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: joshuav@jhu.edu
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”
Contributors
StatsCarey E. Priebe
Glen A. CoppersmithMark Dredze
Data CollectionSusan Resnick
Connectome InferenceWill R. GrayJohn BogovicJerry Prince
WisdomR. Jacob Vogelstein
Support: various grants
Simplest. Example. Ever.
V1
M1A1
Blind People
V1
M1A1
Deaf People
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!!!
Realest. Example. Ever.MR Connectome Gender Classification
statistical graph model graph invariants
> 83% accuracy < 75% accuracy
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
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
1. Collect Data:Multi-Modal MR Imaging
• 49 senior individuals; 25 male, 24 female
• diffusion: standard DTI protocol
• structural: standard MPRAGE protocol
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/
3. Data Assumptions:Signal Subgraph
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
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
6. Check Assumptions:Synthetic Data Analysis
vertex
verte
xCorrelation Matrix
100 200 300
100
200
300
−1
−0.5
0
0.5
1
7. Extensions
• relax the independent edge assumption
• relax binary edge assumption
Discussion
• 83% > 75%
• yay statistical modeling!
Q(&A)
• anything?
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
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
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
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