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Connectome Classification: Statistical Connectomics for Analysis of Connectome Data
 

Connectome Classification: Statistical Connectomics for Analysis of Connectome Data

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    Connectome Classification: Statistical Connectomics for Analysis of Connectome Data Connectome Classification: Statistical Connectomics for Analysis of Connectome Data Presentation Transcript

    • 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
    • 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