|
OF CARDIOVASCULAR DATA |
 |
| |LEVEL 0| |HOMEPAGE| |
|
OF CARDIOVASCULAR DATA |
|
| |LEVEL 0| |HOMEPAGE| |
Measure of the statistical dependency between two random variables based on Shannon's entropy
Given a discrete random variables 
with probability distribution p1 ...pm ...pM
its Shannon's entropy is:
) is
a measure of the uncertainity on the values
may assume.
with probability distribution q1 ...qm ...qN
. If the joint variables 
are
characterized by the joint probability density {sm,n}, then
the entropy of the joint variables
is:
,)
) is a measure of the uncertainity on the valuesand
may jointly assume.
,)
) is maximum if
and
are statistically independent (completely uncoupled): in this case
,)
)=H()+H(),)
) is minimum for deterministic coupling (i.e.,
is function of ):
in this case
,)
)=H()
[ =H() ]The definition of Mutual Information between
and
naturally follows from the properties of H( (,)
).
Mutual Information MI is defimed as:
,)
=H()+H()-H(
(,)
)
and .
,)
= 0
and
are independent (uncoupled)
The highest possible value of MI is
,)
=H() [=H()]
is function of
(deterministic coupling).
and .
,)
=H()-[H(
(,)
)-H()]
)-H( | )where H( | )
is the uncertainty on
once that
is known.
Given two random processes (t)
and (t),
we can choose a lag
and
evaluate MI ((t),(t+))
When evaluated as a function of ,
MI is called Cross Mutual Information Function, CMIF().
References
Hoyer
D et al (2002) Mutual information and phase dependencies: measures of
reduced nonlinear cardiorespiratory interactions after myocardial infarction.
Med Eng Phys.
Pompe
B et al (1998) Using mutual information to measure coupling in the cardiorespiratory
system. IEEE Eng Med Biol Mag.
Osaka
M et al (1998) Mutual information discloses relationship between hemodynamic
variables in artificial heart-implanted dogs. Am J Physiol.
Osaka
M et al (1997) Nonlinear pattern analysis of ventricular premature beats
by mutual information. Methods Inf Med.