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## Spectral Independent Component Analysis of Heart Rate Variability

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### 'Independent component analysis (ICA) is a method for finding ... Grate accuracy and fastest convergence for ergodic system, like HRV. Conclusion (continue) ... – PowerPoint PPT presentation

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Title: Spectral Independent Component Analysis of Heart Rate Variability

1
Spectral Independent Component Analysis of Heart
Rate Variability
• Alexander Martynenko
• Kharkov National University

2
What is ICA?
• Independent component analysis (ICA) is a
method for finding underlying factors or
components from multivariate (multi-dimensional)
statistical data. What distinguishes ICA from
other methods is that it looks for components
that are both statistically independent, and
nongaussian.
• A.Hyvarinen, A.Karhunen, E.Oja
• Independent Component Analysis

3
Classical ICA (fast ICA) estimation
Observing signals
Original source signal
ICA
4
ICA estimation principles by A.Hyvarinen,
A.Karhunen, E.Oja Independent Component
Analysis
• Principle 1 Nonlinear decorrelation. Find the
matrix W so that for any i ? j , the components
yi and yj are uncorrelated, and the transformed
components g(yi) and h(yj) are uncorrelated,
where g and h are some suitable nonlinear
functions.
• Principle 2 Maximum nongaussianity. Find the
local maxima of nongaussianity of a linear
combination yWx under the constraint that the
variance of is constant. Each local maximum gives
one independent component.

5
ICA mathematical approach from A.Hyvarinen,
A.Karhunen, E.Oja Independent Component Analysis
• Given a set of observations of random
variables x1(t), x2(t)xn(t), where t is the time
or sample index, assume that they are generated
as a linear mixture of independent components
yWx, where W is some unknown matrix. Independent
component analysis now consists of estimating
both the matrix W and the yi(t), when we only
observe the xi(t).

6
Applications from A.Hyvarinen, A.Karhunen, E.Oja
Independent Component Analysis
• In brain imaging, we often have different
sources in the brain emit signals that are mixed
up in the sensors outside of the head, just like
in the basic blind source separation model.
• In econometrics, we often have parallel time
series, and ICA could decompose them into
independent components that would give an insight
to the structure of the data set.
• A somewhat different application is in image
feature extraction, where we want to find
features that are as independent as possible.

7
How to apply ICA to HRV?
• We observe only one mixed signal RR-intervals.
• How we can use ICA for estimation more than one
source signals, that generates observed RR?
• How much independent source signals formed
RR-intervals?
• How we can made the independence stronger?

8
Spectral ICA estimation
Original source signal
Observing mixtures signal
spectral ICA
9
Keys for resolving
• Applying F.Takens theorem to HRV time series.
• Using correlation between spectrum of ICA
estimated signals for determining true
independent signals.
• Shift ICA process from time domain to frequencies
domain.

10
Observed RR and spectrum (8 min of registration)
Spectrum of signal
RR intervals
11
ICA separation on 2 signals (partially true)
ICA separated signals
Spectrum of signals
Correlation(, ) 0
Correlation(, ) 0.1
12
ICA separation on 3 signals (true)
ICA separated signals
Spectrum of signals
Correlation(, ) 0
Correlation(, ) 0.2
Correlation(, ) 0
Correlation(, ) 0.3
13
ICA separation on 4 signals (false)
ICA separated signals
Spectrum of signals
There are different signals in time domain but
the same in frequencies domain
Correlation(, ) 0
Correlation(, ) 0.99
14
Using Spectral ICA for HRV by A.Martynenko,
A.Antonova, A.Yegorenkov ICA HRV
• Allows to obtain no more than three components
forming the rhythmogramm of health person. This
fact rationally represents physiological
hypotheses about regulation systems taking part
in forming HRV phenomenon
• Applying ICA to HRV approves itself on timing
intervals from 4 to 15 minutes. Breaking the
limit of this timing interval causes essential
worsening of quality of components forming the
rhythmogramm
• Optimal application of ICA for splitting initial
registered HRV signal into components, according
to quality, is using ICA with five-minute HRV
registering protocol

15
Classic ICA vs. Spectral ICA
Spectrum of signals separated in frequencies
domain (spectral ICA) Convergence after 6
iteration
Spectrum of signals separated in time domain
(classic ICA) Convergence after 9 iteration
Correlation(, ) 0.32
Correlation(, ) 0.88
16
Classic ICA vs. Spectral ICA (continue)
• Classic ICA estimation of independency (for k
momentum of distribution Ek)
• Ekh(y)g(y) - Ekh(y) Ekg(y) gt min
• Spectral ICA for ergodic system always satisfy to
statistically independency (for k spectral
momentum of distribution Mk)
• Mkh(y)g(y) Mkh(y) Mkg(y)

17
Conclusion
• Presented new method for Independent Component
Analysis of Heart Rate Variability Spectral ICA
• Spectral ICA
• Excellent for use for time series analyzing
• Key to recognizing of true independent components
in observing signal
• Grate accuracy and fastest convergence for
ergodic system, like HRV

18
Conclusion (continue)
• Using Spectral ICA for HRV analyzing
• Allows to obtain no more than three components
forming the rhythmogramm of health person. This
fact rationally represents physiological
hypotheses about regulation systems taking part
in forming HRV phenomenon.
• Applying ICA to HRV approves itself on timing
intervals from 4 to 15 minutes.
• Optimal application of ICA for splitting initial
registered HRV signal into components, according
to quality, is using ICA with five-minute HRV
registering protocol.