1. Classification of FDG-PET* Brain Data
* Fluorodeoxyglucose positron emission tomography
Deborah Mudali 1,* Michael Biehl 1
Klaus L. Leenders Jos B.T.M. Roerdink 1,3
1 Johann Bernoulli Institute for Mathematics
and Computer Science, University of Groningen, NL
2 Department of Neurology
University Medical Center Groningen, NL
3 Neuroimaging Center
* Mbarara University of Science & Technology, Uganda

2. overview Prototype-based classification Learning Vector Quantization
Generalized Matrix Relevance Learning (GMLVQ)
Example application
Classification of Parkinsonian Syndromes
based on FDG-PET brain data
Combination: PCA + GMLVQ
comparison with DT, SVM
Conclusion and Outlook

3. Learning Vector Quantization
N-dimensional data, feature vectors
∙ identification of prototype vectors from labeled example data
∙ (dis)-similarity based classification (e.g. Euclidean distance)
competitive learning: Winner-Takes-All LVQ1 [Kohonen, 1990, 1997]
feature space
• initialize prototype vectors
for different classes
• present a single example
• identify the winner
(closest prototype)
• move the winner
- closer towards the data (same class)
- away from the data (different class)

4. prototype based classifier
- represent data by one or
several prototypes per class
classify a query according to the
label of the nearest prototype
(or alternative voting schemes) ?
local decision boundaries according
to (e.g.) Euclidean distances
feature space +
robustness to outliers, low storage needs and computational effort +
parameterization in feature space, interpretability -
model selection: number of prototypes per class, etc. ?
appropriate distance / (dis-) similarity measure

5. Learning Vector Quantization
fixed distance measures:
- choice based on prior knowledge or preprocessing
- determine prototypes from example data
by means of (iterative) learning schemes
e.g. heuristic LVQ1, cost function based Generalized LVQ
relevance learning, adaptive distances:
- employ parameterized distance measure
- update parameters in one training process with prototypes
- optimize adaptive, data driven dissimilarity
example: Matrix Relevance LVQ

6. Relevance Matrix LVQ generalized quadratic distance in LVQ:
[Schneider et al., 2009]
relevance matrix:
quantifies importance of features and pairs of features
summarizes relevance of feature j
( for equally scaled features )
training: optimize prototypes and Λ w.r.t. classification of examples
variants: global/local matrices (piecewise quadratic boundaries)
diagonal relevances (single feature weights)
rectangular (low-dim. representation)

7. cost function based training
12/24/2017
cost function based training
one example: Generalized LVQ [Sato & Yamada, 1995]
minimize
two winning prototypes:
linear
E favors large margin separation of classes, e.g.
sigmoidal (linear for small arguments), e.g.
E approximates number of misclassifications
small , large
E favors class-typical prototypes

8. cost function based LVQ
12/24/2017
cost function based LVQ
There is nothing objective about objective functions
James McClelland

9. classification of FDG-PET data
FDG-PET (Fluorodeoxyglucose positron emission tomography, 3d-images)
n=18 HC
Healhy controls
n= 20 PD
Parkinson’s Disease
n=21 MSA
Multiple System Atrophy
n=17 PSP
Progressive Supranuclear
Palsy
condition
Glucose uptake [

10. work flow Scaled Subprofile Model PCA
based on a given group of subjects
subjects 1….P
subjects 1….P
SSMPCA
subject socres 1….P
Group Invariant
Subprofile (GIS)
Subject Residual Profile SRP
high-intensity voxels
log-transformed
voxels 1….N (N≈200000)
data and pre-processing:
D. Mudali, L.K. Teune, R. J. Renken, K. L. Leenders,
J. B. T. M. Roerdink. Computational and Mathematical Methods in Medicine. March 2015, Art.ID , 10p.
and refs. therein

11. work flow ? Scaled Subprofile Model PCA
based on a given group of subjects
applied to
novel subject
subjects 1….P
test
subjects 1….P
SSMPCA
subject socres 1….P
Group Invariant
Subprofile (GIS)
Subject Residual Profile SRP
high-intensity voxels
log-transformed
voxels 1….N (N≈200000) ?
labels
(condition)
GMLVQ classifier
prototypes and distance

12. example: HC vs. PD Healthy controls vs. Parkinson’s Disease
38 leave-one-out validation runs
averaged…
prototypes relevance matrix
ROC of leave-one-out
prediction
(w/o z-score transform.)

13. example: HC vs. PSP
Healthy controls vs. Progressive Supranuclear Palsy
35 leave-one-out validation runs,
averaged…
prototypes relevance matrix
ROC of leave-one-out
prediction
(w/o z-score transform.)

14. performance comparison
GMLVQ
NPC
accuracies
Decision tree
(C4.5)
using all PC
Mudali et al.
2015
Note:
maximum margin perceptron - aka SVM with linear kernel - (Matlab svmtrain)
achieves performance similar to GMLVQ

15. four classes: HC / PD / MSA / PSP
leave-one-out confusion matrix for the four-class problem GM
class acc.
77.8 %
65.0 %
64.7 %
76.2 %
lin.
(1 vs 1)
class acc.
66.7 %
60.0 %
52.9 %
89.0 %

16. HC / PD / MSA / PSP GMLVQ MSA PD HC PSP visualization of training
data set in terms of the leading eigenvectors of Λ

17. diseases only: PD / MSA / PSP
leave-one-out confusion matrix for the three-class problem
(1 vs 1)
lin.

18. diseases only: PD / MSA / PSP
GMLVQ PD
MSA
visualization of training
data set in terms of the leading eigenvectors of Λ
PSP

19. discussion / conclusion
detection and discrimination of Parkinsonian syndromes:
GMLVQ classifier and SVM clearly outperform decision trees
decision trees
serious limitations:
small data set
leave-one-out validation
over-fitting
accuracy is not enough:
can we obtain better insight into the classifiers ?

20. outlook/work in progress
larger data sets
optimization of the number of PCs used as features
shown to improve decision tree performance
potential improvement for other classifiers
understanding relevances in voxel-space
relevant PC hint at discriminative between-patient variability
PCA:
recent example:
diagnosis of rheumatoid arthritis based on cytokine expression
[L. Yeo et al., Ann. of the Rheumatic Diseases, 2015]

21. links Pre- and re-prints etc.: http://www.cs.rug.nl/~biehl/
Matlab code:
Relevance and Matrix adaptation in Learning Vector
Quantization (GRLVQ, GMLVQ and LiRaM LVQ):
A no-nonsense beginners’ tool for GMLVQ:

22. 12/24/2017
Questions ?