Talk at HBM11 (duration: 10 minutes)

1. Connectome Classification:
Statistical Connectomics for
Analysis of Connectome Data
Joshua T. Vogelstein, PhD
d: Applied Math. & Stats
u: Johns Hopkins
w: jovo.me
e: joshuav@jhu.edu

2. Statistical Connectomics
Statistics “the art of data collection and analysis”
Connectomics “the study of connectomes”
Statistical “the art of connectome data collection
Connectomics and analysis”

3. Contributors
Stats
Carey E. Priebe Data Collection
Glen A. Coppersmith Susan Resnick
Mark Dredze
Connectome Inference
Will R. Gray Wisdom
John Bogovic R. Jacob Vogelstein
Jerry Prince
Support: various grants

4. Simplest. Example. Ever.
Blind People Deaf People
V1 V1
A1 M1 A1 M1

5. Simplest. Example. Ever.
Blind People Deaf People
V1 No possible classifier V1
based on graph
invariants can perform
this insanely simple
classification
A1 M1 A1 M1
problem!!!

6. Realest. Example. Ever.
MR Connectome Gender Classification
statistical graph model graph invariants
> 83% accuracy < 75% accuracy

7. Statistical Connectomics
1. 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

8. Statistical Connectomics
1. 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

9. 1. Collect Data:
Multi-Modal MR Imaging
• 49 senior individuals; 25 male, 24 female
• diffusion: standard DTI protocol
• structural: standard MPRAGE protocol

10. 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/

11. 3. Data Assumptions:
Signal Subgraph

12. 4. Construct a Decision Rule:
Robust Bayes Plugin Classifier
• asymptotically optimal and robust
• finite sample niceness
auv 1−auv
y=
ˆ puv|y (1
ˆ − puv|y )
ˆ πy
ˆ
ˆ
(u,v)∈S

13. 5. Evaluate Performance:
Leave-One-Out X-Validation
incoherent estimator coherent estimator
0.5
misclassification rate
# signal−vertices
0.5 L π
ˆˆ = 0. 5 ˆ
L n b = 0. 41 ˆ
L c o h= 0. 16
10 0.4
0.25 20 0.3
ˆ
L i n c= 0. 27
30
0 0 1 2 3
0.16
10 10 10 10 200 400 600 800 1000
log size of signal subgraph size of signal subgraph
some coherent estimators zoomed in coherent estimator
0.5
lassification rate
0.5
star−vertices
15
0.4
18
0.25 0.3
0.16 21

14. 6. Check Assumptions:
Synthetic Data Analysis
Correlation Matrix
1
100 0.5
vertex
0
200
−0.5
300
−1
100 200 300
vertex

15. 7. Extensions
• relax the independent edge assumption
• relax binary edge assumption

16. Discussion
• 83% 75%
• yay statistical modeling!

17. Q(A)
• anything?

18. 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

19. 4. Construct a Decision Rule:
Signal Subgraph Estimation
negative log incoherent coherent
significance matrix estimate estimate
# correct = 15
# correct = 7
20
vertex
n=64
40
60
20 40 60 −4.4 −1.
vertex

20. 6. Check Assumptions:
incoherent estimator coherent estimator
1
misclassification rate
# star−vertices
0.75 0.7
10
0.25
0.5
Synthetic Data Analysis 20 0.5
30 0.3
0 0.18
0 1 2 3 200 400 600 800 1000
10 10 10 10
log size of signal subgraph size of signal subgraph
1 0.5
misclassification rate
missed−edge rate
coh
0.4 inc
0.3 nb
0.5
0.2
0.1
0
0 20 40 60 80 100 0 20 40 60 80 100
# training samples # training samples