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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. VisionQuest Biomedical, LLC University of New Mexico.

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H davis 1 2 s posse 2 e c witting 2 and p soliz 1 2

Comparison of Boosting and Partial Least Squares Techniques for Real-time Pattern Recognition of Brain Activation in Functional Magnetic Resonance Imaging

H. Davis1,2, S. Posse2, E. C. Witting2, and P. Soliz1,2

VisionQuest Biomedical, LLC

University of New Mexico


Functional magnetic resonance imaging fmri
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


Research goals
Research Goals Imaging (fMRI)

  • 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


Real time fmri
Real-time fMRI Imaging (fMRI)

  • Motivation

    • Biofeedback for pain

    • PTSD: Exposure and Response Prevention

    • Lie detection

  • Limitation: Computation time

    • Real-time training

    • Real-time classification

    • Real-time calibration


Experiment
Experiment Imaging (fMRI)

  • 20 Subjects

    • 184 scans

  • Stimuli

    • 4 stimuli

    • Used MR compatible LCD goggles and headphones

  • UNM IRB approved


Original results
Original Results Imaging (fMRI)

  • 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


Stimuli
Stimuli Imaging (fMRI)


T map from visual stimulus
t-Map from Visual Imaging (fMRI) Stimulus


Conditions
Conditions Imaging (fMRI)

  • 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


Segmentation
Segmentation Imaging (fMRI)

  • Brain segmented into 12 areas by Broadman map

    • Left and Right Side

    • Segments

      • Brain Stem

      • Cerebellum

      • Frontal

      • Occupital

      • Parietal

      • Sucortical

      • Temporal


Svm analysis
SVM Analysis Imaging (fMRI)

  • 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


Linearization by Mapping into Higher Dimension Imaging (fMRI)

Value of discriminant function

class 1

class 1

class 2

1

2

4

5

6


Boosting
Boosting Imaging (fMRI)

  • 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


Linear regression
Linear Regression Imaging (fMRI)

  • Equation: y = Xβ + ε

    • Y nx1 vector of observed values

    • X nxp matrix of independent values

    • βpx1 vector of regression parameters

    • εnx1 vector of residuals

  • Normal Equations

    • Gauss-Markov


Issues
Issues Imaging (fMRI)

  • 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


Matrix factorization
Matrix Factorization Imaging (fMRI)

  • X = TL

    • T

      • nxn

      • T orthogonal (T’T diagonal or I)

    • Lnxp

  • X ≈ T1L1

    • T1nxk, k<<p

  • y = Xβ + ε ≈ T1(L1β)+ ε = T1γ + ε

    • T1 orthogonal => NE well conditioned


Factorization routines
Factorization Imaging (fMRI) 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


Comparison
Comparison Imaging (fMRI)

  • PCR

    • X ≈ T1L1 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 T1 gives the best predictor of y possible

    • Optimization based on correlation of X with y

    • This is the problem we wish to solve


Results true class membership
Results: True class Imaging (fMRI)membership

1.2

1.2

1.0

1.0

0.8

0.8

Predicted Value

0.6

0.6

Predicted Value

0.4

0.4

0.2

0.2

0

0

-

0.2

-

0.2

Other

Visual

Other

Motor

1.2

1.2

1.0

1.0

0.8

0.8

Predicted Value

0.6

0.6

Predicted Value

0.4

0.4

0.2

0.2

0

0

-

0.2

-

0.2

Other

Cognitive

Other

Auditory


Svm vs pls
SVM vs. PLS Imaging (fMRI)

  • 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


Performance comparison
Performance Imaging (fMRI) Comparison

SVM

PLS

Accuracy

15.3%

14%

Std. Dev.

3.7%

1.8%

Time

90 sec

<1 sec


Conclusion
Conclusion Imaging (fMRI)

  • 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


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