Connectome Classification:     Statistical Connectomics for    Analysis of Connectome Data        Joshua T. Vogelstein, PhD...
Statistical Connectomics  Statistics   “the art of data collection and analysis”Connectomics “the study of connectomes”  S...
Contributors         Stats   Carey E. Priebe        Data Collection Glen A. Coppersmith       Susan Resnick    Mark Dredze...
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 ...
Realest. Example. Ever.MR Connectome Gender Classification statistical graph model   graph invariants    > 83% accuracy    ...
Statistical              Connectomics1. Collect Data                  Multi-Modal MR Imaging2. Preprocess Data            ...
Statistical              Connectomics1. Collect Data                  Multi-Modal MR Imaging2. Preprocess Data            ...
1. Collect Data:  Multi-Modal MR Imaging• 49 senior individuals; 25 male, 24 female • diffusion: standard DTI protocol • s...
2. Preprocess Data:MR Connectome Automated Pipeline• coherent collection of code• fully automatic and modular• about 12 hr...
3. Data Assumptions:   Signal Subgraph
4. Construct a Decision Rule:Robust Bayes Plugin Classifier• asymptotically optimal and robust• finite sample niceness      ...
5. Evaluate Performance:    Leave-One-Out X-Validation                                      incoherent estimator          ...
6. Check Assumptions:Synthetic Data Analysis                 Correlation Matrix                                       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 differen...
4. Construct a Decision Rule: Signal Subgraph Estimation                   negative log                       incoherent  ...
6. Check Assumptions:                                          incoherent estimator                                       ...
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Connectome Classification: Statistical Connectomics for Analysis of Connectome Data

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Connectome Classification: Statistical Connectomics for Analysis of Connectome Data

  1. 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. 2. Statistical Connectomics Statistics “the art of data collection and analysis”Connectomics “the study of connectomes” Statistical “the art of connectome data collectionConnectomics and analysis”
  3. 3. 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
  4. 4. Simplest. Example. Ever.Blind People Deaf People V1 V1 A1 M1 A1 M1
  5. 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. 6. Realest. Example. Ever.MR Connectome Gender Classification statistical graph model graph invariants > 83% accuracy < 75% accuracy
  7. 7. 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
  8. 8. 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
  9. 9. 1. Collect Data: Multi-Modal MR Imaging• 49 senior individuals; 25 male, 24 female • diffusion: standard DTI protocol • structural: standard MPRAGE protocol
  10. 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. 11. 3. Data Assumptions: Signal Subgraph
  12. 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. 13. 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
  14. 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. 15. 7. Extensions• relax the independent edge assumption• relax binary edge assumption
  16. 16. Discussion• 83% 75%• yay statistical modeling!
  17. 17. Q(A)• anything?
  18. 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. 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. 20. 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
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