Biomedical Engineering Reference
In-Depth Information
virtual laboratory so much so that “what was once done
in
atubeisnow
being done
on
the tube.”
∗
3.1.2 Problem and Application Domains
Since the 1950s, many computational techniques have been developed, which
incorporated various learning theories and concepts from statistics and
mathematics. These CI techniques are part of a broader field known as
machine learning
, which focuses on solving several core problems from math-
ematics and engineering as described in the following:
a.
Classification or pattern recognition
. The most popular application of
CI is classification or pattern recognition. In this problem, one is given
a set of labelled data and the machine is trained to recognize the rela-
tionship between the data structure and the class label. Formally, let
x
=
{
(
x
1
,y
1
)
,
(
x
2
,y
2
)
, ...,
(
x
n
,y
n
)
}
be a set of
n
couples each consist-
ing of a vector
x
i
∈
m
generated by some unknown gen-
erating function
f
θ
(
x
i
,
θ
). The parameter space
θ
=
and
y
i
∈
N
{
θ
1
,θ
2
, ..., θ
z
}
n
. We would like to derive a
is a linear z-dimensional subspace of
function,
f
E
(
x
), where
f
E
(
x
)
F
such that
f
E
(
x
) approximates the
true function
f
(
x
i
,
θ
) as closely as possible. The space of integers
∈
N
indicates that the outputs of the true function take on only discrete
values, symbolizing the number of classes involved in the classification
problem. The function
f
E
(
x
) represents a separating boundary or sur-
face and is referred to as the classifier. Classifiers such as ANNs and
SVMs have been successfully applied to a plethora of problems such as
text recognition, speech recognition, and video and image recognition.
Currently, classification is the most relevant problem in biomedical
engineering where classifiers have been developed for data from ECGs,
EEGs, x-rays, ultrasound images, and MRI images to assist with the
diagnosis of diseases.
b.
Function estimation/regression
. Function estimation is a more gen-
eral problem than classification where an unknown generating func-
tion is estimated using only the corresponding inputs and output
responses. More formally, let
x
=
{
(
x
1
,y
1
)
,
(
x
2
,y
2
)
, ...,
(
x
n
,y
n
)
}
be
a set of
n
couples, each consisting of a vector
x
i
∈
m
and
y
i
∈
generated by some unknown generating function
f
θ
(
x
i
,
θ
). Note that
in this case, the function output
y
is allowed to be a real number
instead of integers as with classification. The parameter space
θ
=
{θ
1
,
θ
2
, ..., θ
z
}
n
. We are required
is a linear z-dimensional subspace of
to derive a function,
f
E
(
x
), where
f
E
(
x
)
F
such that
f
E
(
x
) approx-
imates the true function
f
(
x
i
,
θ
) as closely as possible. The class
F
is
assumed to contain a broad class of smooth functions and the task
would be to determine the space
θ
as accurately as possible. The
function,
f
E
(
x
) is known as the
regressor
and several methods have
∈
∗
M. Witten,
High Performance Computational Medicine
in Held et al. (1991).
Search WWH ::
Custom Search