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
Applicationsfrom 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.