Connectome Classification: Statistical Connectomics for Analysis of Connectome Data

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

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

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

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

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!!!

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

Statistical Connectomics1. Collect Data Multi-Modal MR Imaging2. Preprocess Data MR Connectome Pipeline3. Assumptions Signal Subgraph4. Construct a Decision Rule Robust Bayes Plugin Classiﬁer5. Evaluate Performance Leave-One-Out X-Validation6. Check Assumptions Synthetic Data Analysis7. 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 auv 1−auv y= ˆ puv|y (1 ˆ − puv|y ) ˆ πy ˆ ˆ (u,v)∈S

5. Evaluate Performance: Leave-One-Out X-Validation incoherent estimator coherent estimator 0.5misclassification 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 0.5lassification rate 0.5 star−vertices 15 0.4 18 0.25 0.3 0.16 21

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

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 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

6. Check Assumptions: incoherent estimator coherent estimator 1misclassification 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

Connectome Classification: Statistical Connectomics for Analysis of Connectome Data

by Joshua Vogelstein

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