Connectome Classification: Statistical Connectomics for Analysis of Connectome Data
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Transcript of Connectome Classification: Statistical Connectomics for Analysis of Connectome Data
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Connectome Classification:Statistical Connectomics for
Analysis of Connectome Data
Joshua T. Vogelstein, PhDd: Applied Math. & Statsu: Johns Hopkinsw: jovo.mee: [email protected]
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Statistical Connectomics
Statistics “the art of data collection and analysis”
Connectomics “the study of connectomes”
Statistical Connectomics
“the art of connectome data collection and analysis”
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Contributors
StatsCarey E. Priebe
Glen A. CoppersmithMark Dredze
Data CollectionSusan Resnick
Connectome InferenceWill R. GrayJohn BogovicJerry Prince
WisdomR. Jacob Vogelstein
Support: various grants
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Simplest. Example. Ever.
V1
M1A1
Blind People
V1
M1A1
Deaf People
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Simplest. Example. Ever.
V1
M1A1
Blind People
V1
M1A1
Deaf People
No possible classifier based on graph
invariants can perform this insanely simple
classification problem!!!
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Realest. Example. Ever.MR Connectome Gender Classification
statistical graph model graph invariants
> 83% accuracy < 75% accuracy
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Statistical Connectomics1. Collect Data Multi-Modal MR Imaging
2. Preprocess Data MR Connectome Pipeline
3. Assumptions Signal Subgraph
4. Construct a Decision Rule Robust Bayes Plugin Classifier
5. Evaluate Performance Leave-One-Out X-Validation
6. Check Assumptions Synthetic Data Analysis
7. Extensions Relax assumptions
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Statistical Connectomics1. Collect Data Multi-Modal MR Imaging
2. Preprocess Data MR Connectome Pipeline
3. Assumptions Signal Subgraph
4. Construct a Decision Rule Robust Bayes Plugin Classifier
5. Evaluate Performance Leave-One-Out X-Validation
6. Check Assumptions Synthetic Data Analysis
7. Extensions Relax assumptions
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1. Collect Data:Multi-Modal MR Imaging
• 49 senior individuals; 25 male, 24 female
• diffusion: standard DTI protocol
• structural: standard MPRAGE protocol
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2. Preprocess Data:MR Connectome Automated Pipeline
• coherent collection of code• fully automatic and modular• about 12 hrs/subject/core• yields 70 vertex graph/subject
http://www.nitrc.org/projects/mrcap/
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3. Data Assumptions:Signal Subgraph
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4. Construct a Decision Rule:Robust Bayes Plugin Classifier
• asymptotically optimal and robust
• finite sample niceness
y =�
(u,v)∈S
pauv
uv|y(1− puv|y)1−auv πy
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5. Evaluate Performance:Leave-One-Out X-Validation
100 101 102 1030
0.25
0.5
log size of signal subgraph
mis
clas
sific
atio
n ra
te
incoherent estimator
Lnb=0.41
L i nc=0.27
L ! = 0 .5
size of signal subgraph#
sign
al−v
ertic
es
coherent estimator
L c oh=0.16
200 400 600 800 1000
10
20
300.16
0.3
0.4
0.5
100 101 102 1030
0.160.25
0.5
log size of signal subgraph
mis
clas
sific
atio
n ra
te
some coherent estimators
size of signal subgraph
# st
ar−v
ertic
es
zoomed in coherent estimator
400 500 600
15
18
21
0.16
0.3
0.4
0.5
coherent signal subgraph estimate
verte
x
vertex20 40 60
20
40
60
threshold
coherogram
0.04 0.14 0.29 0.55
20
40
600
10
20
30
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6. Check Assumptions:Synthetic Data Analysis
vertex
verte
xCorrelation Matrix
100 200 300
100
200
300
−1
−0.5
0
0.5
1
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7. Extensions
• relax the independent edge assumption
• relax binary edge assumption
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Discussion
• 83% > 75%
• yay statistical modeling!
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Q(&A)
• anything?
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4. Construct a Decision Rule:Signal Subgraph Estimation
• for each edge, we compute the significance of the difference between the two classes using Fisher’s exact test
• the incoherent signal subgraph estimator finds the s edges that are most significant
• the coherent signal subgraph estimator finds the s edges that are most significant incident to m vertices
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4. Construct a Decision Rule:Signal Subgraph Estimation
n=64
verte
x
vertex
negative logsignificance matrix
20 40 60
20
40
60
incoherentestimate
# co
rrect
= 7
coherentestimate
# co
rrect
= 1
5
−4.4 −1.6 −0.9
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6. Check Assumptions:Synthetic Data Analysis
100 101 102 1030
0.25
0.5
0.75
1
log size of signal subgraph
mis
clas
sific
atio
n ra
te
incoherent estimator
size of signal subgraph
# st
ar−v
ertic
es
coherent estimator
200 400 600 800 1000
10
20
300.18
0.3
0.5
0.7
0 20 40 60 80 1000
0.5
1
# training samples
mis
sed−
edge
rate
0 20 40 60 80 100
0.1
0.2
0.3
0.4
0.5
# training samplesm
iscl
assi
ficat
ion
rate
cohincnb