zigkolis c fcm brain responses
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Conditional Fuzzy C Means
A fuzzy clustering approach for mining event-related dynamics
Christos N. Zigkolis
Aristotle University of Thessaloniki2
Contents
• The problem
• Our approach
• Fuzzy Clustering
• Conditional Fuzzy Clustering
• Graph-Theoretic Visualization techniques
• The experiments and the datasets
• Applications
• Future Work
• Conclusions
Aristotle University of Thessaloniki3
The problem
Visualizing the variability of MEG responses
understanding the single-trial variability
Describe the single-trial (EEG) variability in the presence of artifacts
make single-trial analysis robust, robust prototyping
Aristotle University of Thessaloniki4
Our approach
CLUSTERING
FUZZY
CONDITIONAL
creating clusters
0 or 1 [0, 1]
partial membership
content constraints
criteria grades
Aristotle University of Thessaloniki5
Every Pattern to only one clusterEvery Pattern to every cluster with partial membership
ClusteringFuzzy Clustering
Aristotle University of Thessaloniki6
Fuzzy C Means
CNC
N
uu
uu
1
111
],...,,[ 21 CVVVV
U membership matrix Centroids Objective function
|)1()(| tQtQ
Iterative procedure
CONTINUE STOP
XdataNxp
Aristotle University of Thessaloniki7
FCM 2D Example
compact groupsspurious patterns
FCM sensitivity to noisy data
Aristotle University of Thessaloniki8
Conditional Fuzzy Clustering
The presence of Condition(s)
Condition(s)Pattern
mark
Aristotle University of Thessaloniki9
Conditional Fuzzy C Means
scaled to [0, 1]
],...,,[ 21 NfffF
<Xdata, F> CFCM <U, Centroids>
F affects the computations of U matrix and consequently the centroids.
Aristotle University of Thessaloniki10
FCM VS CFCM
FCM
uij
uij
uij
uijCFCM
uij
uij
uij
uij
FkVS
Aristotle University of Thessaloniki11
Graph-theoretic Visualization Techniques
Topology Representing Graphs
Build a graph G [C x C] Topological relations between prototypes
Gij corresponding to the strength of connection between prototypes O i and Oj
Computation of the graph G
- For each pattern find the nearest prototypes and increase the corresponding values in G matrix
- Simple elementwise thresholding Adjacency Matrix A
A: a link connects two nearby prototypes only when they are natural neighbors over the manifold
Aristotle University of Thessaloniki12
Aristotle University of Thessaloniki13
Graph-theoretic Visualization Techniques
Compute the G graph via CFCM results
Apply CFCM algorithm: (O, U) = CFCM(X, Fk, C)
Build )(.,][ ''' ijijijCxNij uuuthatsuchuU
Compute G = U’.U’T FCG: Fuzzy Connectivity Graph
Aristotle University of Thessaloniki14
Graph-theoretic Visualization Techniques
Minimal Spanning Tree MST-ordering
12
3
4
5
67
root
Aristotle University of Thessaloniki15
Minimal Spanning Tree with MST-ordering
Aristotle University of Thessaloniki16
Graph-theoretic Visualization Techniques
Locality Preserving Projections
Dimensionality Reduction technique Rp Rr r<pLinear approach ≠ MDS, LE, ISOMAP
Alternative to PCA: different criteria, direct entrance of a new point into the subspace
- generalized eigenvector problem
- use of FCG matrix
- select the first r eigenvectors and tabulate them (Apxr matrix)
P = [pij]Cxr = OA
Aristotle University of Thessaloniki17
Aristotle University of Thessaloniki18
The experiments
Magnetoencephalography Electroencephalography
+ 197 single trials
+ control recording
110 single trials
Online outlier rejection
Aristotle University of Thessaloniki19
The datasetsFeature Extraction
MEG EEG
X_data [197 x p1], p:number of features X_data [110 x p2], p:number of features
pT
msec msec
μV
Aristotle University of Thessaloniki20
Applications (MEG)Exploit the background noise for better clustering
Spontaneous activity as a auxiliary set of signals
MEG single trials +
Exploit the distances to extract the grades
Aristotle University of Thessaloniki21
Aristotle University of Thessaloniki22
Applications (EEG)Robust Prototyping
Elongate the possible outliers
from the clustering procedure
Find the distances from the nearest neighbors and compute the grades for every pattern
Aristotle University of Thessaloniki23
FCM
Aristotle University of Thessaloniki24
CFCM
Aristotle University of Thessaloniki25
Future Work
Knowledge-Based Clustering Algorithms
• horizontal collaborative clustering
wavelet transform• conditional fuzzy clustering
wavelet transform
Aristotle University of Thessaloniki26
Conclusions
Through the proposed methodology
• exploit the presence of noisy data
• elongate the outliers from the clustering procedure
Graph-Theoretic Visualization Techniques
• study the variability of brain signals
• study the relationships between clustering results
Paper submitted
“Using Conditional FCM to mine event-related dynamics”
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