1. Comparison of Boosting and Partial Least Squares Techniques for Real-time Pattern Recognition of Brain Activation in Functional Magnetic Resonance Imaging H. Davis 1,2, S. Posse 2, E. C. Witting 2, and P. Soliz 1,2 1.VisionQuest Biomedical, LLC 2.University of New Mexico

2. Functional Magnetic Resonance Imaging (fMRI) MRI of the brain while the brain is functioning Allows insight into patterns of brain activity Based on concept that a part of the brain is active when the related mental task is being performed

3. Research Goals Demonstrate Training & Classifications Methodologies that can process new scans and produce results for the neuro-scientist to modify experiment while patient is still in the scanner – The broader goal will include data acquisition – Train on new set of data – Classify new activation maps

4. Real-time fMRI Motivation – Biofeedback for pain – PTSD: Exposure and Response Prevention – Lie detection Limitation: Computation time – Real-time training – Real-time classification – Real-time calibration

5. Experiment 20 Subjects – 184 scans Stimuli – 4 stimuli – Used MR compatible LCD goggles and headphones UNM IRB approved

6. Original Results M Martinez-Ramon, V Koltchinskii, G Heilman and S Posse, “fMRI Pattern Classification using Nueroanatomically Constrained Boosting,” Neuroimage, 31(2006)1129-1141 We are comparing PLS to the results of this paper – Used SVM with distributed boosting

7. Stimuli

8. t-Map from Visual Stimulus

9. Conditions 2 Scanners – 1.5T Siemens Sonata Scanner – 4T Brucker MedSpec Scanner Varied analysis for robustness – 32x32 vs. 64x64 voxels – High bandpass filter vs. low bandpass filter

10. Segmentation Brain segmented into 12 areas by Broadman map – Left and Right Side – Segments Brain Stem Cerebellum Frontal Occupital Parietal Sucortical Temporal

11. SVM Analysis Local classifiers – SVM classifier for each segment SVM uses quadratic programming to provide the widest margin of separation between classes SVM is kernel based – Allows transformation into higher dimensional space – Non-linear transformation can linearize discrimination

12. Linearization by Mapping into Higher Dimension 12 Value of discriminant function 12456 class 2 class 1

13. Boosting Boosting is a method of aggregating the multiple models to give a single robust model – Use SVM’s as local classifiers – Outputs the optimal convex combination of the local classifiers Experiment repeated with randomly selected training sets – Gives a robust classifier

14. Linear Regression Equation: y = Xβ + ε – Y nx1 vector of observed values – X nxp matrix of independent values – β px1 vector of regression parameters – ε nx1 vector of residuals Normal Equations – Gauss-Markov –

15. Issues X ‘X not full rank – E.g. p>n – No unique solution to normal equations X ‘X nearly not full rank – X highly multi-colinear E.g. the columns of X are highly correlated – The numerical solution to the normal equations is unstable

16. Matrix Factorization X = TL – T nxn T orthogonal (T’T diagonal or I) – L nxp X ≈ T 1 L 1 – T 1 nxk, k<<p y = Xβ + ε ≈ T 1 (L 1 β) + ε = T 1 γ + ε – T 1 orthogonal => NE well conditioned

17. Factorization Routines Principal Components Analysis – Called Principal Components Regression Partial Least Squares PCR and PLS in common use – Part of a larger class called “shrinkage methods” – Sacrifice bias for better prediction

18. Comparison PCR – X ≈ T 1 L 1 is as accurate as possible (in m.s. sense) – Most parsimonious representation of X – This is not the problem we wish to solve – Optimization based on correlation of X with itself PLS – Most parsimonious solution to – That is T 1 gives the best predictor of y possible – Optimization based on correlation of X with y – This is the problem we wish to solve

19. Results: True class membership Other Cognitive -0.2 0 0.4 0.6 0.8 1.0 1.2 Predicted Value Other Visual -0.2 0 0.4 0.6 0.8 1.0 1.2 Predicted Value Other Motor -0.2 0 0.4 0.6 0.8 1.0 1.2 Predicted Value Other Auditory -0.2 0 0.4 0.6 0.8 1.0 1.2 Predicted Value

20. SVM vs. PLS Used 182 scans – Randomly split into two sets – 90 used to calibrate a model – 92 used to validate the model Ran the experiment 5 times – SVM and PLS used the same data split This cross-validation is conservative since the model is based on half of the data – It gave a quick way to run SVM and PLS face-to-face

21. Performance Comparison Accuracy Std. Dev. Time 15.3% 3.7% 90 sec 14% 1.8% <1 sec SVMPLS

22. Conclusion Linear PLS gave accurate answers – The non-linear capability of SVM was not needed Represented a large improvement in computation time – Quick enough to make real-time analysis feasible