Transcript of The power of low rank TENSOR Approximations in Smart ...
PowerPoint-presentatieEUSIPCO 2017: 25th European Signal Processing
Conference Kos Island, Greece
August 28-September 2, 2017
in Smart Patient Monitoring
Prof. Sabine Van Huffel
•Examples in ECG based Cardiac Monitoring •Examples in Magnetic
Resonance (Spectroscopic) Imaging •Conclusions and new
directions
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stratification
Smart Patient
Blind source separation Signal analysis difficult because of
artefacts REMOVE Matrix based Blind Source Separation (BSS)
Non-unique Constraints are needed!
o sources orthogonal (PCA), o sources statistically independent
(ICA) o sources uncorrelated and of different autocorrelation
(CCA)
EEG A ?
ST ?=4
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Uniqueness means Interpretable
Contributors (nonexhaustive list): L. De Lathauwer, P. Comon, T.
Kolda, B. Bader, L-H Lim, C. Van Loan, E. Acar, A. Cichocki, O.
Alter, R. Bro, M. Morup, N. Sidiropoulos, I. Domanov, M. Sorensen,
L. Sorber, M. Ishteva, L. Albera, M. Haardt, …. and
collaborators
kA + kB + kC
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βα
βα
βα
βα
βα
βα
CORE tensor S is in general full (not pseudodiagonal), but
0...
forSS βαβα
*special case of LMLRA, also called Higher-order SVD (HOSVD) or
Tucker Decomposition
U,
U
1
b
a
b
a
b
a
b
a
b
a
b
a
¹
Computation of MLSVD : matrix unfolding
• From 3D tensor to regular matrix by slicing in different
directions and juxtaposition (reformatting)
• The ranks of the different unfoldings are in general different
!!
• Left singular vectors (U- matrix of the SVD) of each of the
unfoldings delivers U-matrix of MLSVD
horizontal
frontal
vertical
Block Tensor Decomposition
De Lathauwer et al., SIMAX, 2008; Sorber et al., SIOPT, 2013
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www.tensorlab.net
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Sorber L, Van Barel M, De Lathauwer L, IEEE J. of Selected Topics
in Signal Proc., 2015 12
Contents Overview
•T wave alternans detection •Irregular heartbeat detection
•Multiscale approaches
•Examples in Magnetic Resonance (Spectroscopic) Imaging
•Conclusions and new directions
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addresses spatio-temporal heart dynamics exploits multi-mode
correlations
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Tensor-based detection of T wave alternans in multilead ECG
signals
T wave alternans detection Goal: Automatic detection of T wave
alternans
Abnormal pattern ABABAB in T wave amplitude
T wave segmentation
CPD : tensor decomposition TWA detection
(1) Goovaerts, G., Vandenberk, B., Willems, R., Van Huffel, S.
(2015). Tensor-based detection of T wave alternans using ECG. Proc.
of the 37th international conference of the IEEE Engineering in
Medicine and Biology Society. EMBC 2015. Milan, Italy, 25-29 Aug.
2015(pp. 6991-6994).
(2) Goovaerts, G., Vandenberk, B., Willems, R., Van Huffel, S.
(2017). Tensor-based Detection of T Wave Alternans in Multilead ECG
Signals. Automatic Detection of T wave Alternans Using Tensor
Decompositions in Multilead ECG Signals. Physiological Measurement
38:1513-1528
• Correlated with risk of arrhythmia • Predictor of Sudden Cardiac
Death
after Myocardial Infarction (MI) • Linked with repolarization of
heart • T-wave Differences ~ microVolts
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3D: 1. Channels 2. Time 3. T waves
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A1
B1
C1
A1
B1
C1
AR
BR
CR
A
B
C
Here: 1 component, with 3 factors (~ 3 dimensions) • B1 = Time:
‘Average T wave’ • A1 = Channels • C1 = T waves : T wave
changes
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From CPD to PARAFAC2
• PROBLEM: T waves not very well aligned o Differences in heart
rate o (Movement) artefacts o Natural variation
No rank-1 decomposition possible
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Examples
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Clinical data: patients with multiple TWA tests TWA (4 subjects, 13
signals) versus Control (5 subjects, 20 signals) Proposed clinical
threshold 13 microV
Good results for both methods in ideal circumstances Real-life
circumstances: PARAFAC2
Allows heart rate differences Good results under moderate
noise
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Irregular heartbeat classification
Aim: Assess risk on sudden Cardiac death and other cardiac
disorders
Similar approach:
2. Construct heartbeat tensor
3. Tensor decomposition CPD
Other approach: Kronecker Product Equations Goovaerts, G., De Wel,
O., Vandenberk, B., Willems, R., Van Huffel, S. (2015). Detection
of Irregular Heartbeats using tensors. Proc. of the 42nd Annual
Computing in Cardiology. CinC 2015. Nice, France, Sep. 2015 (pp.
