Uncertainty and Information
Integration in Biomedical Applications
Claudia Plant
Research Group for Bioimaging
TU München
Outline
1) Motivation: massive increase of data
2) Integration and Uncertainty
• Neurosciences: fMRI and EEG data.
• Proteomics: Peptide Profiling.
3) Conclusion
Uncertainty and Information Integration in Biomedical Applications
Motivation: Data Explosion in Medicine and Life
Sciences
100
intensity
80
60
40
20
0
-20
-7.86026E-05
2176.5303
8707.7758
19593.737
m/z value
The amount of scientific data doubles each year.
Szalay et Grey, Nature 2006
Uncertainty and Information Integration in Biomedical Applications
BMBF Project: Understanding Resting-state Brain
Aktivity
• Metabolism of the brain is not significantly reduced in comparison to task.
• Other regions become active during rest, so-called resting state networks.
Goal of this project:
• Understand function of
Resting state networks,
• compare healthy persons
And subjects with functional
brain disorders.
Methods:
fMRI, EEG
Challenge for data mining:
Massive data sets, uncertainty, information integration
Uncertainty and Information Integration in Biomedical Applications
fMRI Imaging: Principle and Setup
Uncertainty and Information Integration in Biomedical Applications
fMRI Imaging: Spatial Aspect
VOXEL
(Volumetric Pixel)
Slice Thickness
e.g., 6 mm
In-plane resolution
e.g., 192 mm / 64
= 3 mm
3 mm
6 mm
SAGITTAL SLICE
IN-PLANE SLICE
Number of Slices
e.g., 10
Matrix Size
e.g., 64 x 64
Field of View (FOV)
e.g., 19.2 cm
Uncertainty and Information Integration in Biomedical Applications
3 mm
fMRI Imaging: Temporal Aspect
With spatial resolution 3x3x6 mm approximately 80,000 voxels the brain.
3 mm
Temporal resolution:
up to some hundreds of timepoints.
6 mm
3 mm
Uncertainty and Information Integration in Biomedical Applications
EEG/MEG
Low spatial
but high temporal resolution
(milliseconds).
Can we combine the benefits
of the two modalites?
fMRI: high spatial, low
temporal resolution
EEG/MEG: high temporal, low
spatial resolution
Uncertainty and Information Integration in Biomedical Applications
The Cocktail Party Problem
electrode/
voxel
brain process
Space: (x +/- e1, y +/- e1, z +/- e1)
Time: t +/- e2
Space: (x +/- e3, y +/- e3, z +/- e3)
Time: t +/- e4
With
e1 >>> e2
And e3 << e4
Uncertainty and Information Integration in Biomedical Applications
For Single Type of Microphone: ICA
brain process
Successfully applied for spatial and temporal de-mixing of fMRI and
EEG data.
V. D. Calhoun, T. Adali, M. Stevens, K. A. Kiehl, and J. J. Pekar, Semi-Blind ICA of FMRI: A Method for
Utilizing Hypothesis-Derived Time Courses in a Spatial ICA Analysis, NeuroImage, vol. 25, pp. 527-538,
2005.
V. D. Calhoun, J. J. Pekar, and G. D. Pearlson, Alcohol Intoxication Effects on Simulated Driving: Exploring
Alcohol-Dose Effects on Brain Activation Using Functional MRI, Neuropsychopharmacology, vol. 29, pp.
2097-2107, 2004.
Uncertainty and Information Integration in Biomedical Applications
Temporal ICA with FastICA
Example
temporal ICA
u = u1, …, un
v = v1, …, vn
2) Fix Point Iteration:
wi = E{uw (g(wiT-uw)} – E{uw(g‘(wiT-uw)}
1) Centering and Whitening
De-correlate and standardizise
uw = L-1/2 * VT * (u-m)
3) Konvergence
M = V * L-1/2 * W, S = X * M-1
Uncertainty and Information Integration in Biomedical Applications
Results of Spatial ICA on Task-fMRI
Experiment: Subject hits buttom as soon she sees a red light.
Spatial ICA
X
=
M
Time series
S
IC
IC1: visual cortex
IC2: basal regions
The red time series of IC1 preceeds
the green of IC2.
Uncertainty and Information Integration in Biomedical Applications
Existing Approches to Joint ICA
EEG
1) Scale to common resolution and perform usual ICA
Problem: Information Loss!
fMRI
V. D. Calhoun., T. Adali, N. R. Giuliani, J. J. Pekar, K. A. Kiehl and G. D. Pearlson, Method for multimodal analysis of independent source differences
in schizophrenia: combining gray matter structural and auditory oddball functional data, HBM, vol. 27, pp. 47-62, 2006
Uncertainty and Information Integration in Biomedical Applications
Existing Approaches to Joint ICA
EEG
2) Perform ICA on each modality separately
Problem: How to interpret the result?
3) Parallel ICA:
Change the objective function of ICA to
find similar components in both modalities
Problem: Objective function has now two
different goals. How to weight them?
Parametrization difficult.
Perhaps use concepts of Information
Theory for this? -> Later
fMRI
Uncertainty and Information Integration in Biomedical Applications
Our Idea: Probabilistic ICA
Represent each object (x,y,z,t) as PDF and perform Joint ICA.
How to represent?
As PDF
Uncertainty and Information Integration in Biomedical Applications
Probabilistic ICA combined with Information-theoretic
Clustering
Classical ICA model assumes a global mixing matrix A.
This is not always the case, especially for data from different modalites. Do
not force integration by parameters, let the data decide.
Combine ICA with Clustering!
Uncertainty and Information Integration in Biomedical Applications
OCI: Outlier-robust Clustering using Independent
Components (Sigmod 2008)
…so far only for certain data.
Parameterfree clustering
Non-Gaussian
Clusters
noise
Uncertainty and Information Integration in Biomedical Applications
Relationship between PDFs and Data Compression
Suppose we know the mixing Matrix and have two candidate PDFs for coordinate zi
too many bits
good fit
too few
bits
Information Theory:
We want to transmit the data and
sender and receiver know the
correct PDF.
The minimum description length is:
?
?
We do not know the
correct PDF.
Try both!
Uncertainty and Information Integration in Biomedical Applications
ICA and Data Compression
ICA yields mixing matrix with directions of minimal entropy -> Efficient coding.
Apply FastICA algorithm at a cluster level.
x before
Centering
Whitening
x after
After 1 iteration
After 4 iterations
ICA minimizes Entropy
-> reduces uncertainty
-> reduces compression cost
Uncertainty and Information Integration in Biomedical Applications
Data Integration and Information Theory
Concepts of Information Theory provide means to measure how different
Information of different sources is.
If information is similar, it can be compressed effectively together.
Therefore, information-theoretic clustering is a parameter-free approch to data
Integration.
Uncertainty and Information Integration in Biomedical Applications
Conclusion
• Integrative mining of uncertain data is a challenging task
of emerging importance in many applications,
• We discussed an example from Neurosciences and
some ideas for possible but there are many, many
others.. (applications and ideas)
• This is a very interesting problem specification for basic
research in data mining.
• Have fun!
Uncertainty and Information Integration in Biomedical Applications