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

1
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

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

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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

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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

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Linearization by Mapping into Higher Dimension
Value of discriminant function
class 1
class 1
class 2
1
2
4
5
6
13
Boosting

• Boosting is a method of aggregating the multiple
  models to give a single robust model
• Use SVMs as local classifiers
• Outputs the optimal convex combination of the
  local classifiers
• Experiment repeated with randomly selected
  training sets
• Gives a robust classifier

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Linear Regression

• Equation y Xß e
• Y nx1 vector of observed values
• X nxp matrix of independent values
• ß px1 vector of regression parameters
• e nx1 vector of residuals
• Normal Equations
• Gauss-Markov

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Issues

• X X not full rank
• E.g. pgtn
• 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

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Matrix Factorization

• X TL
• T
• nxn
• T orthogonal (TT diagonal or I)
• L nxp
• X T1L1
• T1 nxk, kltltp
• y Xß e T1(L1ß) e T1 ? e
• T1 orthogonal gt NE well conditioned

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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

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Comparison

• 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

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Results True class 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
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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

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Performance Comparison
SVM
PLS
Accuracy
15.3
14
Std. Dev.
3.7
1.8
Time
90 sec
lt1 sec
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