573-576).
Kronecker Product (KP) Equations: What? multilinear systems
KP structure on the solution
= vec(v uT) generalizes outer productKP definition: 27
KP Equations solver: Nonlinear least squares algorithms
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↓
Solve KPE and match:
Every heartbeat of a particular channel can then be expressed as KP
equat ion
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Classification of new heartbeat: formulate as computation of KP
equation
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heartbeat
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Ongoing work: CinC challenge 2017 AF classification from short
single lead ECG recordings Classify: normal sinus rhythm, Atrial
fibrillation, Alternative rhythm, too noisy
Bousse M., Vervliet N., Domanov I., Debals O., De Lathauwer L.,
``Linear Systems with a Canonical Polyadic Decomposition
Constrained Solution: Algorithms and Applications'‘, Numerical
Linear Algebra with Applications, 2017, submitted. Bousse M.,
Goovaerts G., Vervliet N., Debals O., Van Huffel S., De Lathauwer
L., ``Irregular Heartbeat Classification Using Kronecker Product
Equations'', Proc. 39th Annual International Conference of the IEEE
Engineering in Medicine & Biology Society (EMBC'17, JeJu
Island, South Korea).
generalizes to multichannel heartbeat classification
IIT Guwahati 32
Multiscale decomposition of multilead ECG (1)
IIT Guwahati 34
IIT Guwahati 35
Multiscale MLSVDhighest compression rate (CR)
Multiscale MLSVD exploits all 3 types of correlations achieves
highest CR of 45:1 Acceptable distortion levels
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Third-order tensor fuses and analyses information from multiple
cardiac cycles and multiple leads
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•Introduction •Examples in ECG based cardiac monitoring •Examples
in Magnetic Resonance (Spectroscopic) Imaging •Conclusions and new
directions
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Overview
spectroscopic imaging (MRSI)
APPLICATION 2: MR-based unsupervised brain tumor recognition
Method 1 Non-negative (N) CPD applied to MRSI
Method 2 NCPD applied to multi-parametric (MP) MRI
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MR Scanner
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. .
.
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Individual metabolite profiles
Metabolite maps
APPLICATION 1- MRSI and water suppression
= =1
=
50Aim: Suppress the large water peak from all voxels
ROI
FFT
Hankel based water suppression- MLSVD* • Each individual source
component in time domain can be well
approximated by complex-damped exponentials. • For each voxel in
the MRSI signal construct a Hankel matrix
from the free induction decay (FID) signal and form tensor.
• Parameters of the complex-damped exponentials can be obtained
using MLSVD and shift-invariance property of (1)
• Reconstruct water signal from sources outside ROI 0.25-4.2 ppm •
Subtract from measured signal
H = A ×1 (1) × () ×3 (3)
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Simulation: • Metabolite spectra generated using in-vitro signals.
• Residual water generated using scaled water reference measured
in-vivo
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0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Box-plot of error on simulated MRSI data
Tensor based water suppression- Results
Box-plot of difference in variance on in-vivo MRSI data
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• Water suppression methods tested on 28 in-vivo measured MRSI
signals.
APPLICATION 2: MR-based unsupervised brain tumor recognition
Grade IV Glioblastoma patient: Edema
Active tumor
Necrosis
Gliomas: 30% of all primary brain tumors and 80% of the malignant
brain tumors. WHO grade of malignancy: grade I-IV. 5-year survival
rates:
Anaplastic astrocytoma (grade III): 26% Glioblastoma multiforme
(grade IV): 5%
Aim: To identify active tumor and tumor core pathological
region
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normal tissue active tumor necrosis
Y = matrix of spectra, Y ≈ W H
min || Y - W H || such that W ≥ 0, H ≥ 0
W = tissue-specific spectral patterns:
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Hierarchical NMF (hNMF) Improved results on MRSI data only (Li et
al., NMR in BioMed. 2013)
Y = Coregistered MP-MRI data
Wsource1, Hsource1 (tumour, necrosis,...)
Wtumor, Htumor Wnecrosis, Hnecrosis WWM, HWM WGM, HGM ...
Mask needed!
Validation Based on manual segmentation by radiologist (only
pathological tissue types)
1) Dice-scores (based on H)
2) Correlation coefficients (based on W)
A B ( )2
b
Brain tumor recognition using NCPD*
• It reduces the length of spectra without losing vital information
required for tumor tissue type differentiation.
• It gives more weight to the peaks and makes the signal
smoother.
68 *H. N. Bharath, D. M. Sima, N. Sauwen, U. Himmelreich, L. De.
Lathauwer, and S. Van. Huffel, “Non-negative canonical polyadic
decomposition for tissue type differentiation in gliomas,” IEEE
Journal of Biomedical and Health Informatics, vol. PP, no. 99, pp.
