
Feature vector clustering
Assign equal weight to every cluster
Fix and re-estimate weights of
mixtures using EM
5
Beam Search

• Although the Viterbi Algorithm has linear
  complexity in the length of signal, it still has
  quadratic complexity in the number of model
  states.
• Generic Viterbi
• Beam Search

the set of active state at time t
6
Part 7 System

• CSE717, SPRING 2008
• CUBS, Univ at Buffalo

7
A Handwriting Recognition System Using HMM
Sliding Window Features
Embedded Training
Char HMM
Word HMM
PCA/LDA (optional)
Char HMM
Word HMM
Training
Feature Extraction
Viterbi Decoding
Recognition
n-gram
8
Feature Extraction

• Divide the word image into vertical frames
• Each frame is further divided into a number of
  cells
• A fixed number of features are computed per cell
• Frame level feature vectors are treated as a
  multivariate time series

ft
f1 f2
9
Embedded Training in The HMM
Features
Embedded Training
Char HMM
Word HMM

• Feature vectors are represented by Gaussian
  Mixture Models (GMM)
• Embedded training using the Baum-Welch algorithm
  shared character HMMs are trained using word
  images
• Initialize character-level HMMs
• Make word-level composite HMMs by concatenating
  character HMMs
• Align training word images to word models
  (Baum-Welch)
• Re-estimate GMM and state transition of each
  character HMM Go to step 3

10
Composite Word Model
d
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g