Transcript PARAFAC Analysis of 3

PARAFAC Analysis of 3-D
Tongue Shape
Yanli Zheng, Mark Hasegawa-Johnson
ECE Department
University of Illinois at Urbana-Champaign
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Part I. Background
WHY is the factor analysis of tongue shape
meaningful?
1. Speech Motor System
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Part I. Background (cont. Why?)
2. Representing Vowel
• Frequency Domain
• Anatomical View
Basic Vowel Diagram
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Part I. Background
HOW to analysis the vowels
in the context of anatomy?
2-D PARAFAC analysis by Richard Harshman(1977)
X-ray images
Measuring Scheme
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Background (cont. Results of Harshman)
Results:Two Factors account for 92% variance.
Grids Factors
Vowels Loading
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Part I. Background
Why is 3D Different from 2D?
1.
•
•
Linear Source-Filter Theory:
Vowel Quality is Determined by Areas
Area Correlated w/Midsagittal Width
2.
Distinguish important in Speech Synthesis
3.
Clinic Application
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Part II. Algorithms Introduction
1. PARAFAC (Parallel Factor Analysis)
xijk: tongue shape measurement for ith data point, jth vowel and kth speaker.
aif: fth factor contribution to ith data point
bjf: loading of phoneme j on fth factor
ckf: loading of speaker k on fth facotor
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Part II. Algorithms Introduction
2. Tucker3 Model(used in the validation of
PARAFAC model)
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Part III. 3-D Factor Analysis of MRI-Derived
Tongue Shapes
1.
2.
Subjects: 5 subjects successfully imaged (three male speaker:
m1,m2, m3; and two female speaker: f1,f2).
MRI Image Collection
•T1-weighted
•GE Signa 1.5T
•3mm slices
•24 cm FOV
•256 x 256 pixels
•Coronal, Axial
•11-18 Sounds
per Subject.
•Breath-hold in
vowel position
for 25 seconds
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Part III. 3-D Factor Analysis of MRI-Derived Tongue Shapes
3. Image Viewing and Segmentation:
the CTMRedit GUI and toolbox
• Display series of CT or
MR image slices
• Segment ROI manually or
automatically
• Interpolate and
reconstruct ROI in 3D
space
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Part III. 3-D Factor Analysis of MRI-Derived Tongue
Shapes
4. PARAFAC Analysis
2) How to define the
measuring grid?
X-Y Plane
120
110
y-axis(from posterior to anterior)
1) 3D-Tongue Shape
100
90
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60
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-40
-30
-20
-10
0
10
20
x-axis (from right to left)
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Part III. 3-D Factor Analysis of MRI-Derived Tongue Shapes
4. PARAFAC Analysis(cont.)
3) Result: 2 Factors are extracted, with 83.8729 % variance
explained
compenent2
compenent1
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20
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-10
2
-20
10
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0
-2 0
-10 0
coronal view
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-5
-5
-10
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-15
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-15
-10
-5
0
sagittal view
coronal view
sagittal view
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0
0
-5
-5
-10
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-10
-0.5
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1.5
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Vowel Loadings
0.6
Speaker Loadings
0.8
f2
had
0.55
head
0.7
hid
0.5
0.6
0.45
m3
0.5
Factor 2
Factor 2
0.4
0.35
f1
0.4
m2
0.3
0.3
0.25
put
0.2
shoe
hayed
0.1
0.2
0.15
0.1
0.3
0
hod
hoed
heed
-0.1
0.38
0.31
0.32
m1
0.33
0.34
Factor 1
0.35
0.36
0.37
0.39
0.4
0.41
0.42
0.43
Factor 1
0.44
0.45
0.46
0.47
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Part III. 3-D Factor Analysis of MRI-Derived Tongue Shapes
4)Validation of the Result
a) Split-half test (example for f1,f2 and m3)
compenent2
compenent1
10
10
0
0
-10
5
5
-20
10
0
-10
2
-10 0
coronal view
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5
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0
0
-5
-5
-10
-10
1
2
3
4
-15
-10
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-5
0
0
-1
0
coronal view
sagittal view
10
-15
1
5
10
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0
0
-5
-5
-10
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sagittal view
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1
2
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-10
-0.5
0
0.5
1
1.5
Vowel Loadings
0.6
had
hid
Correlation Coefficients
Grid Contribution 0.9646
Vowel Loading
0.9279
0.5
head
Factor 2
0.4
put
0.3
shoe
0.2
hoed
0.1
0
0.3
0.32
0.34
Factor 1
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heed
hod
-0.1
0.28
hayed
0.36
0.38
0.4
4)Validation of the Result
b) Check the reliability of the solution
• Try different start points, check whether all the solutions
converge to the same solution.
c) Core Consistency Testing (by Rasmus Bro,1998)
Core consistency -4.4798% (yellow target)
Core consistency 99.9955% (yellow target)
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1.2
1.5
1
1
0.8
Core Size
Core Size
0.5
0.6
0.4
0
-0.5
0.2
-1
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-1.5
-0.2
-2
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Core elements (green should be zero/red non-zero)
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Core elements (green should be zero/red non-zero)
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Degenerated result for 3-factor PARAFAC Model
compenent1
20
compenent3
compenent2
10
10
10
0
0
-10
2
-10
1
0
-10
-20
5
0
20
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0
-10
-20
sagittal view
20
-1 0
coronal view
10
10
5
coronal view
sagittal view
-5
-10
-10
1
2
3
4
5
-15
-10
-5
0
5
10
sagittal view
10
10
5
5
5
5
0
0
0
0
-5
-5
-5
-5
0
0
5
0
-2 0
coronal view
-20
5
0
-10
1
2
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-10
-0.5
-10
0
0.5
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1.5
1
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-10
-0.5
0
0.5
Correlation Coefficients
Grid Contribution
1&2
-0.5362
2&3
0.9632
1&3
-0.6045
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Part IV. Conclusion
• 3-D PARAFAC Analysis of Tongue Shape suggests the
“Hierarchical Control”
• This research and the follow-up expected research in
the MR Microscopy, and Dynamic Imaging aim to :
1. Provide new anatomical information to speech scientists and
speech pathologists
2. Lay the foundation for future research with disordered
populations.
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