1–1, 2016
Brain tumor recognition using NCPD- XXT tensor
• Construct a 3-D tensor by stacking XXT from each voxel. • MRSI
tensor couples the peaks in the spectra because of
the XXT in the frontal slices.
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Brain tumor recognition using NCPD
• Non-negative (N) constraint is applied on all 3-modes. • To
maintain symmetry in frontal slices common factor (S) is
used in both mode 1 and mode 2.
≈ [, ,] = =1
: , : , (: , )
• NCPD is performed in Tensorlab* using structured data fusion with
l1 regularization on abundances H(sparse): [∗,∗] = min
, − ∑=1 : , : , (: , )
+ 1
70 * Vervliet N., Debals O., Sorber L., Van Barel M. and De
Lathauwer L. Tensorlab 3.0, Available online, Mar. 2016. URL:
http://www.tensorlab.net/
Brain tumor recognition using NCPD- Results
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DWI MRSI
73 *H. N. Bharath, N. Sauwen, D. M. Sima, U. Himmelreich, L. De
Lathauwer and S. Van Huffel, "Canonical polyadic decomposition for
tissue type differentiation using multi-parametric MRI in
high-grade gliomas," 2016 24th European Signal Processing
Conference (EUSIPCO), Budapest, 2016, pp. 547-551.
Edema
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Similarly, NCPD used with symmetry in frontal slices and l1
regularization on H(sparse)
Brain tumor recognition using MP-MRI:- results
NCPD-l1 hNMF Dice
Tumor Dice Core
Tumor source Correlation
Tumor source Correlation
Mean 0.83 0.87 0.95 0.78 0.85 0.81 Standard deviation 0.07 0.1 0.05
0.09 0.13 0.19
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•Introduction •Examples in ECG based Cardiac monitoring •Examples
in Magnetic Resonance (Spectroscopic) Imaging •Conclusions and new
directions
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Conclusions o Many BSS problems in Smart Patient Monitoring of low
rank solve via matrix or tensor factorization plus
constraints
o Successful examples shown, e.g., in ECG based cardiac monitoring
and brain tumor recognition using MR(S)I
o Extensions to biomedical data fusion emerge,e.g. EEG-fMRI solve
via coupled matrix/tensor decompositions (E. Acar, S.
Van Eyndhoven, H. Beckers, M. Morup, B. Hunyadi,…)
o Other BSS applications: bioinformatics (O. Alter, E. Acar), fMRI
(C. Chatzichristos), BCI (Cichocki, Mørup, Martinez-Montes), mobile
EEG (R. Zink), multichannel ECG (Padhy) and MI classification,
fetal ECG extraction (L. De Lathauwer), neonatal monitoring (W.
Deburchgraeve, V. Matic), multiple sclerosis progression (C.
Stamile), nonconvulsive epileptic seizures (Y. R. Aldana),
etc.
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o Multiscale multimodal approaches o New emerging applications,
e.g. in C(hr)onnectome
analysis modelling dynamic brain connectivity networks exploit full
potential of existing Tensor(lab) toolboxes
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Acknowledgment University Hospitals Leuven Gasthuisberg ZNA
Middelheim, Queen Paola Children’s hospital EMC Rotterdam KU
Leuven, Dept. Electrical Engineering-ESAT, division STADIUS &
MICAS Ghent University, Dept. Telecommunication and Information
Processing, TELIN-IPI Eindhoven University of Technology
ERC advanced grant 339804 BIOTENSORS in collaboration with L. De
Lathauwer and group
The power of low rankTENSOR Approximations in Smart Patient
Monitoring
Contents Overview
Tensor Decompositions
Slide Number 10
Slide Number 11
Slide Number 12
Tensor-based detection of T wave alternans in multilead ECG
signals
T wave alternans detection
Physionet database: TWA challenge
Irregular heartbeat classification
Kronecker Product (KP) Equations:What? multilinear systems KP
structure on the solution
KP Equations solver:Nonlinear least squares algorithms
Application to ECG
Classification of new heartbeat: formulate as computation of KP
equation
Slide Number 31
Slide Number 32
Slide Number 34
Slide Number 35
Contents Overview
INTRODUCTION:Metabolite quantification for MRS Imaging (MRSI)
APPLICATION 1- MRSI and water suppression
Hankel based water suppression- MLSVD*
Tensor based water suppression- Results
Tensor based water suppression- Results
Slide Number 59
Slide Number 60
Hierarchical NMF (hNMF)
Brain tumor recognition using NCPD- XXT tensor
Brain tumor recognition using NCPD
Brain tumor recognition using NCPD- Results
Brain tumor recognition using NCPD- Results
Brain tumor recognition using MP-MRI*
Brain tumor recognition using MP-MRI:-XXT tensor
Brain tumor recognition using MP-MRI:- results
Contents Overview